Upcoming Talks

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Abstracts of upcoming talks at the MPIM. For an overview see also the calendar.

Recent developments in Quantum Topology -- Cancelled --

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We will review the basics of quantum topology such as the colored Jones polynomial of a knot, its standard conjectures relating to asymptotics, arithmeticity and modularity, as well as the recent quantum hyperbolic invariants of Kashaev et al, their state-integrals and their structural properties. The course is aimed to be accessible by graduate students and young researchers.

Some adjoint L-values and Hilbert modular Eisenstein congruences

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Speaker:
Neil P. Dummigan
Affiliation:
University of Sheffield
Date:
Tue, 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.

The m-step solvable anabelian geometry of finitely generated fields

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Speaker:
Mohamed Saidi
Affiliation:
University of Exeter/MPIM
Date:
Tue, 2020-01-21 14:00 - 15:00
Location:
MPIM Lecture Hall

A celebrated theorem of Neukirch and Uchida states that two number fields are isomorphic if their absolute Galois groups are isomorphic. The Grothendieck birational conjecture predicts a similar result for all finitely generated fields. This has been proved by Pop, using in an essential way the Neukirch-Uchida theorem for global fields.

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

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Speaker:
Bernhard Heim
Affiliation:
GUtech, Oman
Date:
Tue, 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.

IMPRS seminar on various topics: Period domains

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Organiser(s):
C. Kaiser
Date:
Wed, 2019-12-11 13:30 - 15:00
Date:
Wed, 2019-12-18 13:30 - 15:00
Date:
Wed, 2019-12-25 13:30 - 15:00
Date:
Wed, 2020-01-01 13:30 - 15:00
Date:
Wed, 2020-01-08 13:30 - 15:00
Date:
Wed, 2020-01-15 13:30 - 15:00
Date:
Wed, 2020-01-22 13:30 - 15:00
Date:
Wed, 2020-01-29 13:30 - 15:00
Location:
MPIM Seminar Room

Local behaviour of the set of the values of Euler's totient function

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Speaker:
Jean-Marc Deshouillers
Affiliation:
Université Bordeaux 1
Date:
Wed, 2020-01-22 14:30 - 15:30
Location:
MPIM Lecture Hall
Parent event:
Number theory lunch seminar

Let $V$ be the set of the values of the Euler's $\varphi$ function. It is known that the natural density of $V$, namely the limit of $V(x)/x$, as $x$ tends to infinity, is $0$.

In a paper to appear, M. K. Das, P. Eyyunni and B. R. Patil claim that this also applies to a local density of $V$, known as the uniform upper density, or the Banach density, defined by
$$\delta^{*(}V) = \lim_{H \rightarrow \infty} \limsup_{x \rightarrow \infty} \frac{1}{H}\left(V(x+H) -V(x)\right).$$

Higgs bundles on Riemann surfaces, II

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Speaker:
Johannes Schaefer
Affiliation:
MPIM
Date:
Wed, 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.

Lower Bounds for Discrete Negative Moments of the Riemann zeta Function

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Speaker:
Jing Zhao
Date:
Wed, 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.

Coxeter Groups

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Speaker:
Renee Hoekzema
Affiliation:
MPIM
Date:
Thu, 2020-01-23 10:15 - 11:45
Location:
MPIM Seminar Room

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

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Speaker:
Jacob Matherne
Affiliation:
University of Oregon/MPIM
Date:
Thu, 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.

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