# Talk

Talks and seminars, possibly part of a conference or series.

## Talk coaching for Postdocs

Posted in
Speaker:
Matthias Kreck
Zugehörigkeit:
Universität Bonn
Datum:
Don, 2020-01-30 14:00 - 15:00
Location:
MPIM Seminar Room

## 1. Singular Hodge theory of matroids; 2. Logarithmic concavity of weight multiplicities for irreducible sln(C)-representations

Posted in
Speaker:
Jacob Matherne
Zugehörigkeit:
University of Oregon/MPIM
Datum:
Don, 2020-01-23 15:00 - 16:00
Location:
MPIM Lecture Hall
Parent event:
MPI-Oberseminar

Talk 1: Title: Singular Hodge theory of matroids

If you take a collection of planes in R^3, then the number of lines you get by intersecting the planes is at least the number of planes. This is an example of a more general statement, called the “Top-Heavy Conjecture”, that Dowling and Wilson conjectured in 1974.

On the other hand, given a hyperplane arrangement, I will explain how to uniquely associate a certain polynomial (called its Kazhdan–Lusztig polynomial) to it.

## Higgs bundles on Riemann surfaces, II

Posted in
Speaker:
Johannes Schaefer
Zugehörigkeit:
MPIM
Datum:
Mit, 2020-01-22 16:15 - 17:45
Location:
MPIM Seminar Room

On a Riemann Surface $\Sigma$, the moduli space of polystable $\mathrm{SL}_n(\mathbb{C}$)-Higgs bundles can be identified with the space of reductive representations $\pi _1 (\Sigma) \to \mathrm{SL}_n(\mathbb{C})$. In this talk, we discuss a proof of this so called non-abelian Hodge correspondence. Our goal is to understand how
to construct a Higgs bundle from a given representation and how this construction relates to the theory of harmonic maps.

## -- Cancelled -- Powers of the Dedekind eta function and the Bessenrodt-Ono inequality

Posted in
Speaker:
Bernhard Heim
Zugehörigkeit:
GUtech, Oman
Datum:
Die, 2020-01-21 16:30 - 17:30
Location:
MPIM Lecture Hall
Parent event:
Number theory lunch seminar

In this talk I present recent results obtained with Markus Neuhauser towards the non-vanishing of the coefficients of the Dedekind eta function in the spirit of G.-C. Rota. This includes Serre’s table, pentagonal numbers, results of Kostant in the context of simple affine Lie algebras and the Lehmer conjecture. In the second part I will talk about partition numbers and the Bessenrodt-Ono inequality.

## Lower Bounds for Discrete Negative Moments of the Riemann zeta Function

Posted in
Speaker:
Jing Zhao
Datum:
Mit, 2020-01-22 16:30 - 17:30
Location:
MPIM Lecture Hall
Parent event:
Number theory lunch seminar

I will talk about lower bounds for the discrete negative 2k-th moment of the derivative of the Riemann zeta function for all
fractional
k > 0. The bounds are in line with a conjecture of Gonek and Hejhal. This is a joint work with Winston Heap and
Junxian Li.

## Estimates for binary quadratic forms and Apollonian circle packings

Posted in
Speaker:
Zugehörigkeit:
Universität Bonn
Datum:
Mit, 2020-02-05 16:30 - 17:30
Location:
MPIM Lecture Hall
Parent event:
Number theory lunch seminar

Given a positive definite integral binary quadratic form, it is a classical problem in number theory to count the integers that are represented by this form. A modern treatment was given in 2006 by Valentin Blomer and Andrew Granville.

## Some Feynman diagrams in pure algebra

Posted in
Speaker:
Dror Bar-Natan
Zugehörigkeit:
University of Toronto
Datum:
Mon, 2020-01-20 16:30 - 17:30
Location:
MPIM Lecture Hall
Parent event:
MPIM Topology Seminar

I will explain how the computation of compositions of maps of a certain natural class, from one polynomial ring into another, naturally leads to a certain composition operation of quadratics and to Feynman diagrams. I will also explain, with very little detail, how this is used in the construction of some very well-behaved poly-time computable knot polynomials.

## Algebraic knot theory

Posted in
Speaker:
Dror Bar-Natan
Zugehörigkeit:
University of Toronto
Datum:
Mon, 2020-01-20 15:00 - 16:00
Location:
MPIM Lecture Hall
Parent event:
MPIM Topology Seminar

This will be a very "light" talk: I will explain why about 13 years ago, in order to have a say on some problems in knot theory, I've set out to find tangle invariants with some nice compositional properties. In my second talk in Bonn I will explain how such invariants were found - though they are yet to be explored and utilized.

## Some adjoint L-values and Hilbert modular Eisenstein congruences

Posted in
Speaker:
Neil P. Dummigan
Zugehörigkeit:
University of Sheffield
Datum:
Die, 2020-01-21 10:15 - 12:00
Location:
MPIM Lecture Hall

I will start from the situation of a cuspidal Hecke eigenform f of real quadratic character, congruent to its complex conjugate modulo a prime P ramified in the coefficient field.

