Videos and presentation materials from other INI events are also available.
Event  When  Speaker  Title  Presentation Material 

HHHW01 
2nd July 2018 10:00 to 11:00 
Emily Riehl 
The modelindependent theory of (∞,1)categories (1)
Coauthor: Dominic Verity (Macquarie University) In these talks we use the nickname "∞category" to refer to either a quasicategory, a complete Segal space, a Segal category, or 1complicial set (aka a naturally marked quasicategory)  these terms referring to Quillen equivalent models of (∞,1)categories, these being weak infinitedimensional categories with all morphisms above dimension 1 weakly invertible. Each of these models has accompanying notions of ∞functor, and ∞natural transformation and these assemble into a strict 2category like that of (strict 1)categories, functors, and natural transformations. In the first talk, we'll use standard 2categorical techniques to define adjunctions and equivalences between ∞categories and limits and colimits inside an ∞category and prove that these notions relate in the expected ways: eg that right adjoints preserve limits. All of this is done in the aforementioned 2category of ∞categories, ∞functors, and ∞natural transformations. In the 2category of quasicategories our definitions recover the standard ones of Joyal/Lurie though they are given here in a "synthetic" rather than their usual "analytic" form. In the second talk, we'll justify the framework introduced in the first talk by giving an explicit construction of these 2categories. This makes use of an axiomatization of the properties common to the Joyal, Rezk, Bergner/Pellissier, and Verity/Lurie model structures as something we call an ∞cosmos. In the third talk, we'll encode the universal properties of adjunction and of limits and colimits as equivalences of comma ∞categories. We also introduce co/cartesian fibrations in both onesided and twosided variants, the latter of which are used to define "modules" between ∞categories, of which comma ∞categories are the prototypical example. In the fourth talk, we'll prove that theory being developed isn’t just "modelagnostic” (in the sense of applying equally to the four models mentioned above) but invariant under changeofmodel functors. As we explain, it follows that even the "analyticallyproven" theorems that exploit the combinatorics of one particular model remain valid in the other biequivalent models. Related Links


HHHW01 
2nd July 2018 11:30 to 12:30 
Thomas Nikolaus  Higher categories and algebraic Ktheory (1)  
HHHW01 
2nd July 2018 13:30 to 14:30 
Tobias Dyckerhoff  Higher Segal spaces (1)  
HHHW01 
2nd July 2018 14:30 to 15:30 
John Francis  Factorization homology (1)  
HHHW01 
2nd July 2018 16:00 to 17:00 
Sarah Yeakel 
Isovariant homotopy theory
An isovariant map between Gspaces is an equivariant map which preserves isotropy groups. Isovariant homotopy theory appears in situations where homotopy is applied to geometric problems, for example, in surgery theory. We will describe some new results in isovariant homotopy theory, including two model structures and an application to intersection theory. This is work in progress, based on conversations with Cary Malkiewich, Mona Merling, and Kate Ponto.


HHHW01 
3rd July 2018 10:00 to 11:00 
Emily Riehl 
The modelindependent theory of (∞,1)categories (2)
Coauthor: Dominic Verity (Macquarie University) In these talks we use the nickname "∞category" to refer to either a quasicategory, a complete Segal space, a Segal category, or 1complicial set (aka a naturally marked quasicategory)  these terms referring to Quillen equivalent models of (∞,1)categories, these being weak infinitedimensional categories with all morphisms above dimension 1 weakly invertible. Each of these models has accompanying notions of ∞functor, and ∞natural transformation and these assemble into a strict 2category like that of (strict 1)categories, functors, and natural transformations. In the first talk, we'll use standard 2categorical techniques to define adjunctions and equivalences between ∞categories and limits and colimits inside an ∞category and prove that these notions relate in the expected ways: eg that right adjoints preserve limits. All of this is done in the aforementioned 2category of ∞categories, ∞functors, and ∞natural transformations. In the 2category of quasicategories our definitions recover the standard ones of Joyal/Lurie though they are given here in a "synthetic" rather than their usual "analytic" form. In the second talk, we'll justify the framework introduced in the first talk by giving an explicit construction of these 2categories. This makes use of an axiomatization of the properties common to the Joyal, Rezk, Bergner/Pellissier, and Verity/Lurie model structures as something we call an ∞cosmos. In the third talk, we'll encode the universal properties of adjunction and of limits and colimits as equivalences of comma ∞categories. We also introduce co/cartesian fibrations in both onesided and twosided variants, the latter of which are used to define "modules" between ∞categories, of which comma ∞categories are the prototypical example. In the fourth talk, we'll prove that theory being developed isn’t just "modelagnostic” (in the sense of applying equally to the four models mentioned above) but invariant under changeofmodel functors. As we explain, it follows that even the "analyticallyproven" theorems that exploit the combinatorics of one particular model remain valid in the other biequivalent models. Related Links


HHHW01 
3rd July 2018 11:30 to 12:30 
Thomas Nikolaus  Higher categories and algebraic Ktheory (2)  
HHHW01 
3rd July 2018 13:30 to 14:30 
Tobias Dyckerhoff  Higher Segal spaces (2)  
HHHW01 
3rd July 2018 14:30 to 15:30 
John Francis  Factorization homology (2)  
HHHW01 
3rd July 2018 16:00 to 17:00 
Andrew Blumberg 
Thirteen ways of looking at an equivariant stable category
Motivated both by new higher categorical foundations as well as the technology emerging from HillHopkinsRavenel, there has been a lot of recent work by various authors on formal characterizations of the equivariant stable category. In this talk, I will give an overview of this story, with focus on the perspective coming from the framework of Ninfinity operads. In particular, I will describe incomplete stable categories of "Ospectra" associated to any Ninfinity operad O as well as some indications of what we can say in the case when G is an infinite compact Lie group.


HHHW01 
4th July 2018 10:00 to 11:00 
Emily Riehl 
The modelindependent theory of (∞,1)categories (3)
Coauthor: Dominic Verity (Macquarie University) In these talks we use the nickname "∞category" to refer to either a quasicategory, a complete Segal space, a Segal category, or 1complicial set (aka a naturally marked quasicategory)  these terms referring to Quillen equivalent models of (∞,1)categories, these being weak infinitedimensional categories with all morphisms above dimension 1 weakly invertible. Each of these models has accompanying notions of ∞functor, and ∞natural transformation and these assemble into a strict 2category like that of (strict 1)categories, functors, and natural transformations. In the first talk, we'll use standard 2categorical techniques to define adjunctions and equivalences between ∞categories and limits and colimits inside an ∞category and prove that these notions relate in the expected ways: eg that right adjoints preserve limits. All of this is done in the aforementioned 2category of ∞categories, ∞functors, and ∞natural transformations. In the 2category of quasicategories our definitions recover the standard ones of Joyal/Lurie though they are given here in a "synthetic" rather than their usual "analytic" form. In the second talk, we'll justify the framework introduced in the first talk by giving an explicit construction of these 2categories. This makes use of an axiomatization of the properties common to the Joyal, Rezk, Bergner/Pellissier, and Verity/Lurie model structures as something we call an ∞cosmos. In the third talk, we'll encode the universal properties of adjunction and of limits and colimits as equivalences of comma ∞categories. We also introduce co/cartesian fibrations in both onesided and twosided variants, the latter of which are used to define "modules" between ∞categories, of which comma ∞categories are the prototypical example. In the fourth talk, we'll prove that theory being developed isn’t just "modelagnostic” (in the sense of applying equally to the four models mentioned above) but invariant under changeofmodel functors. As we explain, it follows that even the "analyticallyproven" theorems that exploit the combinatorics of one particular model remain valid in the other biequivalent models. Related Links


HHHW01 
4th July 2018 11:30 to 12:30 
Thomas Nikolaus  Higher categories and algebraic Ktheory (3)  
HHHW01 
5th July 2018 10:00 to 11:00 
Emily Riehl 
The modelindependent theory of (∞,1)categories (4)
Coauthor: Dominic Verity (Macquarie University) In these talks we use the nickname "∞category" to refer to either a quasicategory, a complete Segal space, a Segal category, or 1complicial set (aka a naturally marked quasicategory)  these terms referring to Quillen equivalent models of (∞,1)categories, these being weak infinitedimensional categories with all morphisms above dimension 1 weakly invertible. Each of these models has accompanying notions of ∞functor, and ∞natural transformation and these assemble into a strict 2category like that of (strict 1)categories, functors, and natural transformations. In the first talk, we'll use standard 2categorical techniques to define adjunctions and equivalences between ∞categories and limits and colimits inside an ∞category and prove that these notions relate in the expected ways: eg that right adjoints preserve limits. All of this is done in the aforementioned 2category of ∞categories, ∞functors, and ∞natural transformations. In the 2category of quasicategories our definitions recover the standard ones of Joyal/Lurie though they are given here in a "synthetic" rather than their usual "analytic" form. In the second talk, we'll justify the framework introduced in the first talk by giving an explicit construction of these 2categories. This makes use of an axiomatization of the properties common to the Joyal, Rezk, Bergner/Pellissier, and Verity/Lurie model structures as something we call an ∞cosmos. In the third talk, we'll encode the universal properties of adjunction and of limits and colimits as equivalences of comma ∞categories. We also introduce co/cartesian fibrations in both onesided and twosided variants, the latter of which are used to define "modules" between ∞categories, of which comma ∞categories are the prototypical example. In the fourth talk, we'll prove that theory being developed isn’t just "modelagnostic” (in the sense of applying equally to the four models mentioned above) but invariant under changeofmodel functors. As we explain, it follows that even the "analyticallyproven" theorems that exploit the combinatorics of one particular model remain valid in the other biequivalent models. Related Links


HHHW01 
5th July 2018 11:30 to 12:30 
Thomas Nikolaus  Higher categories and algebraic Ktheory (4)  
HHHW01 
5th July 2018 13:30 to 14:30 
Rune Haugseng 
Higher categories of higher categories
I will describe a construction of a higher category of enriched (infinity,n)categories, and attempt to convince the audience that this is interesting.


