# Seminars (NST)

Videos and presentation materials from other INI events are also available.

Search seminar archive

Event When Speaker Title
NSTW01 9th September 2002
10:00 to 11:00
WG Dwyer Localizations \& homotopy theory of diagrams (1)
NSTW01 9th September 2002
11:30 to 12:30
Obstruction theory for structured ring spectra (1)
NSTW01 9th September 2002
14:00 to 15:00
Operadic, $A_\infty$ and n-categories (1)
NSTW01 9th September 2002
16:00 to 17:00
J Smith Abstract homotopy theory (1)
NSTW01 10th September 2002
10:00 to 11:00
WG Dwyer Localizations \& homotopy theory of diagrams (2)
NSTW01 10th September 2002
11:30 to 12:30
Obstruction theory for structured ring spectra (2)
NSTW01 10th September 2002
14:00 to 15:00
Operads and motivic homotopy theory (2)
NSTW01 10th September 2002
16:00 to 17:00
J Smith Abstract homotopy theory (2)
NSTW01 11th September 2002
10:00 to 11:00
S Schwede Triangulated categories and models (1)
NSTW01 11th September 2002
11:30 to 12:30
Problem session
NSTW01 11th September 2002
14:00 to 15:00
NSTW01 12th September 2002
10:00 to 11:00
I Madsen The stable moduli space of Riemann surfaces (1)
NSTW01 12th September 2002
11:30 to 12:30
Cosimplical objects and little $n$-cubes (1)
NSTW01 12th September 2002
14:00 to 15:00
S Schwede Triangualted categories and models (2)
NSTW01 12th September 2002
16:00 to 17:00
Simplicial \& operad methods in algebraic topology (1)
NSTW01 13th September 2002
10:00 to 11:00
I Madsen The stable moduli space of Riemann surfaces (2)
NSTW01 13th September 2002
11:30 to 12:30
Cosimplical objects and little $n$-cubes
NSTW01 13th September 2002
14:00 to 15:00
Simplicial \& operad methods in algebraic topology (2)
NSTW01 13th September 2002
16:00 to 17:00
Axiomatic stable homotopy theory
NSTW01 16th September 2002
10:00 to 11:00
R Jardine Stable homotopy theories for simplicial presheaves (1)
NSTW01 16th September 2002
11:30 to 12:30
${\Bbb A}^1$ homotopy theory (1)
NSTW01 16th September 2002
14:00 to 15:00
Introduction to algebraic cobordism (1)
NSTW01 16th September 2002
16:00 to 17:00
trace methods in algebraic K theory - I
NSTW01 17th September 2002
10:00 to 11:00
R Jardine Stable homotopy theories for simplicial presheaves (2)
NSTW01 17th September 2002
11:30 to 12:30
${\Bbb A}^1$ homotopy theory (2)
NSTW01 17th September 2002
14:00 to 15:00
Mixed Tate motives (2)
NSTW01 17th September 2002
16:00 to 17:00
Trace methods in algebraic K-theory - II
NSTW01 18th September 2002
10:00 to 11:00
Questions related to motives
NSTW01 18th September 2002
11:30 to 12:30
Glaors descent for the K-theory of commutatice {\$}-algebras NSTW01 18th September 2002 14:00 to 15:00 Structured stable homotopy theory \& descent in algebraic K theory (1) NSTW01 18th September 2002 16:00 to 17:00${\Bbb A}^1$-representability of hermitian K-theory and Witt groups \& Morel's conjectures on${\Bbb A}^1$-homotopy groups of spheres NSTW01 19th September 2002 10:00 to 11:00 Equivariant motives phenomena (1) NSTW01 19th September 2002 11:30 to 12:30 An examplein the theory of Witt groups of algebraic varieties using Steenrod operations on Chow groups NSTW01 19th September 2002 14:00 to 15:00 A Vishik Quadratic Grassmannians \& Steenrod operations (1) NSTW01 19th September 2002 16:00 to 17:00 Structured stable homotopy theory \& descent in algebraic K theory (2) NSTW01 20th September 2002 10:00 to 11:00 Equivariant motivic phenomena (2) NSTW01 20th September 2002 11:30 to 12:30 B Toen Homotopical algebraic geometry NSTW01 20th September 2002 14:00 to 15:00 A Vishik Quadratic Grassmannians \& Steenrod operations (2) NSTW01 20th September 2002 16:00 to 17:00 C Weibel Homological algebra in DM NST 26th September 2002 14:00 to 15:00 N Yagita Algebraic cobordism of simply connected Lie groups NST 26th September 2002 15:15 to 16:15 Non-torsion elements in algebraic k-theory of number fields, Mordell-Weil groups and l-adic representations NST 27th September 2002 14:00 to 15:00 B Kahn Informal geometry seminar series: Birational motives NSTW03 30th September 2002 10:00 to 11:00 Zeta elements and modular forms shall explain the construction of zeta elements' in K_k of Kuga-Sato varieties which form an Euler system, related via the dual exponential to critical L-values of weight k cusp forms, and via the regulator to non-critical values. NSTW03 30th September 2002 11:30 to 12:30${\bf G}_{a}$, motives, polylogarithms