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# Seminars (KAH)

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Event When Speaker Title Presentation Material
KAHW01 13th January 2020
10:00 to 11:00
Charles Weibel K-theory and motivic cohomology - 1
Constructions and basic properties of K-theory
KAHW01 13th January 2020
11:30 to 12:30
Charles Doran Calabi-Yau Manifolds, Mirrors, and Motives - 1
KAHW01 13th January 2020
13:30 to 14:30
Vesna Stojanoska Introduction to Motivic Homotopy Theory I: Motivic Spaces
KAHW01 13th January 2020
14:30 to 15:30
Charles Weibel K-theory and motivic cohomology - 2
Motivic Cohomology, and basic theorems
KAHW01 13th January 2020
16:00 to 17:00
Francis Brown Periods, cohomology of algebraic varieties and beyond - 1
KAHW01 14th January 2020
10:00 to 11:00
Charles Doran Calabi-Yau Manifolds, Mirrors, and Motives - 2
KAHW01 14th January 2020
11:30 to 12:30
Anthony Scholl Algebraic Cycles and Hodge Theory I
KAHW01 14th January 2020
13:30 to 14:30
Vesna Stojanoska Introduction to Motivic Homotopy Theory II: Motivic Spectra
KAHW01 14th January 2020
14:30 to 15:30
Charles Weibel K-theory and motivic cohomology - 3
The connection between K-theory and motivic cohomology
KAHW01 14th January 2020
16:00 to 17:00
Matthias Flach Special values of Motivic L-functions I - 1
KAHW01 15th January 2020
09:00 to 10:00
Charles Doran Calabi-Yau Manifolds, Mirrors, and Motives - 3
KAHW01 15th January 2020
10:00 to 11:00
Francis Brown Periods, cohomology of algebraic varieties and beyond - 2
KAHW01 15th January 2020
11:30 to 12:30
Vesna Stojanoska Introduction to Motivic Homotopy Theory III: Highlights and Applications
KAHW01 16th January 2020
10:00 to 11:00
Matthias Flach Special values of Motivic L-functions II - 2
KAHW01 16th January 2020
11:30 to 12:30
Francis Brown Periods, cohomology of algebraic varieties and beyond - 3
KAHW01 16th January 2020
13:30 to 14:30
Anthony Scholl Algebraic Cycles and Hodge Theory II
KAH 16th January 2020
14:45 to 15:45
Study group on recent work of Golyshev-Zagier on the gamma conjecture in mirror symmetry and of Bloch-Vlasenko on motivic gamma functions.
KAH 16th January 2020
14:45 to 15:45
Study group on recent work of Golyshev-Zagier on the gamma conjecture in mirror symmetry and of Bloch-Vlasenko on motivic gamma functions. (copy)
KAHW01 17th January 2020
10:00 to 11:00
Anthony Scholl Algebraic Cycles and Hodge Theory III
KAHW01 17th January 2020
11:30 to 12:30
Matthias Flach Zeta - functions of arithmetic schemes - 3
KAH 20th January 2020
15:00 to 16:00
Patrick Brosnan Toroidal compactifications and incompressibility of exceptional congruence covers.
Suppose a finite group G acts faithfully on an irreducible variety X. We say that the G-variety X is compressible if there is a dominant rational morphism from X to a faithful G-variety Y of strictly smaller dimension. Otherwise we say that X is incompressible. In a recent preprint, Farb, Kisin and Wolfson (FKW) have proved the incompressibility of a large class of covers related to the moduli space of principally polarized abelian varieties with level structure. Their arithmetic methods, which use Serre-Tate coordinates in an ingenious way, apply to diverse examples such as moduli spaces of curves and many Shimura varieties of Hodge type. My talk will be about joint work with Fakhruddin and Reichstein, where our goal is to recover some of the results of FKW via the fixed point method from the theory of essential dimension. More specifically, we prove incompressibility for some Shimura varieties by proving the existence of fixed points of finite abelian subgroups of G in smooth compactifications. Our results are weaker than the results of FKW for Hodge type Shimura varieties, because the methods of FKW apply in cases where there is no boundary, while we need a nonempty boundary to find fixed points. However, our method has the advantage of extending to many Shimura varieties which are not of Hodge type, in particular, those associated to groups of type E7. Moreover, by using Pink's extension of the Ash, Mumford, Rapoport and Tai theory of toroidal compactifications to mixed Shimura varieties, we are able to prove incompressibility for congruence covers corresponding to certain universal families: e.g., the universal families of principally polarized abelian varieties.
KAH 23rd January 2020
11:15 to 12:15
Hossein Movasati Variational Hodge conjecture and Hodge loci
Grothendieck’s variational Hodge conjecture (VHC) claims that if we have a continuous family of Hodge cycles  (flat section of the Gauss-Manin connection) and the Hodge conjecture is true at least for one Hodge cycle of the family then it must be true for all such Hodge cycles. A stronger version of this (Alternative Hodge conjecture, AHC),  asserts that the deformation of an algebraic cycle Z togther with the projective variety X, where it lives,  is the same as the deformation of the cohomology class of Z in X. There are many simple counterexamples to AHC, however, in explict situations, like algebraic cycles inside hypersurfaces, it becomes a challenging problem. In  this talk I will review few cases in which AHC is true (including Bloch's semi-regular and local complete intersection  algebraic cycles) and other cases in which it is not true.   The talk is mainly based on the article  arXiv:1902.00831.