HHHW01 
5th July 2018 14:30 to 15:30 
Christopher SchommerPries 
The Relative Tangle Hypothesis
I will describe recent progress on a nonlocal variant of the cobordism hypothesis for higher categories of bordisms embedded into finite Euclidean spaces.


HHHW01 
5th July 2018 16:00 to 17:00 
Kathryn Hess 
A Künneth theorem for configuration spaces of products
Bill Dwyer, Ben Knudsen, and I recently constructed a model for the configuration space of a product of parallelizable manifolds in terms of the derived BoardmanVogt tensor product of right modules over the operads of little cubes of the appropriate dimensions. In this talk, after recalling our earlier work, I will introduce a spectral sequence Ben and I have developed for computing the homology of this model.


HHHW01 
6th July 2018 10:00 to 11:00 
Claudia Scheimbauer 
Dualizability in the higher Morita category
In this talk I will explain how one can use geometric arguments to obtain results on dualizablity in a ``factorization version’’ of the Morita category. We will relate our results to previous dualizability results (by DouglasSchommerPriesSnyder and BrochierJordanSnyder on TuraevViro and ReshetikinTuraev theories). We will discuss applications of these dualiability results: one is to construct examples of lowdimensional field theories “relative” to their observables. An example will be given by Azumaya algebras, for example polynomial differential operators (Weyl algebra) in positive characteristic and its center. (This is joint work with Owen Gwilliam.)


HHHW01 
6th July 2018 11:30 to 12:30 
Markus Spitzweck 
Hermitian Ktheory for Waldhausen infinity categories with genuine duality
In the talk we will introduce the concept of an infinity category with genuine duality,
a refinement of the notion of a duality on an infinity category.
We will then define the infinity category of Waldhausen infinity categories with genuine
duality and study the hermitian/real Ktheory functor on this category.
In particular we will state and indicate a proof of the Additivity theorem in this context.
This is joint work with Hadrian Heine and Paula Verdugo.


HHH 
10th July 2018 14:00 to 15:00 
Ben Knudsen  Connectivity and growth in the homology of graph braid groups  
HHH 
10th July 2018 15:30 to 16:30 
Tyler Lawson  Stable power operations  
HHH 
12th July 2018 15:30 to 15:45 
Paul Goerss  Approaches to chromatic splitting  
HHH 
12th July 2018 15:45 to 16:00 
John Greenlees  Sheaves over an elliptic curve and U(1)spectra'  
HHH 
12th July 2018 16:00 to 16:15 
Lennart Meier  Splittings of tmf_1(n)  
HHH 
12th July 2018 16:15 to 16:30 
Stefan Schwede  Categories and orbispaces  
HHH 
17th July 2018 14:00 to 15:00 
Julie Bergner 
The Waldhausen Sconstruction as an equivalence of homotopy theories
The notion of unital 2Segal space was defined independently
by DyckerhoffKapranov and GalvezCarrilloKockTonks as a generalization of a
category up to homotopy. The notion of unital 2Segal space was defined
independently by DyckerhoffKapranov and GalvezCarrilloKockTonks as a
generalization of a category up to homotopy. A key example of both sets of
authors is that the output of applying Waldhausen's Sconstruction to an exact
category is a unital 2Segal space. In joint work with Osorno, Ozornova,
Rovelli, and Scheimbauer, we expand the input of this construction to augmented
stable double Segal spaces and prove that it induces an equivalence on the
level of homotopy theories. Furthermore, we prove that exact categories and
their homotopical counterparts can be recovered as special cases of augmented
stable double Segal spaces.


HHH 
17th July 2018 15:30 to 16:30 
Bjorn Ian Dundas  The Geometric Diagonal  
HHH 
19th July 2018 15:30 to 15:45 
Jesper Grodal  Have you seen this homology class??  
HHH 
19th July 2018 15:45 to 16:00 
Kathryn Lesh  Labeled complexes and homological stability  
HHH 
19th July 2018 16:00 to 16:15 
Michael Mandell  1.3 Thoughts on N∞ Ring Spectra  
HHH 
19th July 2018 16:15 to 16:30 
Brooke Shipley  Commuting homology and homotopy inverse limits  
HHH 
24th July 2018 14:00 to 15:00 
Thomas Schick  Geometric models of twisted Khomology  
HHH 
24th July 2018 15:30 to 16:30 
Clark Barwick  Exodromy  
HHH 
26th July 2018 15:30 to 15:45 
Tobias Barthel  HHH Gong Show  On beyond Chouinard  
HHH 
26th July 2018 15:45 to 16:00 
Irina Bobkova  HHH Gong Show  Small Picard groups  
HHH 
26th July 2018 16:00 to 16:15 
Fabian Hebestreit  HHH Gong Show  Algebraic cobordism categories  
HHH 
26th July 2018 16:15 to 16:30 
Tomer Schlank  HHH Gong Show  Noncommutative rational spectra and marked configuration spaces  
HHH 
31st July 2018 14:00 to 15:00 
Clemens Berger 
Derived modular envelopes and moduli spaces of bordered Riemann surfaces
We study the derived modular envelope of several cyclic
operads. More specifically, using a cyclic Wconstruction as
cofibrant replacement we get a derived modular envelope (of
the cyclic operad of planar structures) which can be interpreted as a
ribbon graph model for the corresponding moduli space of
bordered Riemann surfaces. (Joint work with Ralph Kaufmann). 

HHH 
31st July 2018 15:30 to 16:30 
Gregory Arone 
Tree complexes and obstructions to embeddings.
Using the framework of the calculus of functors
(a combination of manifold and orthogonal calculus) we define a sequence of
obstructions for embedding a smooth manifold (or more generally a CW complex) M
in R^d. The first in the sequence is essentially Haefliger’s obstruction. The
second one was studied by Brian Munson. We interpret the nth obstruction as a
cohomology of configurations of n points on M with coefficients in the homology
of a complex of trees with n leaves. The latter can be identified with the
cyclic Lie_n representation. When M is a union of circles, we conjecture that
our obstructions are closely related to Milnor invariants. When M is of
dimension 2 and d=4, we speculate that our obstructions are related to ones
constructed by Schneidermann and Teichner. This is very much work in progress. 

HHH 
2nd August 2018 15:30 to 15:45 
Agnes Beaudry  Linearize this!  
HHH 
2nd August 2018 15:45 to 16:00 
Joshua Hunt  Lifting endotrivial modules  
HHH 
2nd August 2018 16:00 to 16:15 
Magdalena Kedziorek  Galois extensions, a fairy tale  
HHH 
2nd August 2018 16:15 to 16:30 
Vesna Stojanoska  Dreamy Pics  
HHH 
7th August 2018 14:00 to 15:00 
Oscar RandalWilliams 
Cellular E_kalgebras and homological stability
I will explain recent joint work with S Galatius and A. Kupers in which we use the notion of cellular E_kalgebras and their derived indecomposables to study homological stability for things such as mapping class
groups, automorphism groups of free groups, or general linear groups. Using these tools also suggests new types of results in homological stability, such as a secondorder form of stability. In this talk I will suppress the details specific to each case, and instead focus on the general calculational aspects of the homology of cellular E_kalgebras with few cells.


HHH 
7th August 2018 15:30 to 16:30 
Nicholas Kuhn 
A tutorial on constructions of finite complexes with specified cohomology (after Steve Mitchell and Jeff Smith)
Central to the study of modern homotopy theory is the Periodicity Theorem of Mike Hopkins and Jeff Smith, which says that any type n finite complex admits a v_n self map. Their theorem follows from the DevanitzHopkinsSmith Nilpotence Theorem once one has constructed at least one example of v_n self map of a type n complex.
The construction of such an urexample uses a construction due to Jeff Smith making use of the modular representation theory of the symmetric groups. This followed the first construction of a type n complex for all n by Steve Mitchell, which used the modular representation theory of the general linear groups over Z/p.
The fine points of the Smith construction are not in the only published source: Ravenel's writeup in his book on the Nilpotence Theorems. I'll discuss some of this, and illustrate the ideas with a construction of a spectrum whose mod 2 cohomology is free on one generator as a module over A(3), the 1024 dimensional subalgebra of the Steenrod algebra generated by Sq^1, Sq^2, Sq^4, and Sq^8.


HHH 
9th August 2018 15:30 to 15:45 
Agnes Beaudry  Linearize this!  
HHH 
9th August 2018 15:45 to 16:00 
HansWerner Henn  Unexpected and confusing Pics  
HHH 
9th August 2018 16:00 to 16:15 
Gijs Heuts  A Whitehead theorem for periodic homotopy groups?  
HHH 
9th August 2018 16:15 to 16:30 
Dylan Wilson  Koszul to keep cool  
HHH 
10th August 2018 14:00 to 15:00 
Markus Land 
On the Ktheory of pullbacks
In this talk I will report on joint work with Georg Tamme
about excision results in Ktheory and related invariants.
We show that, associated to any pullback square of E_1
ring spectra, there is an associated pullback diagram of Ktheory spectra in
which one of the corners is the Ktheory of a new E_1 ring canonically
associated to the original pullback diagram.
I will explain the main ingredients for the proof and
then concentrate on simple consequences of this theorem.
These include Suslin’s results on excision (for
Torunital ideals) and the fact that (what we call) truncating invariants
satisfy excision, nil invariance and cdh descent. If time permits I will also
discuss how to deduce that in certain cases (bi)relative Kgroups are torsion
groups of bounded exponent, improving results of Geisser—Hesselholt.