## tba

Posted in
Speaker:
Sigmundur Gudmundsson
Zugehörigkeit:
Lund University
Datum:
Don, 2020-02-27 13:00 - 14:00
Location:
MPIM Lecture Hall
Parent event:
Number theory lunch seminar

## Regulators of number fields and abelian varieties

Posted in
Speaker:
Fabien Pazuki
Zugehörigkeit:
University of Copenhagen
Datum:
Mit, 2020-02-05 14:30 - 15:30
Location:
MPIM Lecture Hall
Parent event:
Number theory lunch seminar

In the general study of regulators, we present three inequalities. We first bound from below the regulators of number fields, following previous works of Silverman and Friedman. We then bound from below the regulators of Mordell-Weil groups of abelian varieties defined over a number field, assuming a conjecture of Lang and Silverman. Finally we explain how to prove an unconditional statement for elliptic curves of rank at least 4. This third inequality is joint work with Pascal Autissier and Marc Hindry.

## tba

Posted in
Speaker:
Fabian Waibel
Zugehörigkeit:
Universität Bonn
Datum:
Mit, 2020-02-26 14:30 - 15:30
Location:
MPIM Lecture Hall
Parent event:
Number theory lunch seminar

## tba

Posted in
Speaker:
Wouter Van Limbeek
Zugehörigkeit:
University of Michigan/MPIM
Datum:
Don, 2020-04-16 13:00 - 14:00
Location:
MPIM Lecture Hall

## Localization techniques for singular algebraic varietieties

Posted in
Speaker:
Magdalena Zielienkiewicz
Zugehörigkeit:
University of Warsaw/MPIM
Datum:
Die, 2020-02-04 14:00 - 15:00
Location:
MPIM Lecture Hall

The standard ways of computing, or indeed defining, invariants of singular varietis use the procedure of resolution of singularities. To explicitly know a resolution, however, requires a good understanding of the singularities of the variety in question.

I will talk about methods that can be applied to the study of singular varieties without resolution of singularities, which originate from localization theorems in topology. As an example, I will present some computations involving the torus-equivariant cohomology of the (refined) Hilbert scheme of points on the plane.

## Global Koszul duality

Posted in
Speaker:
Andrey Lazarev
Zugehörigkeit:
University of Lancaster/MPIM, Bonn
Datum:
Die, 2020-01-28 14:00 - 15:00
Location:
MPIM Lecture Hall

Koszul duality is a phenomenon that shows up in rational homotopy theory, deformation theory and other subfields of algebra and topology. Its modern formulation is due to the works of Hinich, Keller-Lefevre and Positselski. It is a certain correspondence between categories of differential graded (dg) algebras and conilpotent dg coalgebras; there is also a module-comodule level version of it. In this talk I explain what happens if one drops the condition of conilpotency on the coalgebra side; the consequences turn out to be quite dramatic.

## Construction of stable rank 2 sheaves on projective space

Posted in
Speaker:
Alexander Tikhomirov
Zugehörigkeit:
HSE, Moscow/MPIM, Bonn
Datum:
Die, 2020-02-18 14:00 - 15:00
Location:
MPIM Lecture Hall

## New guests at the MPIM

Posted in
Speaker:
Sarah Blackwell, Enrica Mazzon
Datum:
Don, 2020-01-16 15:00 - 16:00
Location:
MPIM Lecture Hall
Parent event:
MPI-Oberseminar

## Coxeter Groups

Posted in
Speaker:
Renee Hoekzema
Zugehörigkeit:
MPIM
Datum:
Don, 2020-01-23 10:15 - 11:45
Location:
MPIM Seminar Room

## Higgs bundles on Riemann surfaces, I

Posted in
Speaker:
Alessandro Giacchetto
Zugehörigkeit:
MPIM
Datum:
Mit, 2020-01-15 16:15 - 17:45
Location:
MPIM Seminar Room

The relation between representations of the fundamental group of a Riemann surface into the unitary group, flat connections on Hermitian vector bundles, and stable holomorphic bundles on the surface, goes back to the celebrated theorem of Narasimhan and Seshadri. The case of representations into a non-compact reductive Lie group required the introduction of new holomorphic objects on the Riemann surface, called Higgs bundles.

## L-functions and isogenies of abelian varieties

Posted in
Speaker:
Harry Justus Smit
Zugehörigkeit:
Universiteit Utrecht
Datum:
Mit, 2020-01-15 14:30 - 15:30
Location:
MPIM Lecture Hall
Parent event:
Number theory lunch seminar

Faltings's isogeny theorem states that two abelian varieties
over a number field are isogenous precisely when the characteristic
polynomials associated to the reductions of the abelian varieties at all
prime ideals are equal. This implies that two abelian varieties defined
over the rational numbers with the same L-function are necessarily
isogenous, but this is false over a general number field.

In order to still use the L-function to determine the underlying field