KAH 23rd January 2020
15:00 to 16:00
Don Zagier Study group on recent work of Golyshev-Zagier on the gamma conjecture in mirror symmetry and of Bloch-Vlasenko on motivic gamma functions. (copy)
KAH 27th January 2020
15:00 to 16:00
Masha Vlasenko Gamma functions, monodromy and Apéry constants
In their paper on the gamma conjecture in mirror symmetry, Golyshev and Zagier introduce a sequence of Apéry constants associated to an ordinary linear differential operator with a choice of two singular points and a path between them. Their setting also involves assumptions on the local monodromies around the two points (maximally unipotent and reflection point respectively). In particular, these assumptions are satisfied in the situation of Apéry's proof of irrationality of zeta(3), and in this case Golyshev and Zagier discover that (numerically, with high precision) the higher constants in the sequence seem to be rational linear combinations of weighted products of zeta and multiple zeta values. In the joint work with Spencer Bloch we show that, quite generally, the generating series of Apéry constants is a Mellin transform of a solution of the adjoint differential operator. This peculiar property explains why Apéry constants of geometric differential operators are periods, which seems to be the first step in the study of their motivic nature.

KAH 29th January 2020
11:15 to 12:15
Takamichi Sano On the local Tamagawa number conjecture and functional equations of Euler systems
KAH 29th January 2020
16:00 to 17:00
Spencer Bloch Rothschild Lecture: Elliptic curves associated to two-loop graphs (Feynman diagrams)
Two loop Feynman diagrams give rise to interesting cubic hypersurfaces in n variables, where n is the number of edges. When n=3, the cubic is obviously an elliptic curve. (In fact, a family of elliptic curves parametrized by physical parameters like momentum and masses.) Remarkably, elliptic curves appear also for suitable graphs with n=5 and n=7, and conjecturally for an infinite sequence of graphs with n odd. I will describe the algebraic geometry involved in proving this. Physically, the amplitudes associated to one-loop graphs are known to be dilogarithms. Time permitting, I will speculate a bit about how the presence of elliptic curves might point toward relations between two-loop amplitudes and elliptic dilogarithms.

This is joint work with C. Doran, P. Vanhove, and M. Kerr.

KAH 30th January 2020
11:15 to 12:15
Gabriela Guzman Rational and p-local motivic homotopy theory
KAH 30th January 2020
15:00 to 16:00
Masha Vlasenko Study group
KAH 3rd February 2020
15:00 to 16:00
John Christian Ottem Enriques surface fibrations with non-algebraic integral Hodge classes
I will explain a construction of a certain pencil of Enriques surfaces with non-algebraic integral Hodge classes of non-torsion type. This gives the first example of a threefold with trivial Chow group of zero-cycles on which the integral Hodge conjecture fails. If time permits, I will explain an application to a classical question of Murre on the universality of the Abel-Jacobi maps in codimension three. This is joint work with Fumiaki Suzuki.​

KAH 6th February 2020
11:15 to 12:15
Clélia Pech Motivic integration for some varieties with a torus action
Motivic integration was introduced by Kontsevich in 1995 and has proved useful in birational geometry and singularity theory. It assigns to constructible subsets of the arc space of a variety a "volume" which takes values in the Grothendieck ring of algebraic varieties, and it behaves in many ways just like usual integration. I will explain how motivic integration can be used to compute Batyrev's "stringy invariants", which are a generalization of Hodge numbers to singular varieties, for a family of varieties with a torus action. A potential application is to the study of mirror symmetry for these varieties. (Joint with K. Langlois and M. Raibaut.)