etc NSTW03 30th September 2002 14:00 to 15:00 C Soule Bounds on the torsion in the K-theory of algebraic integers Given a natural integer$m$and a number field$F$we find an upper bound for the cardinality of the torsion in$K_{m}(A)$, where$A$is the ring of integers of$F$. The bound depends on$m$, the absolute degree of$F$and its absolute discriminant. This bound seems much too big but it is explicit. NSTW03 30th September 2002 15:30 to 16:30 Noncommutative Iwasawa Theory NSTW03 1st October 2002 10:00 to 11:00 Stark's conjecture and new Stickelberger phenomena NSTW03 1st October 2002 11:30 to 12:30 I Fesenko Analysis on arithmetic surfaces A new kind of measure matching properties of two-dimensional structures on arithmetic surfaces is used to define zeta integrals on$K$-delic groups and to study its properties. NSTW03 1st October 2002 14:00 to 15:00 Z Wojtkoviak l-adic polylogarithms NSTW03 1st October 2002 15:30 to 16:30 C Pedrini Finite-dimensional motives and the Beilinson-Bloch conjectures NSTW03 2nd October 2002 10:00 to 11:00 de Rham discriminants NSTW03 2nd October 2002 11:30 to 12:30 Analogue of the Grothendieck conjecture for higher dimensional local fields NSTW03 3rd October 2002 10:00 to 11:00 S Lichtenbaum Weil \'{e}tale cohomology NSTW03 3rd October 2002 11:30 to 12:30 On equivariant Tamagawa numbers, Weil \'{e}tale cohomology and values of L-functions We show that, in certain cases, Lichtenbaum's Weil-Etale cohomology leads to a more explicit interpretation of the (equivariant) Tamagawa number conjecture. We then use this interpretation to formulate, and in certain cases also prove, a universal refinement of the well known (and seemingly rather different) conjectures of Stark, of Gross, of Tate, of Rubin and of Darmon concerning the values of derivatives of abelian L-functions. NSTW03 3rd October 2002 14:00 to 15:00 Weil \'{e}tale motivic cohomology over finite fields NSTW03 3rd October 2002 15:30 to 16:30 Rational and numerical equivalence on certain abelian varieties over finite fields NSTW03 4th October 2002 10:00 to 11:00 U Jannsen Kato complexes: conjectures and results For rather general schemes Kato defined complexes which are Galois cohomology analogues of the Gersten complexes in K-theory (Crelle 366: A Hasse principle for 2-dimensional local fields'). He stated some conjectures and proved them in low dimensions. I will report on the results known so far (partly due to myself) and some relationships with étale dulaity (recent joint work with Saito and Sato). NSTW03 4th October 2002 11:30 to 12:30 Relative K-groups and class field theory of arithmetic surfaces NSTW03 4th October 2002 14:00 to 15:00$K_{4}$of curves and syntomic regulators NSTW03 4th October 2002 15:30 to 16:30 K-theory and classical conjectures in the arithmetic of cyclotomic fields NST 9th October 2002 16:00 to 17:00 tmf(3) and other tmf module spectra NST 10th October 2002 16:00 to 17:00 Blow-ups and mixed motives NST 17th October 2002 14:00 to 15:00 K-theory and derived equivalences NST 17th October 2002 16:00 to 17:00 The status of the telescope conjecture NST 24th October 2002 14:00 to 15:00 The structure of E$(n)_*E(n)$comodules NST 24th October 2002 16:00 to 17:00 General linear group homology NST 31st October 2002 14:00 to 15:00 Guises of the second Chern class: the circle-equivariant sigma orientation NST 31st October 2002 16:00 to 17:00 The rank conjecture for fields, and higher Chow groups NST 6th November 2002 14:00 to 15:00 Euler characteristics of nearly perfect complexes NST 7th November 2002 14:00 to 15:00 Rational torus-equivariant cohomology theories NST 14th November 2002 14:00 to 15:00 Equivariant formal groups NST 21st November 2002 14:00 to 15:00 JF Jardine Higher order stacks NST 28th November 2002 14:00 to 15:00 The Bass conjecture and acyclic groups NST 28th November 2002 16:00 to 17:00 Hochschild homology and closed geodesics NST 5th December 2002 14:00 to 15:00 AJ Baker Minimal atomic complexes NST 5th December 2002 16:00 to 17:00 Algebraic K-theory of topological K-theory NSTW04 9th December 2002 08:15 to 09:00 Registration NSTW04 9th December 2002 09:00 to 10:00 Topological aspects of elliptic cohomology NSTW04 9th December 2002 10:00 to 11:00 Two-vector bundles and elliptic objects We (Baas, Dundas, Rognes) define a two-vector bundle over a base space X as a kind of family of two-vector