HHHW02 
13th August 2018 10:00 to 11:00 
Daniel Dugger 
Surfaces with involutions
I will talk about the classification of surfaces with involution, together with remarks on the RO(Z/2)graded Bredon cohomology of these objects.


HHHW02 
13th August 2018 11:30 to 12:30 
Jeremiah Heller  A motivic Segal conjecture  
HHHW02 
13th August 2018 14:30 to 15:30 
Agnes Beaudry 
Pic(EZ/4) and Tools to Compute It
In this talk, we describe tools to compute the Picard group of the category of EGmodule spectra where E is Morava Etheory at n=p=2 and G is a finite cyclic subgroup of the Morava stabilizer of order 4. We discuss two tools: 1) A group homomorphism from RO(G) to Pic(EG) and methods for computing it. 2) The Picard Spectral sequence and some of its equivariant properties.
This work is joint with Irina Bobkova, Mike Hill and Vesna Stojanoska


HHHW02 
13th August 2018 16:00 to 17:00 
Clark Barwick 
Exodromy and endodromy
On the étale homotopy type of a scheme, there is a natural stratification. We describe both it and its dual, and we discuss some of the ramification information it captures. Joint work with Saul Glasman, Peter Haine, Tomer Schlank.


HHHW02 
14th August 2018 09:00 to 10:00 
Marc Levine 
Quadratic Welschinger invariants
This is report on part of a program to give refinements of numerical invariants arising in enumerative geometry to invariants living in the GrothendieckWitt ring over the basefield. Here we define an invariant in the GrothendieckWitt ring for ``counting'' rational curves. More precisely, for a del Pezzo surface S over a field k and a positive degree curve class $D$ (with respect to the anticanonical class $K_S$), we define a class in the GrothendiekWitt ring of k, whose rank gives the number of rational curves in the class D containing a given collection of distinct closed points $\mathfrak{p}=\sum_ip_i$ of total degree $D\cdot K_S1$. This recovers Welschinger's invariants in case $k=\mathbb{R}$ by applying the signature map. The main result is that this quadratic invariant depends only on the $\mathbb{A}^1$connected component containing $\mathfrak{p}$ in $Sym^{3d1}(S)^0(k)$, where $Sym^{3d1}(S)^0$ is the open subscheme of $Sym^{3d1}(S)$ parametrizing geometrically reduced 0cycles.


HHHW02 
14th August 2018 11:30 to 12:30 
Magdalena Kedziorek 
Algebraic models for rational equivariant commutative ring spectra
I will recall different levels of commutativity in Gequivariant stable homotopy theory and show how to understand them rationally when G is finite or SO(2) using algebraic models. This is joint work with D. Barnes and J.P.C. Greenlees.


HHHW02 
14th August 2018 14:30 to 15:30 
Marc Hoyois 
Motivic infinite loop spaces and Hilbert schemes
Coauthors: Elden Elmanto (Northwestern University), Adeel A. Khan (Universität Regensburg), Vladimir Sosnilo (St. Petersburg State University), Maria Yakerson (Universität DuisburgEssen)We prove a recognition principle for motivic infinite loop spaces over a perfect field of characteristic not 2. This is achieved by developing a theory of framed motivic spaces, which is a motivic analogue of the theory of Einfinityspaces. Our main result is that grouplike framed motivic spaces are equivalent to the full subcategory of motivic spectra generated under colimits by suspension spectra. As a consequence, we deduce some representability results for suspension spectra of smooth varieties and various motivic Thom spectra in terms of Hilbert schemes of points in affine spaces.Related Linkshttps://arxiv.org/abs/1711.05248  preprint


HHHW02 
14th August 2018 16:00 to 17:00 
Vesna Stojanoska 
Galois extensions in motivic homotopy theory
There are two notions of homotopical Galois extensions in the motivic setting; I will discuss what we know about each, along with illustrative examples. This is joint work in progress with Beaudry, Heller, Hess, Kedziorek, and Merling.


HHHW02 
15th August 2018 09:00 to 10:00 
Doug Ravenel 
Model category structures for equivariant spectra
We
will discuss methods for constructing a model structure the category of
orthogonal equivariant spectra for a finite group G. The most convenient
one is two large steps away from the most obvious one.


HHHW02 
15th August 2018 10:00 to 11:00 
Oliver Roendigs 
On very effective hermitian Ktheory
We argue that the very effective cover of hermitian Ktheory in the sense of motivic homotopy theory is a convenient algebrogeometric generalization of the connective real topological Ktheory spectrum. This means the very effective cover acquires the correct Betti realization, its motivic cohomology has the desired structure as a module over the motivic Steenrod algebra, and that its motivic Adams and slice spectral sequences are amenable to calculations. The latter applies to provide the expected connectivity for its unit map from the motivic sphere spectrum. This is joint work with Alexey Ananyevskiy and Paul Arne Ostvaer.


HHHW02 
15th August 2018 11:30 to 12:30 
Teena Gerhardt 
Hochschild homology for Green functors
Hochschild homology of a ring has a topological analogue for ring spectra, topological Hochschild homology (THH), which plays an essential role in the trace method approach to algebraic Ktheory. For a C_nequivariant ring spectrum, one can define C_nrelative THH. This leads to the question: What is the algebraic analogue of C_nrelative THH? In this talk, I will define twisted Hochschild homology for Green functors, which allows us to describe this algebraic analogue. This also leads to a theory of Witt vectors for Green functors, as well as an algebraic analogue of TRtheory. This is joint work with Andrew Blumberg, Mike Hill, and Tyler Lawson.


HHHW02 
16th August 2018 09:00 to 10:00 
Mark Behrens 
C_2 equivariant homotopy groups from real motivic homotopy groups
The Betti realization of a real motivic spectrum is a genuine C_2 spectrum. It is well known (c.f. the work of DuggerIsaksen) that the homotopy groups of the Betti realization of a complex motivic spectrum can be computed by "inverting tau". I will describe a similar theorem which describes the C_2equivariant RO(G) graded homotopy groups of the Betti realization of a cellular real motivic spectrum in terms of its bigraded real motivic homotopy groups. This is joint work with Jay Shah.


HHHW02 
16th August 2018 10:00 to 11:00 
Tom Bachmann 
Motivic normed spectra and Tambara functors
Motivic normed spectra are a motivic analogue of the Gcommutative ring spectra from genuine equivariant stable homotopy theory. The category of Gcommutative ring spectra such that the underlying genuine equivariant spectrum is concentrated in degree zero (i.e. is a Mackey functor) is in fact equivalent to the category of GTambara functors. I will explain an analogous motivic result: the category of normed motivic spectra (over a field), such that the underlying motivic spectrum is an effective homotopy module, is equivalent to a category of homotopy invariant presheaves with generalized transfers and étale norms.


HHHW02 
16th August 2018 11:30 to 12:30 
Anna Marie Bohmann 
Graded Tambara functors
Let E be a Gspectrum for a finite group G. It's long been known that homotopy groups of E have the structure of "Mackey functors." If E is G commutative ring spectrum, then work of Strickland and of Brun shows that the zeroth homotopy groups of E form a "Tambara functor." This is more structure than just a Mackey functor with commutative multiplication and there is much recent work investigating nuances of this structure.
I will discuss work with Vigleik Angeltveit that extends this result to include the higher homotopy groups of E. Specifically, if E has a commutative multiplication that enjoys lots of structure with respect to the G action, the homotopy groups of E form a graded Tambara functor. In particular, genuine commutative G ring spectra enjoy this property.


HHHW02 
16th August 2018 14:30 to 15:30 
Mona Merling 
Toward the equivariant stable parametrized hcobordism theorem
Waldhausen's introduction of Atheory of spaces revolutionized the early study of pseudoisotopy theory. Waldhausen proved that the Atheory of a manifold splits as its suspension spectrum and a factor Wh(M) whose first delooping is the space of stable hcobordisms, and its second delooping is the space of stable pseudoisotopies. I will describe a joint project with C. Malkiewich aimed at telling the equivariant story if one starts with a manifold M with group action by a finite group G.


HHHW02 
16th August 2018 16:00 to 17:00 
Fabien Morel 
Etale and motivic variations on Smith's theory on action of cyclic groups
In this talk, after recalling some facts on Smith's theory in classical topology, I will present some analogues in algebraic geometry using \'etale cohomology first, and I will also give analogues in \A^1homotopy theory and motives of Smith's theory concerning the multiplicative group \G_m, which behaves like a "cyclic of order 2".


HHHW02 
17th August 2018 09:00 to 10:00 
Aravind Asok 
On Suslin's Hurewicz homomorphism
I will discuss some recent progress on an old conjecture of Suslin about the image of a certain ``Hurewicz" map from Quillen's algebraic Ktheory of a field F to the Milnor Ktheory of F. This is based on joint work with J. Fasel and T.B. Williams.


HHHW02 
17th August 2018 10:00 to 11:00 
Carolyn Yarnall 
Klein fourslices of HF_2
The slice filtration is a filtration of equivariant spectra analogous to the Postnikov tower that was developed by Hill, Hopkins, and Ravenel in their solution to the Kervaire invariantone problem. Since that time there have been several new developments, many dealing with cyclic groups. In this talk, we will focus our attention on a noncyclic group! After recalling a few essential definitions and previous results, we will investigate some computational tools that allow us to leverage homotopy results of HollerKriz to determine the slices of integer suspensions of HF_2 when our group is the Klein four group. We will end with a few slice tower and spectral sequence examples demonstrating the patterns that arise in the filtration.
This is joint work with Bert Guillou.