KAH 6th February 2020
14:30 to 15:30
Spencer Bloch Golyshev-Zagier Second Paper
KAH 10th February 2020
15:00 to 16:00
Paul Balmer Tensor-triangular fields
KAH 13th February 2020
11:15 to 12:15
Nicolas Garrel Mixed graded structures for the K-theory of Azumaya algebras
If we encode Morita theory for R-algebras as a monoidal category where morphisms are bimodules, then algebraic K-theory becomes a (lax) monoidal functor from this category to graded abelian groups. We show that if we restrict to Azumaya algebras, strong symmetry properties coming from the Goldman element allow to coherently lift certain Brauer subgroups to the the level of Morita equivalences, which gives rise to (graded-)commutative algebras of K-theory, graded over the corresponding Brauer subgroup. We also study analogue constructions for hermitian K-theory of Azumaya algebras with involution

KAH 17th February 2020
15:00 to 16:00
Veronika Ertl A rigid analytic approach to Hyodo-Kato theory
KAH 20th February 2020
11:15 to 12:15
Martin Gallauer Motivic tt-geometry
This talk shall be an introduction to the field of motivic
tensor-triangular geometry. We hope to convey some of its flavor by
explaining recent developments, and to discuss several possible
directions for future research.

KAH 24th February 2020
15:00 to 16:00
Mao Sheng Arithmetic version of Deligne’s semisimplicity theorem, and beyond.
A fundamental result in the theory of variation of Hodge structure is the Deligne’s semisimplicity theorem. In this talk, I am going to present an arithmetic version of this theorem. The novel thing is the introduction of the notion of periodic logarithmic de Rham/Higgs bundles. A basic result, which underlies the arithmetic semisimplicity theorem, is that a geometric logarithmic de Rham/Higgs bundle is periodic. We conjecture the converse, and in particular we shall propose the Semisimplicity conjecture: a periodic logarithmic de Rham/Higgs bundle is semisimple. I shall explain an unexpected relation between a very special case of the Semisimplicity conjecture with a basic result of N. Elkies: there exist infinitely many supersingular primes for any elliptic curve defined over $\mathbb Q$. This is a joint work with Raju Krishnamoorthy.

KAH 26th February 2020
11:15 to 12:15
Jose Burgos Gil Higher height paining and extensions of mixed Hodge structures.
The height pairing between algebraic cycles over global fields is an important arithmetic invariant. It can be written as  sum of  local contributions, one for each place of the ground field. Following Hain, the Archimedean components of the height pairing can be  interpreted in terms of biextensions of mixed Hodge structures. In this talk we will explore how to extend the Archimedean contribution of the height pairing to higher cycles in the Bloch complex and interpret it as an invariant associated to a mixed Hodge structure. This is joint work with S. Goswami and G. Pearlstein.

KAH 27th February 2020
11:15 to 12:15
Claudio Pedrini The transcendental motive of a a cubic fourfold
The transcendental part $t(X)$ of the motive of a cubic fourfold  $X$  is isomorphic to the (twisted) transcendental part $h^{tr}_2(F(X))$ in a suitable Chow-K\"unneth decomposition for the motive of the Fano variety of lines $F(X)$. Similarly to the case of a cubic 3-fold, the transcendental motive $t(X)$ is isomorphic to the {\it Prym motive} associated to the surface $S_l \subset F(X)$ of lines meeting a general line $l$. If $X$ is a special cubic fourfold in the sense of Hodge theory,  and $F(X) \simeq S^{[2]}$, with $S$ a K3 surface then     $t(X)\simeq t_2(S)(1)$, where $t_2(S)$ is the transcendental motive.  If $X$ is very general then $t(X)$ cannot be isomorphic to the (twisted) transcendental motive of a surface.  The existence  of an isomorphism $t(X) \simeq t_2(S)(1)$ is related to the  conjectures by Hassett and Kuznetsov on the rationality of a special cubic fourfold.  I will also consider the case of  other hyper-K\"alher varieties than $F(X)$ associated to a cubic fourfold $X$.