spaces (in the sense of Kapranov and Voevodsky) parametrized over X. The rank 1 case recovers the notion of a Dixmier-Douady gerbe over X. The equivalence classes of two-vector bundles over X form an abelian monoid, whose Grothendieck group completion is the zero-th generalized cohomology group of X represented by the algebraic K-theory of the symmetric bimonoidal category of two-vector spaces. We argue that this K-theory agrees with the algebraic K-theory of the S-algebra (= A-infinity ring spectrum) representing connective topological K-theory, which by explicit computation (Ausoni, Rognes) is a connective, integrally defined form of elliptic cohomology, i.e., has chromatic complexity two. Two-vector bundles are thus geometric objects over X which provide the "cycles" for an elliptic cohomology theory at X. We also wish to indicate how a two-vector bundle over X leads to a virtual (anomaly) vector bundle over the free loop space of X, and an associated action functional for compact oriented surfaces over X. NSTW04 9th December 2002 15:30 to 16:30 S Stolz The spinor bundle on the free loop space The spinor bundle$S(E)$associated to an even dimensional real vector bundle$E$with spin structure has (at least) two roles in life: from a homotopy theory point of view it represents the$K$-theory Euler class of$E$; from a geometric/analytic point of view, the Dirac operator acts on the sections of the spinor bundle$S(TX)$associated to the tangent bundle of a spin manifold$X$. Analogously, it is believed that the {\it spinor bundle} or {\it Fock space bundle}$\mathcal F(E)\to LX$over the free loop space$LX$associated to an even dimensional vector bundle$E\to X$with string structure' plays a similar dual role: it should represent the Euler class of$E$in$tmf^*(X)$, and there should be a Dirac-Witten operator' acting on the sections of$\mathcal F(TX)$, whose$S^1$-equivariant index is the Witten genus of$X$. The main result of this joint work with Peter Teichner is that the spinor bundle$\mathcal F(E)$can be equipped with additional structures we call conformal connection' and fusion'. We speculate that vector bundles over$LX$equipped with these two structures represent elements in$tmf^*(X)$. NSTW04 10th December 2002 09:00 to 10:00 I Grojnowski Hilbert schemes and integrable system: the cohomology ring of a compactification of configuration space NSTW04 10th December 2002 10:00 to 11:00 The tangent complex for the moduli stack of formal groups The main purpose of this talk is to explain and explore the object in the title and to outline why it might be useful. In particular, I hope to organize the following questions: when can (chromatic-type) homology theories be realized by structured ring spectra and, if they can, what can you say about maps between them? Both problems can be formulated in terms of an Andre'-Quillen cohomology calculation, which is where the tangent complex comes in. With any luck, I will get to the point where I can talk about some of the applications to elliptic spectra arising from the moduli stack of elliptic curves. I am, of course, following closely in the footsteps of others, in particular of Mike Hopkins and Haynes Miller. NSTW04 10th December 2002 15:30 to 16:30 G Segal What is an elliptic object? NSTW04 10th December 2002 16:30 to 17:30 G Mason Orbifold conformal field theory and cohomology of the monster We explain what is known and what is conjecture concerning rational orbifold models (ie 'good' vertex operator algebras and their automorphism groups) and the passage to the associated topological field theory. We explain how such theories may be used to detect group cohomology, and illustrate with the example of the Monster simple group, where there is a surprising prediction. NSTW04 11th December 2002 09:00 to 10:00 Algebraic groups and equivariant cohomology theories Equivariant cohomology theories E_G^*(.) are represented by G-spectra. When G is a torus and the theories are rational, there is a complete and calculable algebraic model A(G) of rational G-spectra (based on the idea that E_G^*(.) is built from its behaviour at each isotropy group). This model is formally very similar to a category of sheaves on an algebraic group C. Based on this, one can investigate the properties of cohomology theories E_G^*(.) based on the group C. In several cases of interest (including the case when C