HHHW02 
17th August 2018 11:30 to 12:30 
Kirsten Wickelgren 
Some results in A1enumerative geometry
We
will discuss several applications of A1homotopy theory to enumerative
geometry. This talk includes joint work with Jesse Kass and Padmavathi
Srinivasan.


HHH 
17th August 2018 13:15 to 14:15 
Lifting Gstable endotrivial modules  
HHHW02 
17th August 2018 14:30 to 15:30 
Thomas Nikolaus 
Cyclotomic spectra and Cartier modules
We start by reviewing the notion of cyclotomic spectra and basic examples such as THH. Then we introduce the classical algebraic notion of an (integral, ptypical) Cartier module and its higher generalization to spectra (topological Cartier modules). We present examples such as Witt vectors and Ktheory of endomorphisms. The main result, which is joint work with Ben Antieau, is that there is a close connection between the two notions.


HHH 
21st August 2018 14:00 to 15:00 
Wolfgang Steimle 
An Additivity Theorem for cobordism categories, with applications to Hermitian Ktheory
The goal of this talk is to explain that Genauer's
computation of the cobordism category with boundaries is a precise analogue of
Waldhausen's additivity theorem in algebraic Ktheory, and to give a new,
parallel proof of both results. The same proof technique also applies to
cobordism categories of Poincaré chain complexes in the sense of Ranicki. Here
we obtain that its classifying space is the infinite loop space of a
nonconnective spectrum which has similar properties as Schlichting's
GrothendieckWitt spectrum when 2 is invertible; but it turns out that these
properties still hold even if 2 is not invertible. This talk is partially based
on joint work with B. Calmès, E. Dotto, Y. Harpaz, F. Hebestreit, M. Land, K.
Moi, D. Nardin and Th. Nikolaus.


HHH 
21st August 2018 15:30 to 16:30 
Fabian Hebestreit 
Parametrised homotopy theory via symmetric retractive spectra
I shall explain a new framework for parametrised homotopy
theory, based on symmetric spectra objects in retractive
spaces. In contrast to previous model categorical frameworks it
encompasses a wellbehaved symmetric monoidal structure, that models the
Dayconvolution present in the quasicategorical setup. As a small application I will give a simple proof,
that Ktheory as defined through stable homotopy theory agrees with
the original geometric construction (even as highly structured
objects), a fact that seems to be missing from the literature so far.


HHH 
23rd August 2018 15:30 to 15:45 
Steffen Sagave  Commutative cochains  
HHH 
23rd August 2018 15:45 to 16:00 
Marc Levine  T for (SL) two  
HHH 
23rd August 2018 16:00 to 16:15 
Tobias Lenz  Homotopy (Pre)Derivators of Cofibration Categories and QuasiCategories  
HHH 
23rd August 2018 16:15 to 16:30 
Inbar Klang  Homology vs cohomology  
HHH 
28th August 2018 15:30 to 16:30 
Lior Yanovski 
Ambidexterity in the T(n)Local Stable Homotopy Theory
The monochromatic layers of the chromatic filtration on
spectra, that is The K(n)local (stable 00)categories Sp_{K(n)}
enjoy many remarkable properties. One example is the vanishing of the Tate
construction due to
HoveyGreenleesSadofsky. The
vanishing of Tate construction can be considered as a natural equivalence between
the colimits and limits in Sp_{K(n)}
parametrized by finite groupoids. Hopkins and Lurie proved a
generalization of this result where finite groupoids are replaced by arbitrary
\pifinite 00groupoids. There is another possible sequence of (stable 00)categories who can be considered
as "monochromatic layers", Those are the T(n)local 00categories
Sp_{T(n)}. For the Sp_{T(n)} the vanishing of the Tate
construction was proved by Kuhn. We shall prove that the analog of Hopkins and Lurie's result in for Sp_{T(n)}. Our proof will also give an alternative proof for
the K(n)local case. This is a joint work with Shachar Carmieli and Lior
Yanovski


HHH 
30th August 2018 15:30 to 15:45 
David Barnes  Equivariant sheaves aren't always Weyl  
HHH 
30th August 2018 15:45 to 16:00 
Anna Marie Bohmann  Multiplication, not multifarious  
HHH 
30th August 2018 16:00 to 16:15 
Tyler Lawson  Unit groups are confusing  
HHH 
30th August 2018 16:15 to 16:30 
Markus Szymik  Quo whatis quandles?  
HHH 
11th September 2018 14:00 to 15:00 
Robert Bruner  The mod 2 Adams spectral sequence for tmf_*  
HHH 
11th September 2018 15:30 to 16:30 
Irakli Patchkoria 
Polynomial maps, Witt vectors and Real THH
A result of Hesselholt and Madsen asserts that the ring of components of the topological restriction homology (TR) is isomorphic to the ring of Witt vectors. Trying to prove a real analog of this result leads to a surprising algebraic fact: Witt vectors have an extra functoriality with respect to certain polynomial maps. In this talk we will discuss the extra functoriality and its applications to some problems in algebra and topology. This is joint work with E. Dotto and K. Moi.


HHH 
13th September 2018 15:30 to 15:45 
Andrew Baker  BG_2 vs the Joker  
HHH 
13th September 2018 15:45 to 16:00 
Michael Joachim  On twisted spinc bordism and twisted Ktheory  
HHH 
13th September 2018 16:00 to 16:15 
Viktoriya Ozornova  Case of Identity  
HHH 
13th September 2018 16:15 to 16:30 
Mingcong Zeng  RO(G)coefficient ring of constant Mackey functor via duality  
HHH 
18th September 2018 14:00 to 15:00 
Christian Schlichtkrull 
Topological Hochschild homology via generalized Thom spectra
We realize certain quotient spectra of an even ring
spectrum as generalized Thom spectra and we use this to calculate their
topological Hochschild homology. The main point is to analyze how the
topological Hochschild homology varies with different choices of multiplicative
structure on the quotient spectra. We also compare the topological Hochschild
homology to twisted homology of free loop spaces. This represents joint work
with Samik Basu.


HHH 
18th September 2018 15:30 to 16:30 
Nathalie Wahl 
Slopes in homological stability, the classical way
In joint work with David Sprehn, we prove
homological stability with "slope 1" for symplectic, orthogonal and unitary
groups over fields other than F_2, following an argument of Quillen for general
linear groups. Stability with slope 2 has long been known for all four types of
groups over very general rings by a similar, though not equal, argument. I'll
present these results and give an overview of the players in such homological
stability arguments


HHH 
20th September 2018 15:30 to 15:45 
Lars Hesselholt  Ktheory of division algebras over local fields  
HHH 
20th September 2018 15:45 to 16:00 
VietCuong Pham  BrownComenetz dual of some K(2)local spectrum  
HHH 
20th September 2018 16:00 to 16:15 
Constanze Roitzheim  Twisted, not bitter  
HHH 
20th September 2018 16:15 to 16:30 
Hiro Tanaka  MorseTheory(On.Point) vs (MorseTheory.On)Point  
HHHW03 
24th September 2018 10:00 to 11:00 
Agnes Beaudry 
K(n)local homotopy from a Galois theory perspective 1
The goal of these two talks is to give an overview of a perspective on K(n)local homotopy theory that lends itself to computations. I will introduce some of the key players of the workshop such as the Morava K and Etheories. The introduction will emphasize the Galois theory inherent to the situation and be designed to lead us to consider finite resolutions of the K(n)local sphere. I will then explain how these perspectives have helped us gain a better understanding on problems in chromatic homotopy theory such as the study of invertible elements and chromatic reassembly.


HHHW03 
24th September 2018 11:30 to 12:30 
Niko Naumann 
The role of pdivisible groups 1
We will try to give an account of Lurie's treatment of pdivisible groups in spectral algebraic geometry, to the extend available by the date of the workshop.


HHHW03 
24th September 2018 14:30 to 15:30 
Christian Ausoni 
On the topological Hochschild homology of JohnsonWilson spectra
Let E(n) denote the nth JohnsonWilson spectrum at an
odd prime p.
The spectrum E(1) coincides with the Adams summand of
plocal topological Ktheory.
McClure and Staffeldt offered an intriguing computation
of THH(E(1)), showing that it splits as a wedge sum of E(1) and a rationalized
suspension of E(1).
In joint work with Birgit Richter, we study the Morava
Ktheories of THH(E(n)), with an aim at investigating if McClureStaffeldt's
splitting in lower chromatic pieces generalizes. Under the assumption that E(2) is
commutative, we show that
THH(E(2)) splits as a wedge sum of E(2) and its lower
chromatic localizations.


HHHW03 
24th September 2018 16:00 to 17:00 
Lennart Meier 
Topological modular forms with level structure
Topological modular forms with level structure are spectra associated with moduli of elliptic curves with extra structure. These come in a huge variety. We will report on progress on the conjecture that all of these spectra split additively into a few simple pieces.
Another goal is to obtain an understanding of connective variants of TMF with level structure. We will present some constructions and a conjecture on their associated stacks.
This work is partially joined with Viktoriya Ozornova.


HHHW03 
25th September 2018 10:00 to 11:00 
Agnes Beaudry 
Duality and invertibility using finite resolutions  2
In this talk, I will explain applications of the finite resolutions constructed in the first talk to the study of invertibility and duality in the K(n)local category.