KAH 2nd March 2020
15:00 to 16:00
James Plowman A construction of Witt complexes via residual complexes.
The Witt complex of a scheme can be thought of as the negative degree part of Gersten complexes for Milnor-Witt K-theory. Depending on the data of a residual complex, we will describe generalisations of the classical second residue homormophism for Witt groups - which are the prototype for the boundary maps appearing in the Witt complex. We'll sketch why our residue homomorphisms assemble to form a Witt complex - even in characteristic 2 - with a focus on understanding the similarities between our construction and Balmer's

KAH 5th March 2020
11:15 to 12:15
Jens Hornbostel Chow-Witt groups and the real cycle class map.
We sketch and motivate the construction of Chow-Witt groups, also known as oriented Chow groups. Then we discuss some known computations. Finally, we study the real cycle class map to integral singular cohomology. This is joint work with M. Wendt, H. Xie and M. Zibrowius.
KAH 9th March 2020
15:00 to 16:00
Souvik Goswami Higher arithmetic Chow groups.
We give a new definition of higher arithmetic Chow groups for smooth projective varieties defined over a number field, which is similar to Gillet and Soulé's definition of arithmetic Chow groups. We also give a compact description of the intersection theory of such groups. A consequence of this theory is the definition of a height pairing between two higher algebraic cycles, of complementary dimensions, whose real regulator class is zero. This description agrees with Beilinson's height pairing for the classical arithmetic Chow groups. We also give examples of the higher arithmetic intersection pairing in dimension zero that is given by the Bloch-Wigner dilogarithm functions. This is based on the joint work with José Burgos Gil (https://doi.org/10.1016/j.aim.2019.02.003).

KAH 12th March 2020
11:15 to 12:15
Anthony Scholl Regulators and the plectic polylogarithm
I will discuss the construction of the "plectic plylogarithm" (a
refinement of the abelian polylogarithm of Wildeshaus) and potential
applications to higher regulators and special values of L-functions. This
is joint work with Jan Nekovář (Sorbonne, Paris).

KAH 12th March 2020
16:00 to 17:00
Pearl sttein
KAH 16th March 2020
15:00 to 16:00
David Loeffler Iwasawa theory, special values of L-functions, and regulators, I.
I will give a brief introduction to some of the conjectures relating special values of L-functions to regulators of motivic cohomology classes, such as Beilinson's conjecture and the Bloch-Kato conjecture. I will then describe the p-adic 'mirror image' of these conjectures proposed by Perrin-Riou, and how the methods of Iwasawa theory can be used to make substantial progress on these p-adic conjectures. I will illustrate this with the examples of the Riemann zeta function and the L-functions of elliptic curves, and some more
recent developments if time allows.

KAH 17th March 2020
15:00 to 16:00
Charles Weibel K-theory and motivic cohomology (including the Lichtenbaum conjecture for zetaF(1-2i)).
KAH 18th March 2020
15:00 to 16:00
Charles Weibel Motivic homotopy and motivic cohomology.
KAHW02 23rd March 2020
11:30 to 12:30
Federico Binda CANCELLED tba
KAHW02 23rd March 2020
14:30 to 15:30
Takeshi Saito CANCELLED Graded quotients of ramification groups of a local field with imperfect residue field
Filtration by ramification groups of the Galois group of an
extension of local fields with possibly imperfect residue fields is defined
by Abbes and the speaker. The graded quotients are abelian groups and
annihilated by the residue characteristic. We discuss the main ingredients of
the proof and the construction of injections of the character groups of the
graded quotients.
KAHW02 23rd March 2020
16:00 to 17:00
Gunnar Carlsson CANCELLED Representation theoretic models for the algebraic K-theory of fields
Motivic cohomology provides the E_2-term of a spectral sequence converging to the algebraic K-theory of a field F.  It does not directly take into account the absolute Galois group of F.  It turns out that there is a geometric model for the algebraic K-theory of F, build out of the higher dimensional representations of its absolute Galois group.  I will discuss results, conjectures, and approaches.  This is joint work with Roy Joshua.

KAHW02 24th March 2020
10:00 to 11:00
Marc Hoyois CANCELLED Milnor excision for motivic spectra
Let k be a field and E a motivic spectrum over k which is n-torsion for some n invertible in k. We show that the cohomology theory on k-schemes defined by E satisfies Milnor excision. More generally, we give necessary and sufficient conditions for a cdh sheaf to satisfy Milnor excision, following ideas of Bhatt and Mathew. Along the way, we show that the cdh ∞-topos of a quasi-compact quasi-separated scheme of finite valuative dimension is hypercomplete, extending a theorem of Voevodsky to nonnoetherian schemes.