is an elliptic curve over a field of characteristic zero and G is the circle group) these properties are sufficient to determine a _construction_ of the cohomology theory using the model A(G). NSTW04 11th December 2002 10:00 to 11:00 D Freed Loop groups and twisted K-theory NSTW04 11th December 2002 15:30 to 16:30 On the M-theory action on a manifold with boundary NSTW04 11th December 2002 16:30 to 17:30 Gerbes of chiral differential operators In this talk we give a complete classification of a certain important class of vertex algebras, the so called algebras of chiral differential operators (cdo for short). These were introduced by Beilinson and Drinfeld, motivated by the ideas from the conformal field theory. It turned out, that "almost classical" structure of what we call the vertex algebroid controls the world of cdo. This structure consists of two part. The first is a structure of an algebroid Lie, and the other is its extension, both derived from the major identities held in chiral algebras. These extra structures can be fit into a complex of vector spaces which is a direct generalization of the De Rham-Chevalley complex for Lie algebras. The classes of equivalences of cdo are in one to one correspondence with the third cohomology group of this complex. We also provide the description of each isomorphism class. This allows us to study the sheafication of a an important class of cdo over a given manifold X. This is a cdo defined by the Heisenberg algebra and the Clifford algebra, or the free bosons and the free fermions. It turns out that there is a characteristic class which is an obstraction to glueing these local pieces into a sheaf. It has two components, first, is the Atiyah class, and the other is the Simons term. There is a projection of this class into cohomology of X, and the image of this projection is the second component of the Chern character of X. We also describe these algebras for specific classes of manifolds, namely algebraic groups and homogeneous spaces and a conjectural connection of these algebras defined for hypersurfaces to the Vafa orbifold models. NSTW04 12th December 2002 09:00 to 10:00 Equivariant veresion of elliptic spectra Let C be an elliptic curve over an affine scheme S, and let E be an even periodic ring spectrum whose associated formal group is the formal completion of C. This makes E an elliptic spectrum''. Now let A be a finite abelian group. We will describe what it means for an A-equivariant ring spectrum EA to be an equivariant version'' of E, in terms of the theory of equivariant formal groups. We will show how to construct EA when E is K(n)-local for some n. We will then give a method for recovering the general case from the K(n)-local case. The method always produces an A-spectrum EA, but it may not be well-defined or have a ring structure. We will describe some cases in which one can get around these problems. NSTW04 12th December 2002 10:00 to 11:00 K(1)-local topological modular forms, the Witten orientation and E_\infty cellular structures We describe the construction and the orientation of the topological modular forms spectrum tmf in the K(1)-local E_\infty category at the prime 2. We use the theory of theta algebras to decompose tmf and the bordism theory MO into E_infty cells: MO splits into the cone T_\zeta and a free part. Moreover, as was shown by Mike Hopkins, the spectrum tmf is obtained from T_\zeta by attaching one more cell. With this information we give an explicit E_\infty orientation which refines the Witten genus for families of O manifolds. NSTW04 12th December 2002 15:30 to 16:30 Hecke operators and logarithmic cohomology operations We describe how the theory of unstable power operations gives rise to an action of Hecke operators'' on Morava's cohomology theory$E=E_n$; when$n=2$the theory$E$is a version of elliptic cohomology completed at a prime p, and such power operations correspond to Hecke operators on modular forms of$p$-power degree. We then interpret the formula for a certain natural logarithmic cohomology operation on$E$in terms of such operators. NSTW04 12th December 2002 16:30 to 17:30 The elliptic genus of a singular variety I will begin by describing how the elliptic genus of a manifold can be characterised among all characteristic numbers by its "rigidity" properties. Next, I will give my characterization of (one version of) the