HHHW03 
25th September 2018 11:30 to 12:30 
Niko Naumann 
The role of pdivisible groups  2
We will try to give an account of Lurie's treatment of pdivisible groups in spectral algebraic geometry, to the extend available by the date of the workshop.


HHHW03 
25th September 2018 14:30 to 15:30 
Jeremy Hahn 
The spectrum of units of a height 2 theory
The space BSU admits two infinite loop space structures, one arising from addition of vector bundles and the other from tensor product. A surprising fact, due to Adams and Priddy, is that these two infinite loop spaces become equivalent after pcompletion. I will explain how the AdamsPriddy theorem allows for an identification of sl_1(ku_p), the spectrum of units of pcomplete complex Ktheory. I will then describe work, joint with Andrew Senger, that attempts to similarly understand the spectrum of units of the 2completion of tmf_1(3). Our computations seem suggestive of broader phenomena, and I will include discussion of several open questions.


HHHW03 
25th September 2018 16:00 to 17:00 
Tomer Schlank 
Modes, Ambidexterity and Chromatic homotopy.
Spectra can be considered as the universal presentable stable 00category, similarly Set can be considered as the universal presentable 1category and pointed spaces can be considered as the universal pointed presentable. More generally some properties of presentable 00categories can be classified as equivalent to being a module over a universal symmetric monoidal 00category. We call such universal symmetric monoidal 00category "Modes". We describe certain facts about the general theory of modes and present how one can generate new ones from old ones.


HHHW03 
26th September 2018 10:00 to 11:00 
Ben Antieau 
Derived algebraic geometry I
In this series of lectures I will outline the major features of derived algebraic geometry in both the connective and nonconnective settings. The connective setting is what is closer to classical algebraic geometry and the study of geometric moduli spaces, for example moduli of objects in derived categories; the nonconnective setting is what is needed for applications to topological modular forms.


HHHW03 
26th September 2018 11:30 to 12:30 
Tobias Barthel, Nathaniel Stapleton  Transchromatic homotopy theory 1  
HHHW03 
27th September 2018 10:00 to 11:00 
Ben Antieau 
Derived algebraic geometry II
In this series of lectures I will outline the major features of derived algebraic geometry in both the connective and nonconnective settings. The connective setting is what is closer to classical algebraic geometry and the study of geometric moduli spaces, for example moduli of objects in derived categories; the nonconnective setting is what is needed for applications to topological modular forms.


HHHW03 
27th September 2018 11:30 to 12:30 
Tobias Barthel, Nathaniel Stapleton  Transchromatic homotopy theory 2  
HHHW03 
27th September 2018 14:30 to 15:30 
Gijs Heuts  Lie algebras and v_nperiodic spaces  
HHHW03 
27th September 2018 16:00 to 17:00 
Vesna Stojanoska 
Characteristic classes determine dualizing modules
I will address the question of determining the K(n)local SpanierWhitehead dual of the LubinTate spectrum, equivariantly with respect to the action of the Morava stabilizer group. A dualizing module can be constructed abstractly, and we use characteristic classes to relate it to a certain representation sphere, at least when we restrict the action to a finite subgroup. As a consequence in specific examples, explicit calculations of characteristic classes also give explicit formulas for the SpanierWhitehead duals of spectra like TMF and higher real Ktheories.
This is work in progress, joint with Agnes Beaudry, Paul Goerss, and Mike Hopkins.


HHHW03 
28th September 2018 10:00 to 11:00 
Zhouli Xu 
Motivic Ctaumodules and Stable Homotopy Groups of Spheres
I will discuss the equivalence of stable infinity categories, between the motivic Ctaumodules over the complex numbers and the derived category of BP_*BPcomodules. As a consequence, the motivic Adams spectral sequence for Ctau is isomorphic to the algebraic Novikov spectral sequence. This isomorphism of spectral sequences allows computations of classical stable stems at least to the 90stem, with ongoing computations into even higher dimensions. I will also discuss the situation in the real motivic world, and some connections to the new Doomsday Conjecture, if time permits. This is joint work with Mark Behrens, Bogdan Gheorghe, Dan Isaksen and Guozhen Wang.


HHHW03 
28th September 2018 11:30 to 12:30 
Gereon Quick 
Examples of nonalgebraic classes in the BrownPeterson tower
It is a classical problem in algebraic geometry to decide whether a class in the singular cohomology of a smooth complex variety X is algebraic, that is if it can be realized as the fundamental class of an algebraic subvariety of X. One can ask a similar question for motivic spectra: Given a motivic spectrum E, which classes in the topological Ecohomology of X come from motivic classes. I would like to discuss this question and examples of nonalgebraic classes for the tower of BrownPeterson spectra.


HHHW03 
28th September 2018 14:30 to 15:30 
Mark Behrens 
The tmfbased Adams spectral sequence for Z
I will describe some specific and qualitative aspects of the tmfbased Adams spectral sequence for the BhattacharyaEgger type 2 spectrum called "Z". This is joint work with Agnes Beaudry, Prasit Bhattacharya, Dominic Culver, and Zhouli Xu.


HHH 
2nd October 2018 14:00 to 15:00 
Scott Balchin 
Adelic models for Noetherian model categories (joint work with John Greenlees)
The algebraic models for rational Gequivariant
cohomology theories (Barnes, Greenlees, Kedziorek, Shipley) are constructed by
assembling data from each closed subgroup of G. We can compare this to the
usual Hasse square, where we see abelian groups being constructed from data at
each point of Spec(Z) in an adelic fashion.
This style of assembly can be described in a general
fashion using the data contained in the Balmer spectrum of the corresponding
tensortriangulated categories. We show that given a Quillen model category
whose homotopy category is a suitably well behaved tensortriangulated
category, that we can construct a Quillen equivalent model from localized pcomplete
data at each Balmer prime in an adelic fashion.


HHH 
2nd October 2018 15:30 to 16:30 
Jesper Grodal 
The Picard group of the stable module category
The stable module category of a finite group is currently maybe my favourite presentable symmetric monoidal stable infinity category. The goal of the talk is to harness its Picard group, using our old friend the orbit category.
Part of this talk is a report on joint works with Barthel, Hunt, Carlson, Nakano, Mazza....


HHH 
4th October 2018 15:30 to 15:45 
George Raptis  Transfer maps in Atheory  
HHH 
4th October 2018 15:45 to 16:00 
Doug Ravenel  The first English group theorist  
HHH 
4th October 2018 16:00 to 16:15 
Birgit Richter  Higher THH of Z/p^m with reduced coefficients  
HHH 
4th October 2018 16:15 to 16:30 
Stefan Schwede  Proper, equivariant, and stable!  
HHH 
8th October 2018 16:00 to 17:00 
Lars Hesselholt 
Rothschild Lecture: Higher algebra and arithmetic  Monday 8th October 2018
This talk concerns a twentythousandyear old mistake: The natural numbers record only the result of counting and not the process of counting. As algebra is rooted in the natural numbers, the higher of Joyal and Lurie is rooted in a more basic notion of number which also records the process of counting. Long advocated by Waldhausen, the arithmetic of these more basic numbers should eliminate denominators. Notable manifestations of this vision include the BökstedtHsiangMadsen topological cyclic homology, which receives a denominatorfree Chern character, and the related BhattMorrowScholze integral padic Hodge theory, which makes it possible to exploit torsion cohomology classes in arithmetic geometry. Moreover, for schemes smooth and proper over a finite field, the analogue of de Rham cohomology in this setting naturally gives rise to a cohomological interpretation of the HasseWeil zeta function by regularized determinants, as envisioned by Deninger.


HHH 
9th October 2018 14:00 to 15:00 
Michael Ching 
Tangent ∞categories and Goodwillie calculus
Goodwillie calculus is a set of tools in homotopy theory
developed, to some extent, by analogy with ordinary differential calculus. The
goal of this talk is to make that analogy precise by describing a common
categorytheoretic framework that includes both the calculus of smooth maps
between manifolds, and Goodwillie calculus of functors, as examples.
This framework is based on the notion of "tangent
category" introduced first by Rosicky and recently developed by Cockett
and Cruttwell in connection with models of differential calculus in logic, with
the category of smooth manifolds as the motivating example. In joint work with
Kristine Bauer and Matthew Burke (both at Calgary) we generalize to tangent
structures on an (∞,2)category and show that the (∞,2)category of presentable
∞categories possesses such a structure. This allows us to make precise, for
example, the intuition that the ∞category of spectra plays the role of the
real line in Goodwillie calculus. As an application we show that Goodwillie's
definition of nexcisive functor can be recovered purely from the tangent
structure in the same way that njets of smooth maps are in ordinary calculus.
If time permits, I will suggest how other concepts from differential geometry,
such as connections, may play out into the context of functor calculus.


HHH 
9th October 2018 15:30 to 16:30 
Benjamin Böhme 
Equivariant multiplications and idempotent splittings of > Gspectra
My PhD research concerns multiplicative phenomena in
> equivariant stable homotopy theory. Equivariantly
with respect to a
> finite group G, there are many different notions of
a commutative ring
> spectrum. The idempotent summands of the genuine
equivariant versions
> of the sphere spectrum and the topological Ktheory
spectra provide
> natural examples of such objects. I give a complete
characterization
> of the best possible equivariant commutative ring
structures on these
> summands. As an important step in my approach, I
establish a
> classification of the idempotent elements in the
(plocal)
> representation ring of G, which may be of
independent interest.