KAHW02 24th March 2020
11:30 to 12:30
Christian Haesemeyer CANCELLED On K-theories of monoids
Sets with actions by a monoid A are a non-linear analogue of categories of modules, and can be used to define various flavours of K-theory of the monoid in question. K-theory (using projective A-sets) and G-theory (using finitely generated ones) have been previously studied, but do not relate in the expected way. I will discuss joint work with Weibel clarifying why this is the case, and introducing an intermediate category of A-sets whose K-theory exhibits the behaviour analogous to that of the K-theory of finitely generates modules in the linear context

KAHW02 24th March 2020
13:30 to 14:30
Free Time
KAHW02 24th March 2020
14:30 to 15:30
Kirsten Wickelgren CANCELLED A1-Euler classes: six functors formalisms, dualities, integrality and linear subspaces of complete intersections
We equate various Euler classes of algebraic vector bundles, including those of Barge--Morel, Kass--W., Déglise--Jin--Khan, and one suggested by M.J. Hopkins, A. Raksit, and J.-P. Serre. We establish integrality results for this Euler class, and give formulas for local indices at isolated zeros, both in terms of 6-functor formalism of coherent sheaves and as an explicit recipe in commutative algebra of Scheja and Storch. As an application, we compute the Euler classes associated to arithmetic counts of d-planes on complete intersections in P^n in terms of topological Euler numbers over R and C. This is joint work with Tom Bachmann

KAHW02 24th March 2020
16:00 to 17:00
Burt Totaro CANCELLED The integral Hodge conjecture for 3-folds of Kodaira dimension zero.
We prove the integral Hodge conjecture for all 3-folds X of > Kodaira dimension zero with H^0(X, K_X) not zero. > This generalizes earlier results of Voisin and Grabowski. > The assumption is sharp, in view of counterexamples by Benoist and > Ottem. We also prove similar results on the integral Tate conjecture. > For example, the integral Tate conjecture holds for abelian 3-folds in > any characteristic.

KAHW02 25th March 2020
10:00 to 11:00
Vasudevan Srinivas CANCELLED Algebraic versus topological entropy for varieties over finite fields
For an automorphism (or endomorphism) of an algebraic variety, we consider some properties of eigenvalues of the induced linear transformation on l-adic cohomology, motivated by some results from complex dynamics, related to the notion of entropy. This is a report on joint work with H'elene Esnault, and some subsequent work of K. Shuddhodan.

KAHW02 25th March 2020
11:30 to 12:30
Wiesława Nizioł CANCELLED p-adic comparison theorems for rigid analytic spaces
Classical p-adic comparison theorems link p-adic etale cohomology of schemes over local fields of mixed characteristic with their de Rham cohomology preserving all the underlying structures. I will survey the recent work on analogs of these theorems for rigid analytic varieties.
KAHW02 26th March 2020
09:00 to 10:00
Simon Pepin lehalleur CANCELLED Exponential motives and the Fourier transform
Varieties equipped with a regular function admit interesting "exponential" cohomology theories: rapid decay cohomology, twisted de Rham cohomology in characteristic 0, twisted l-adic cohomology in positive characteristic. They exhibit motivic-like properties - weights, a kind of Hodge filtration, a period isomorphism - but do not fit into the classical theory of motives. Building on ideas of Kontsevich-Soibelman and Fresán-Jossen, we construct triangulated categories of exponential Voevodsky motives equipped with functors realising exponential cohomology theories. More generally, we associate to any "six operation formalism" an exponential version. Unlike classical motivic sheaf theories, these exponential sheaf theories come with a built-in Fourier-Deligne transform, which plays a key role in the construction of exponential realisations. This is joint work in progress with Javier Fresán and Martin Gallauer.