elliptic genus by its invariance under "flops", a class of surgeries that comes up naturally in algebraic geometry. Borisov and Libgober proved a stronger invariance property, which allowed them to define the elliptic genus for a large class of singular complex spaces. To find even stronger invariance properties of the elliptic genus, we can try to define the elliptic genus for singular real spaces; I will discuss some calculations which support this possibility. NSTW04 13th December 2002 09:00 to 10:00 Elliptic genera and Thom classes I will survey some features of elliptic genera from the mathematics and physics literature and explain how they look from the point of view of homotopy theory. In particular, I shall explain how features of the "sigma orientation" and its equivariant analogue relate to modularity, rigidity, the two-variable elliptic genus, orbifold elliptic genera, and discrete torsion. NSTW04 13th December 2002 10:00 to 11:00 Complex orientations and Motivic Galois theory Grothendieck's program for an anabelian geometry suggests that the Galois group Gal(Q=Q) possesses very interesting pronilpotent representations, associated to a free Lie algebra on generators conjecturally identied with the values of the zeta function at odd positive integers > 1. Some such automorphism algebra acts on Kontsevich's deformation quantization of Poisson manifolds, and there are rea- sons for thinking there are similar actions on algebras of asymptotic expansions for geometric heat kernels [math.SG/9908070] dened via Ginzburg's cobordism of symplectic manifolds. This is all pretty hypothetical, but there is an interesting concrete representa- tion of such a free Lie algebra in the group of formal dieomorphisms of the line, closely related to a genus associated to the Gamma function by Kontsevich [math.QA/9904055, x4.6]; it is a deformation of the A^-genus, connected to the the- ory of quasisymmetric functions [math.AG/9908065]. This genus seems to be worth investigating, whether one believes any of the conjectures above, or not; this talk is an introduction to its properties. 1 NSTW04 13th December 2002 15:30 to 16:30 Cohomology of the stable mapping class group NSTW04 13th December 2002 16:30 to 17:30 Discussion Session NSTW04 16th December 2002 10:00 to 11:00 A note on Hopkins-Kuhn-Ravenel character Talk being held in the CMS - Wolfson Room NSTW04 16th December 2002 14:00 to 15:00 Spin bordism, contact structure and the cohomology of p-groups? Talk being held in the CMS - Wolfson Room NSTW04 17th December 2002 10:00 to 11:00 Resolutions of the K(2) - local sphere Talk being held in the CMS - Wolfson Room NSTW04 17th December 2002 15:30 to 16:30 What are the elliptic objects of K3 cohomology Talk being held in the CMS - Wolfson Room NSTW04 18th December 2002 10:00 to 11:00 Towards higher chromatic analogues of elliptic cohomology: curves with high formal group laws. Talk being held in the CMS - Wolfson Room Elliptic cohomology is related to v_2-periodicity because the formal group law associated with a certain elliptic curve has height 2. It is known that no elliptic curve will give greater height. In this talk I will display for each prime p and each i>0 a curve C(p,i) whose Jacobian has a 1-dimensional formal summand of height i(p-1). Both the curve and this formal group admit an action by a finite subgroup of the Morava stabilizer group containing an element of order p, which is maximal when p does not divide i. NSTW04 18th December 2002 15:30 to 16:30 Hierarchy of morava K-theories? Talk being held in the CMS - Wolfson Room NSTW04 19th December 2002 10:00 to 11:00 Gamma-cohomology and$E-infinity\$ structures on some periodic spectra Talk being held in the CMS - Wolfson Room
NSTW04 19th December 2002
15:30 to 16:30
Cooperations in elliptic homology and E(n) homology Talk being held in the CMS - Wolfson Room
NSTW04 20th December 2002
10:00 to 11:00
E-infinity maps between Spanier-Whitehead duals Talk being held in the CMS - Wolfson Room
NSTW04 20th December 2002
15:30 to 16:30
An idea of homotopical algebraic geometry Talk being held in the CMS - Wolfson Room
Motivated by "Derived deformation theory" and "brave new algebra," we will present an approach to algebraic geometry in homotopical contexts. We will show some applications of this theory, e.g. to a definition of etale K-theory of "commutative" ring spectra.