HHH 
11th October 2018 15:30 to 15:45 
Agnes Beaudry  Determining the determinant sphere  
HHH 
11th October 2018 15:45 to 16:00 
Julie Bergner  To complete or make discrete? That is the question.  
HHH 
11th October 2018 16:00 to 16:15 
Paolo Salvatore  (Non)formality of little discs spaces and operads  
HHH 
11th October 2018 16:15 to 16:30 
Ulrike Tillmann  Infinite loop space machines and TQFTs  
HHH 
15th October 2018 14:00 to 15:00 
Doug Ravenel  Orthogonal GSpectra I  
HHH 
16th October 2018 13:45 to 14:45 
Lennart Meier 
Real homotopy theory
Real homotopy theory has its origin
in Atiyah capitalizing on the complex conjugation action on complex Ktheory to
obtain the $C_2$spectrum of Real Ktheory. More generally it concerns
$C_2$spectra with a Real orientation. We will discuss several examples and
several results, including some joint work with Hill and Greenlees.


HHH 
16th October 2018 15:15 to 16:15 
Robert Oliver  TBA  
HHH 
17th October 2018 14:00 to 15:00 
Doug Ravenel  Orthogonal GSpectra II  
HHH 
18th October 2018 15:30 to 15:45 
Peter Haine  Constructible étale sheaves and analytic sheaves  
HHH 
18th October 2018 15:45 to 16:00 
Ieke Moerdijk  The 10 minute shuffle  
HHH 
18th October 2018 16:00 to 16:15 
Sam Nariman  Thurston's fragmentation and nonabelian Poincare duality  
HHH 
18th October 2018 16:15 to 16:30 
Vesna Stojanoska  The Tate sphere and duality  
HHH 
23rd October 2018 14:00 to 15:00 
HansWerner Henn 
The exotic part of the Picard group of K(2)local spectra at the prime 2
The exotic part of the Picard group of K(2)local spectra at the prime 2
This is a report on joint work with A. Beaudry, I. Bobkova and P. Goerss.
Exotic elements in the Picard groups Pic(n,p) of K(n)local spectra are represented by spectra
whose Morava module is isomorphic to that of the 0dimensonal sphere. These elements
form a subgroup of Pic(n,p) which for given n is trivial if p is sufficiently large (p>2 if n=1,
and p>3 if n=2). These subgroups have been explicitly known for n=1 and p=2, and for
n=2 and p=3. In this talk we will give a complete description of its isomorphism type if n=p=2.


HHH 
23rd October 2018 15:30 to 16:30 
Lars Hesselholt 
Ktheory of cusps
In the early nineties, the Buonos Aires Cyclic Homology group calculated the Hochschild and cyclic homology of hypersurfaces, in general, and of the coordinate rings of planar cuspical curves, in particular. With Cortiñas' birelative theorem, proved in 2005, this gives a calculation of the relative Ktheory of planar cuspical curves over a field of characteristic zero. By a padic version of Cortiñas' theorem, proved by Geisser and myself in 2006, the relative Kgroups of planar cuspical curves over a perfect field of characteristic p > 0 can similarly be expressed in terms of topological cyclic homology, but the relevant topological cyclic homology groups have resisted calculation. In this talk, I will show that the new setup for topological cyclic homology by Nikolaus and Scholze has made this calculation possible. This is joint work with Nikolaus and similar results have been obtained by Angeltveit.


HHH 
25th October 2018 15:30 to 15:45 
Clemens Berger  DoldKan correspondences and involutive factorisation systems  
HHH 
25th October 2018 15:45 to 16:00 
Paul Goerss  What does it mean to be continuous?  
HHH 
25th October 2018 16:00 to 16:15 
Fabian Hebestreit  Homotopy Cobordism Categories  
HHH 
25th October 2018 16:15 to 16:30 
Oscar RandalWilliams  On the CayleyHamilton Theorem  
HHH 
30th October 2018 14:00 to 15:00 
Hiro Tanaka 
The stack "Broken" and associative algebras
After
reviewing some aspects of Morse theory, I'll talk about "Broken," the
moduli stack of constant Morse trajectories (possibly broken) on a point. Surprisingly,
this stack has the following property: Factorizable sheaves on it are the same
thing as (possibly nonunital) associative algebras. We all know that having
geometric descriptions of algebraic structures should buy us mileage; so what
mileage does this property buy us? If time allows, I'll try to explain why this
theorem leads to a roadmap for constructing Morse chain complexes, and in fact,
for constructing the stable homotopy type of a compact manifold with a Morse
function. (That is, this gives a different way to realize ideas of
CohenJonesSegal.) The motivation is to construct a stable homotopy type for
Lagrangian Floer Theorythe latter is an important invariant in symplectic
geometry and mirror symmetry. This is all joint work with Jacob Lurie.


HHH 
30th October 2018 15:30 to 16:30 
George Raptis 
Devissage theorems in algebraic Ktheory
In this talk I will give an
overview of old and new devissagetype results in algebraic Ktheory.


HHH 
1st November 2018 15:30 to 15:45 
Tobias Barthel  Spooky cats  
HHH 
1st November 2018 15:45 to 16:00 
Anna Marie Bohmann  On the existence of ghosts  
HHH 
1st November 2018 16:00 to 16:15 
John Greenlees  Two skeletons in a cellular cupboard  
HHH 
1st November 2018 16:15 to 16:30 
Constanze Roitzheim  Franke's Scary Models  
HHH 
6th November 2018 14:00 to 15:00 
Carles Broto  Homotopy fixed points by finite pgroup actions on classifying spaces of fusion systems  
HHH 
6th November 2018 15:30 to 16:30 
Kathryn Hess  An introduction to topological coHochschild homology  
HHH 
8th November 2018 15:30 to 15:45 
Andrew Baker  Orientations old and new  
HHH 
8th November 2018 15:45 to 16:00 
Magdalena Kedziorek  Surprise!  
HHH 
8th November 2018 16:00 to 16:15 
Markus Szymik  Adams before Adnams  
HHH 
8th November 2018 16:15 to 16:30 
Sarah Whitehouse  E_r model structures  
HHH 
12th November 2018 14:00 to 15:00 
Doug Ravenel  Outlining the Proof of the Kervaire Invariant Theorem  
HHH 
13th November 2018 14:00 to 15:00 
Tobias Barthel 
Stratifying categories of representations.
Stratifying categories of representations.
Abstract: In this talk, we discuss some aspects of the
global structure of categories of representations from the point of view of
stable homotopy theory. This is joint work with Castellana, Heard, and
Valenzuela.


HHH 
13th November 2018 15:30 to 16:30 
Anna Marie Bohmann 
Tools for understanding topological coHochschild homology
Hochschild homology is a classical invariant of
algebras. A "topological"
version, called THH, has important connections to algebraic Ktheory,
Waldhausen's Atheory, and free loop spaces.
For coalgebras, there is a dual invariant called "coHochschild
homology" and Hess and Shipley have recently defined a topological version
called "coTHH." In this talk,
I'll talk about coTHH (and THH) are defined and then discuss work with Gerhardt,
Hogenhaven, Shipley and Ziegenhagen in which we develop some computational
tools for approaching coTHH.


HHH 
15th November 2018 15:30 to 15:45 
Scott Balchin  Grout (or the story of how my coauthor stopped me from naming things)  
HHH 
15th November 2018 15:45 to 16:00 
Michael Ching  What is a prooperad?  
HHH 
15th November 2018 16:00 to 16:15 
Manuel Krannich  A Hermitian Kgroup via geometry  
HHH 
15th November 2018 16:15 to 16:30 
Mingcong Zeng  Slice Differentials  
HHH 
19th November 2018 14:00 to 15:00 
Doug Ravenel  The Kervaire invariant problem at odd primes  
HHH 
20th November 2018 14:00 to 15:00 
George Raptis 
Devissage theorems in algebraic Ktheory
In this talk I will give an overview of old and new devissagetype results in algebraic Ktheory.


HHH 
20th November 2018 15:30 to 16:30 
Markus Szymik 
Symmetry groups of algebraic structures and their homology
The
symmetric groups, the general linear groups, and the automorphism groups of
free groups are examples of families of groups that arise as symmetry groups of
algebraic structures but that are also dear to topologists. There are many
other less obvious examples of interest. For instance, in joint work with
Nathalie Wahl, this point of view has led to the computation of the homology of
the HigmanThompson groups. I will survey a general context and some more
geometric examples in this talk.


HHH 
22nd November 2018 15:30 to 15:45 
Alexander Berglund  Rational models for automorphisms of fiber bundles  
HHH 
22nd November 2018 15:45 to 16:00 
Jesper Grodal  Savour thy units! (or why the padics sometimes beats the integers)  
HHH 
22nd November 2018 16:00 to 16:15 
Michael Joachim  On the GromovLawsonRosenberg Conjecture  
HHH 
22nd November 2018 16:15 to 16:30 
Doug Ravenel  The Pontrjagin twist  
HHH 
26th November 2018 14:00 to 15:00 
Doug Ravenel  The slice filtration and slice spectral sequence  
HHH 
27th November 2018 14:00 to 15:00 
Claudia Scheimbauer 
Constructing extended AKSZ topological field theories in derived symplectic geometry
Derived
algebraic geometry and derived symplectic geometry in the sense of
PantevToenVaquiéVezzosi allows for a reinterpretation/analog of the
classical AKSZ construction for certain $\sigma$models. It is given by taking
mapping stacks with a fixed target building and describes ``semiclassical
TFTs". Using the formalism of derived algebraic geometry as a blackbox, I will sketch how this
construction yields extended TFTs, which involves harnessing many higher
homotopies. This
is joint work in progress with Damien Calaque and Rune Haugseng.