KAHW02 26th March 2020
10:10 to 11:10
Anand Sawant CANCELLED $\mathbb A^1$-connected components of ruled surfaces
A conjecture of Morel asserts that the sheaf of $\mathbb A^1$-connected components of a space is $\mathbb A^1$-invariant.  We will discuss how the sheaves of naive" as well as `genuine" $\mathbb A^1$-connected components of a smooth projective birationally ruled surface can be determined using purely algebro-geometric methods.  We will discuss a proof of Morel's conjecture for a smooth projective surface birationally ruled over a curve of genus > 0 over an algebraically closed field of characteristic 0.  If time permits, we will indicate why the naive and genuine $\mathbb A^1$-connected components of such a birationally ruled surface do not coincide if the surface is not a minimal model and discuss some open questions and specultions regarding the situation in higher dimensions.  The talk is based on joint work with Chetan Balwe.
KAHW02 26th March 2020
11:30 to 12:30
Toni Annala CANCELLED Derived Algebraic Cobordism
The purpose of this talk is to outline how to use derived
algebraic geometry in order to give a very general geometric construction of
algebraic cobordism in the spirit of Levine and Morel. The new construction
requires no smoothness hypotheses on the variety, and works over a Noetherian
ground ring of finite Krull dimension (as opposed over a field of
characteristic 0). Moreover, the construction is naturally part of a larger
bivariant theory in the sense of Fulton and MacPherson. We will outline what
is known about derived cobordism theory. Most importantly: it has the
expected relationship with the Grothendieck ring of vector bundles and
satisfies projective bundle formula.
KAHW02 26th March 2020
14:30 to 15:30
Nikita Semenov CANCELLED Hopf-theoretic approach to motives of twisted flag varieties
Let G be a split semisimple algebraic group over a field and let A be an oriented cohomology theory in the sense of Levine-Morel. We provide a uniform approach to the A-motives of geometrically cellular smooth projective G-varieties based on the Hopf algebra structure of A(G). Using this approach we provide various applications to the structure of motives of twisted flag varieties. The talk is based on a joint work with Victor Petrov.
KAHW02 26th March 2020
16:00 to 17:00
Adeel Khan CANCELLED Chow-theoretic vs. K-theoretic Gromov-Witten invariants
Let X be a smooth projective complex variety.  We prove the comparison between the Gromov-Witten invariants of X with their K-theoretic variants defined by Givental and Lee.  The key ingredient is a virtual Grothendieck-Riemann-Roch formula on the moduli stack of stable maps, which is used to compare Kontsevich’s virtual fundamental class with the one constructed by Behrend-Fantechi.

KAHW02 27th March 2020
10:00 to 11:00
Georg Tamme CANCELLED On a conjecture of Vorst
Quillen proved that algebraic K-theory is A^1-invariant on regular noetherian schemes. Vorst’s conjecture is a partial converse. Let k be a field, and let A be a k-algebra essentially of finite type and of dimension d. Vorst’s conjecture predicts that if K_{d+1}(A) = K_{d+1}(A[t_1, \dots, t_m]) for all positive integers m, then A is regular. This conjecture was proven by Cortinas, Haesemeyer, and Weibel in case k has characteristic 0. In the talk, I will explain the proof of a slightly weaker version of the conjecture if k has positive characteristic. Joint work with Moritz Kerz and Florian Strunk.

KAHW02 27th March 2020
11:30 to 12:30
Maria Yakerson CANCELLED Motivic generalized cohomology theories from framed perspective
All motivic generalized cohomology theories acquire unique structure of so called framed transfers. If one takes framed transfers into account, it turns out that many interesting cohomology theories can be constructed simply as suspension spectra on certain moduli stacks (and their variations). This way important cohomology theories on schemes get new geometric interpretations, and so do canonical maps between different cohomology theories. In the talk we will explain the general formalism of framed transfers and show how it works for various cohomology theories. This is a summary of joint projects with Tom Bachmann, Elden Elmanto, Marc Hoyois, Joachim Jelisiejew, Adeel Khan, Denis Nardin and Vladimir Sosnilo.

KAHW02 27th March 2020
13:30 to 14:00
Free Time
KAHW03 30th March 2020
10:00 to 11:00
Christopher Deninger CANCELLED tba
KAHW03 30th March 2020
11:30 to 12:30
Minhyong Kim CANCELLED Principal Bundle in Diophantine Geometry
This talk will give an update on the use of non-abelian cohomology varieties in the theory of Diophantine equations

KAHW03 30th March 2020
15:00 to 16:00
Matilde Lalín CANCELLED The Mahler measure of a genus 3 family
The Mahler measure of a polynomial P is defined as certain integral of log|P| over the unit torus. For multivariate polynomials, it often yields special values of L-functions. In this talk I will discuss some of these relationships and prove  an identity between the Mahler measures of a genus 3 polynomial family and of a genus 1 polynomial family that was initially conjectured by Liu and Qin. This is joint work with Gang Wu.