HHH 
27th November 2018 15:30 to 16:30 
David Ayala 
Orthogonal group and adjoints
In this talk I will articulate and contextualize the following sequence of results. The Bruhat decomposition of the general linear group defines a stratification of the orthogonal group.Matrix multiplication defines an algebra structure on its exitpath category in a certain Morita category of categories. In this Morita category, this algebra acts on the category of ncategories  this action is given by adjoining adjoints to ncategories. This result is extracted from a larger program  entirely joint with John Francis, some parts joint with Nick Rozenblyum  which proves the cobordism hypothesis. 

HHH 
29th November 2018 15:30 to 15:45 
Christian Ausoni  On a Greenlees spectral sequence  
HHH 
29th November 2018 15:45 to 16:00 
Rachael Boyd  Homological stability for Artin monoids  
HHH 
29th November 2018 16:00 to 16:15 
Federico Cantero Morán  Spaces of merging submanifold  
HHH 
29th November 2018 16:15 to 16:30 
Christian Schlichtkrull  Higher monoidal monomorphisms  
HHH 
30th November 2018 14:00 to 15:00 
Doug Ravenel  More about the slice filtration and slice spectral sequence  
HHHW04 
3rd December 2018 10:00 to 11:00 
Soren Galatius 
H_{4g6}(M_g)
The set of isomorphism classes of genus g Riemann surfaces carries a natural topology in which it may be locally parametrized by 3g3 complex parameters. The resulting space is denoted M_g, the moduli space of Riemann surfaces, and is more precisely a complex orbifold of that dimension. The study of this space has a very long history involving many areas of mathematics, including algebraic geometry, group theory, and stable homotopy theory.
The space M_g is not compact, essentially because a family of Riemann surface may degenerate into a nonsmooth object, and may be compactified in several interesting ways. I will discuss a compactification due to Harvey, which looks like a compact real (6g6)dimensional manifold with corners, except for orbifold singularities. The combinatorics of the corner strata in this compactification may be encoded using graphs.
Using this compactification, I will explain how to define a chain map from Kontsevich's graph complex to a chain complex calculating the rational homology of M_g. The construction is particularly interesting in degree 4g6, where our methods give rise to many nonzero classes in H_{4g6}(M_g), contradicting some predictions. This is joint work with Chan and Payne (arXiv:1805.10186).


HHHW04 
3rd December 2018 11:30 to 12:30 
Alexander Kupers 
Cellular techniques in homological stability 1: general theory
This is the first of two talks about joint work with S. Galatius and O RandalWilliams on applications higheralgebraic structures to homological stability. The main tool is cellular approximation of E_kalgebras, and we start with a discussion of the general theory of such cellular approximations. This culminates in a generic homological stability result.


HHHW04 
3rd December 2018 14:30 to 15:30 
George Raptis 
The hcobordism category and Atheory
A fundamental link between Waldhausen's algebraic Ktheory of spaces (Atheory) and manifold topology is given by an identification of Atheory in terms of stable
homotopy and the stable smooth hcobordism space. This important result has had many applications in the study of diffeomorphisms of manifolds. In more recent
years, the theory of cobordism categories has provided a different approach to the study of diffeomorphism groups with spectacular applications. In collaboration
with W. Steimle , we revisit the classical Waldhausen Ktheory in light of these developments and investigate new connections and applications. In this talk, I will first
discuss a cobordismtype model for Atheory, and then I will focus on the hcobordism category, the cobordism category of hcobordisms between smooth manifolds
with boundary, and its relationship to the classical hcobordism space of a compact smooth manifold. This is joint work with W. Steimle.


HHHW04 
3rd December 2018 16:00 to 17:00 
Christopher SchommerPries 
The Relative Tangle Hypothesis
I will describe recent progress on a nonlocal variant of the cobordism hypothesis for higher categories of bordisms embedded into finite dimensional Euclidean space.


HHHW04 
4th December 2018 09:00 to 10:00 
Wolfgang Lueck 
On the stable Cannon Conjecture
The Cannon Conjecture for a torsionfree hyperbolic group $G$ with boundary homeomorphic to $S^2$ says that $G$ is the fundamental group of an aspherical closed $3$manifold $M$. It is known that then $M$ is a hyperbolic $3$manifold. We prove the stable version that for any closed manifold $N$ of dimension greater or equal to $2$ there exists a closed manifold $M$ together with a simple homotopy equivalence $M o N imes BG$. If $N$ is aspherical and $pi_1(N)$ satisfies the FarrellJones Conjecture, then $M$ is unique up to homeomorphism. This is joint work with Ferry and Weinberger. 

HHHW04 
4th December 2018 10:00 to 11:00 
Thomas Willwacher 
Configuration spaces of points and real GoodwillieWeiss calculus
The manifold calculus of Goodwillie and Weiss proposes to reduce questions about embedding spaces of manifolds to questions about mapping spaces of the (littledisks modules of) configuration spaces of points on those manifolds. We will discuss real models for these configuration spaces. Furthermore, we will see that a real version of the aforementioned mapping spaces is computable in terms of graph complexes. In particular, this yields a new tool to study diffeomorphism groups and moduli spaces. 

HHHW04 
4th December 2018 11:30 to 12:30 
Alexander Kupers 
Cellular techniques in homological stability 2: mapping class groups
This is the second of two talks about joint work with S. Galatius and O RandalWilliams on applications higheralgebraic structures to homological stability. In it we apply the general theory to the example of mapping class groups of surfaces. After reproving Harer's stability result, I will explain how to prove the novel phenomenon of secondary homological stability; there are maps comparing the relative homology groups of the stabilization map for different genus and there are isomorphisms in a range tending to infinity with the genus.


HHHW04 
4th December 2018 14:30 to 15:30 
Victor Turchin 
Embeddings, operads, graphcomplexes
I will talk about the connection between the following concepts: manifold calculus, little discs operads, embedding spaces, problem of delooping, relative rational formality of the little discs, and graphcomplexes. I will review main results on this connection by Boavida de Brito and Weiss, my coauthors and myself. At the end I will briefly go over the current joint work in progress of Fresse, Willwacher, and myself on the rational homotopy type of embedding spaces. Coauthors: Gregory Arone (Stockholm University), Julien Ducoulombier (ETH, Zurich), Benoit Fresse (University of Lille), Pascal Lambrechts (University of Louvain), Paul Arnaud Songhafouo Tsopméné (University of Regina), Thomas Willwacher (ETH, Zurich). 

HHHW04 
4th December 2018 16:00 to 17:00 
Nathalie Wahl 
Homotopy invariance in string topology
In joint work with Nancy Hingston, we show that the GoreskyHingston coproduct, just like the ChasSullivan product, is homotopy invariant. Unlike the ChasSullivan product, this coproduct is a "compactified operation", coming from a certain compactification of the moduli space of Riemann surfaces. I'll give an idea of the ingredients used in the proof.


HHHW04 
5th December 2018 09:00 to 10:00 
Cary Malkiewich 
Periodic points and topological restriction homology
I will talk about a project to import trace methods, usually reserved for algebraic Ktheory computations, into the study of periodic orbits of continuous dynamical systems (and viceversa). Our main result so far is that a certain fixedpoint invariant built using equivariant spectra can be "unwound" into a more classical invariant that detects periodic orbits. As a simple consequence, periodicpoint problems (i.e. finding a homotopy of a continuous map that removes its nperiodic orbits) can be reduced to equivariant fixedpoint problems. This answers a conjecture of Klein and Williams, and allows us to interpret their invariant as a class in topological restriction homology (TR), coinciding with a class defined earlier in the thesis of Iwashita and separately by Luck. This is joint work with Kate Ponto.


HHHW04 
5th December 2018 10:00 to 11:00 
Christine Vespa 
Higher Hochschild homology as a functor
Higher Hochschild homology generalizes classical Hochschild homology for rings. Recently, Turchin and Willwacher computed higher Hochschild homology of a finite wedge of circles with coefficients in the Loday functor associated to the ring of dual numbers over the rationals. In particular, they obtained linear representations of the groups Out(F_n) which do not factorize through GL(n,Z). In this talk I will explain how viewing higher Hochschild homology of a finite wedge of circles as a functor on the category of free groups provides a conceptual framework which allows powerful tools such as exponential functors and polynomial functors to be brought to bear. In particular, this allows the generalization of the results of Turchin and Willwacher; this gives rise to new linear representations of Out(F_n) which do not factorize through GL(n,Z). (This is joint work with Geoffrey Powell.) 

HHHW04 
5th December 2018 11:30 to 12:30 
Fabian Hebestreit 
The homotopy type of algebraic cobordism categories
Coauthors: Baptiste Calmès (Université d'Artois), Emanuele Dotto (RFWU Bonn), Yonatan Harpaz (Université Paris 13), Markus Land (Universität Regensburg), Kristian Moi (KTH Stockholm), Denis Nardin (Université Paris 13), Thomas Nikolaus (WWU Münster), Wolfgang Steimle (Universität Augsburg). Abstract: I will introduce cobordism categories of Poincaré chain complexes, or more generally of Poincaré objects in any hermitian quasicategory C. One interest in such algebraic cobordism categories arises as they receive refinements of Ranicki's symmetric signature in the form of functors from geometric cobordism categories à la GalatiusMadsenTillmannWeiss. I will focus, however, on a more algebraic direction. The cobordism category of C can be delooped by an iterated Qconstruction, that is compatible with BökstedtMadsen's delooping of the geometric cobordism category. The resulting spectrum is a derived version of GrothendieckWitt theory and I will explain how its homotopy type can be computed in terms of the K and LTheory of C.


HHHW04 
6th December 2018 09:00 to 10:00 
Alexander Berglund 
Rational homotopy theory of automorphisms of manifolds
I will talk about differential graded Lie algebra models for automorphism groups of simply connected manifolds M. Earlier results by Ib Madsen and myself on models for block diffeomorphisms combined with rational models for Waldhausen's algebraic Ktheory of spaces suggest a model for the group of diffeomorphisms homotopic to the identity, valid in the socalled pseudoisotopy stable range. If time admits, I will also discuss how to express the generalized MillerMoritaMumford classes in the cohomology of BDiff(M) in terms of these models.


HHHW04 
6th December 2018 10:00 to 11:00 
Johannes Ebert 
Cobordism categories, elliptic operators and positive scalar curvature
We prove that a certain collection of path components of the space of metrics of positive scalar curvature on a highdimensional sphere has the homotopy type of an infinite loop space, generalizing a theorem by Walsh. The proof uses an version of the surgery method by Galatius and RandalWilliams to cobordism categories of manifolds equipped with metrics of positive scalar curvature. Moreover, we prove that the secondary index invariant of the spin Dirac operator is an infinite loop map. The proof of that fact uses a generalization of the AtiyahSinger index theorem to spaces of manifolds. (Joint work with RandalWilliams)


HHHW04 
6th December 2018 11:30 to 12:30 
Ben Knudsen 
Configuration spaces and Lie algebras away from characteristic zero
There is a close connection between the theory of Lie algebras and the study of additive invariants of configuration spaces of manifolds, which has been exploited in many calculations of rational homology. We begin the computational exploration of this connection away from characteristic zero, exhibiting a spectral sequence converging to the pcomplete complex Ktheory of configuration spacesmore generally, to their completed Morava E(co)homologyand we identify its second page in terms of an algebraic homology theory for Lie algebras equipped with certain power operations. We construct a computationally accessible analogue of the classical ChevalleyEilenberg complex for these Hecke Lie algebras, and we use it to perform a number of computations. This talk is based on joint work in progress with Lukas Brantner and Jeremy Hahn.


HHHW04 
6th December 2018 14:30 to 15:00 
Manuel Krannich 
Contributed talk  Mapping class groups of highly connected manifolds
The group of isotopy classes of diffeomorphisms of a highly connected almost parallelisable manifold of even dimension 2n>4 has been computed by Kreck in the late 70’s. His answer, however, left open two extension problems, which were later understood in some particular dimensions, but remained unsettled in general. In this talk, I will explain how to resolve these extension problems in the case of n being odd, resulting in a complete description of the mapping class group in question in terms of an arithmetic group and the cokernel of the stable Jhomomorphism.


HHHW04 
6th December 2018 15:00 to 15:30 
Rachael Boyd 
Contributed Talk  The low dimensional homology of Coxeter groups
Coxeter groups were introduced by Tits in the 1960s as abstractions of the finite reflection groups studied by Coxeter. Any Coxeter group acts by reflections on a contractible complex, called the Davis complex. This talk focuses on a computation of the first three integral homology groups of an arbitrary Coxeter group using an isotropy spectral sequence argument: the answer can be phrased purely in terms of the original Coxeter diagram. I will give an introduction to Coxeter groups and the Davis complex before outlining the proof.


HHHW04 
6th December 2018 16:00 to 16:30 
Csaba Nagy 
Contributed Talk  The Sullivanconjecture in complex dimension 4
The Sullivanconjecture claims that complex projective complete intersections are classified up to diffeomorphism by their total degree, Eulercharacteristic and Pontryaginclasses. Kreck and Traving showed that the conjecture holds in complex dimension 4 if the total degree is divisible by 16. In this talk I will present the proof of the remaining cases. It is known that the conjecture holds up to connected sum with the exotic 8sphere (this is a result of Fang and Klaus), so the essential part of our proof is understanding the effect of this operation on complete intersections. This is joint work with Diarmuid Crowley.


HHHW04 
6th December 2018 16:30 to 17:00 
Danica Kosanović 
Contributed talk  Extended evaluation maps from knots to the embedding tower
The evaluation maps from the space of knots to the associated embedding tower are conjectured to be universal knot invariants of finite type. Currently such invariants are known to exist only over the rationals (using the existence of Drinfeld associators) and the question of torsion remains wide open. On the other hand, grope cobordisms are certain operations in ambient 3space producing knots that share the same finite type invariants and give a geometric explanation for the appearance of Lie algebras and graph complexes. I will explain how grope cobordisms and an explicit geometric construction give paths in the various levels of the embedding tower. Taking components recovers the result of BudneyConantKoytcheffSinha, showing that these invariants are indeed of finite type. This is work in progress joint with Y. Shi and P. Teichner. 

HHHW04 
7th December 2018 10:00 to 11:00 
Andre Henriques 
The complex cobordism 2category and its central extensions
I will introduce a symmetric monoidal 2category whose objects are 0manifolds, whose 1morphisms are 1dimensional smooth cobordisms, and whose 2morphisms are Riemann surfaces with boundary and cusps. I will introduce a certain central extension by ℝ₊ and explain its relevance in chiral conformal field theory. Finally, I will explain the state of my understanding on the question of classification of such extensions by ℝ₊.


HHHW04 
7th December 2018 11:30 to 12:30 
Sam Nariman 
Topological and dynamical obstructions to extending group actions.
For any 3manifold $M$ with torus boundary, we find finitely generated subgroups of $\Diff_0(\partial M)$ whose actions do not extend to actions on $M$; in many cases, there is even no action by homeomorphisms. The obstructions are both dynamical and cohomological in nature. We also show that, if $\partial M = S^2$, there is no section of the map $\Diff_0(M) \to \Diff_0(\partial M)$. This answers a question of Ghys for particular manifolds and gives tools for progress on the general program of bordism of group actions. This is a joint work with Kathryn Mann.


HHHW04 
7th December 2018 13:30 to 14:30 
Ryan Budney 
Some prospects with the splicing operad
Roughly six years ago I described an operad that acts on spaces of `long knots'. This is the space of smooth embeddings of R^j into R^n. The embeddings are required to be standard (linear) outside of a disc, and come equipped with a trivialisation of their normal bundles. This splicing operad gives a remarkably compact description of the homotopytype of the space of classical long knots (j=1, n=3), that meshes well with the machinery of 3manifold theory: JSJdecompositions and geometrization. What remains to be seen is how useful this splicing operad might be when n is larger than 3. I will talk about what is known at present, and natural avenues to explore.


HHHW04 
7th December 2018 14:30 to 15:30 
Diarmuid Crowley 
Relative kappaclasses
Diff(D^n), the the space of diffeomorphisms of the ndisc fixed near the boundary has rich rational topology. For example, Weiss's discovery of ``surreal'' Pontrjagin classes leads to the existence of rationally nontrivial homotopy classes in BDiff(D^n). For any smooth nmanifold M, extension by the identity induces a map BDiff(D^n) \to BDiff(M). In this talk I will report on joint work with Wolfgang Steimle and Thomas Schick, where we consider the problem of computing the image of the ``Weiss classes'' under the maps on homotopy and homology induced by extension. This problem naturally leads one to consider relative kappaclasses. Via relative kappaclasses, we show that the maps induced by extension are rationally nontrivial for a wide class of manifolds M, including aspherical manifolds (homology, hence also homotopy) and stably parallelisable manifolds (homotopy). When M is aspherical, our arguments rely on vanishing results for kappaclasses due to Hebestreit, Land, Lueck and RandalWilliams. 

HHH 
11th December 2018 14:00 to 15:00 
Ieke Moerdijk  Dendroidal spaces and mapping spaces between little cubes operads.  
HHH 
11th December 2018 15:30 to 16:30 
Paolo Salvatore 
Wonderful FultonMacPherson operads The FultonMacPherson operads are E_n operads that are miraculously invariant under the W cofibrant resolution by BoardmanVogt. This allows a geometric approach to several topics including factorization homology, Koszul duality of E_noperads, cellular operadic subdivision, and E_nalgebra homology. (part of this is joint work with Michael Ching and Benoit Fresse) 

HHH 
13th December 2018 15:30 to 15:45 
Clark Barwick  The line isn’t contractible  
HHH 
13th December 2018 15:45 to 16:00 
Daniela Egas Santander  Wandering down the path to path homology  
HHH 
13th December 2018 16:00 to 16:15 
Gijs Heuts  Whitehead products in v_nperiodic homotopy groups  
HHH 
13th December 2018 16:15 to 16:30 
Martin PalmerAnghel  Homological stability for moduli spaces of disconnected submanifolds  
HHH 
18th December 2018 14:00 to 15:00 
Boris Botvinnik  Positive scalar curvature metrics on manifolds with fibred singularities  
HHH 
18th December 2018 15:30 to 16:30 
Birgit Richter 
Spaces and cochains  yet another approach
Rationally, the homotopy type of any
reasonable space is completely determined by (a minimal model of) the Sullivan
cochain algebra of the space. If you want to be nonrational, then Mandell's
result says that the $E_\infty$algebra structure of the cochains determines
the homotopy type. In joint work with Steffen Sagave we construct a strictly
commutative model of the cochains of a space using the diagram category of
finite sets and injections in order to free things up. We show that this cochain
algebra determines the homotopy type of (finite type, nilpotent) spaces 

HHH 
20th December 2018 15:30 to 15:45 
Robert Bruner  Gröbner bases  
HHH 
20th December 2018 15:45 to 16:00 
Sam Nariman  Vanishing or nonvanishing of kappa_2  
HHH 
20th December 2018 16:00 to 16:15 
Nathalie Wahl  Pushing around, trying to stay normal and positive  
HHH 
20th December 2018 16:15 to 16:30 
Anna Marie Bohmann  Here Happily Have we assembled 