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

p-adic limits of renormalized logarithmic Euler characteristics

Posted in
Speaker: 
Christopher Deninger
Affiliation: 
Universität Münster
Date: 
Tue, 2018-01-30 14:00 - 15:00
Location: 
MPIM Lecture Hall

Given a countable residually finite group $\Gamma$, we write $\Gamma_n \to e$ if $(\Gamma_n)$ is a sequence of normal subgroups of finite index such that any infinite intersection of $\Gamma_n$'s contains only the unit element $e$ of $\Gamma$. Given a $\Gamma$-module $M$ we are interested in the multiplicative Euler characteristics \begin{equation} \chi (\Gamma_n , M) = \prod_i |H_i(\Gamma_n , M)|^{(-1)^i} \end{equation} and the limit in the field $\mathbb{Q}_p$ of $p$-adic numbers \begin{equation} h_p := \lim_{n\to\infty} (\Gamma : \Gamma_n)^{-1} \log_p \chi (\Gamma_n , M) \; .

Rational points on Picard modular surfaces

Posted in
Speaker: 
Dinakar Ramakrishnan
Affiliation: 
Caltech
Date: 
Wed, 2018-01-24 14:30 - 15:30
Location: 
MPIM Lecture Hall

Picard modular surfaces X, which are smooth compactifications of the quotients Y of the complex ball by a discrete subgroups \Gamma of SU(2,1), have been studied from various points of view. They are often defined over an imaginary quadratic field M, and we are interested in the rational points of X over finite extensions k of M. In a joint work with M.

Tilting modules for reductive groups and the Hecke category, III

Posted in
Speaker: 
Geordie Williamson
Organiser(s): 
C. Stroppel
Affiliation: 
University of Sydney
Date: 
Tue, 2018-02-06 16:15 - 18:15
Location: 
MPIM Lecture Hall

Determining the characters of indecomposable tilting modules for reductive groups is one of the most fundamental
open problems in modular representation theory. A solution for GL_n would answer the question of the dimensions
of the simple modules for the symmetric group in characteristic p.
It is related to (but almost certainly harder than) the determination of the simple characters. I will  describe a new
algorithm (based on a long and ongoing series of work with Elias, Riche, Libedinsky, Achar-Makisumi-Riche)

Tilting modules for reductive groups and the Hecke category, II

Posted in
Speaker: 
Geordie Williamson
Organiser(s): 
C. Stroppel
Affiliation: 
University of Sydney
Date: 
Tue, 2018-01-30 16:15 - 18:15
Location: 
MPIM Lecture Hall

Determining the characters of indecomposable tilting modules for reductive groups is one of the most fundamental
open problems in modular representation theory. A solution for GL_n would answer the question of the dimensions
of the simple modules for the symmetric group in characteristic p.
It is related to (but almost certainly harder than) the determination of the simple characters. I will  describe a new
algorithm (based on a long and ongoing series of work with Elias, Riche, Libedinsky, Achar-Makisumi-Riche)

Cabling and the solvable filtration on knot concordance

Posted in
Speaker: 
Arunima Ray
Affiliation: 
MPIM
Date: 
Mon, 2018-01-22 16:30 - 18:00
Location: 
MPIM Lecture Hall
Parent event: 
MPIM Topology Seminar

New guests at the MPIM

Posted in
Speaker: 
Tatsushi Tanaka, Efthymios Sofos, Alexandra-Iulia Otiman
Date: 
Thu, 2018-01-25 15:00 - 16:00
Location: 
MPIM Lecture Hall
Parent event: 
MPI-Oberseminar

Introduction to the Thurston norm

Posted in
Speaker: 
Gabrielle Viaggi
Affiliation: 
MPIM
Date: 
Wed, 2018-01-24 16:30 - 18:00
Location: 
MPIM Seminar Room
Parent event: 
IMPRS seminar

Topological field theory on r-spin surfaces and the Arf invariant

Posted in
Speaker: 
Lorant Szegedy
Affiliation: 
Universität Hamburg
Date: 
Mon, 2018-01-29 16:30 - 18:00
Location: 
MPIM Lecture Hall
Parent event: 
MPIM Topology Seminar

We present a state-sum construction of topological field theories (TFT)
on r-spin surfaces which uses a combinatorial model of r-spin structures
based on the work of Novak. We give an example of such a TFT which
computes the Arf invariant for r even. We use the combinatorial model
and this TFT to calculate diffeomorphism classes of r-spin surfaces with
parametrized boundary, extending results of Geiges and Gonzalo and of
Randal-Williams.

Prime and squarefree values of polynomials in moderately many variables

Posted in
Speaker: 
Kevin Destagnol
Affiliation: 
MPIM
Date: 
Wed, 2018-01-17 16:30 - 17:30
Location: 
MPIM Lecture Hall

We will present a generalisation of Schinzel's hypothesis and of the Bateman-Horn's conjecture concerning
prime values of a system of polynomials in one variable to the case of a integer form in many variables.
In particular, we will establish in this talk that a polynomial in moderately many variables takes infinitely
many prime (but also squarefree) values under some necessary assumptions. The proof will rely on Birch's
circle method and will be achieved in 50% fewer variables than in the classical Birch setting. Moreover it

tba

Posted in
Speaker: 
Alexandra Otiman
Affiliation: 
University of Bucharest/MPIM
Date: 
Thu, 2018-02-01 16:30 - 17:30
Location: 
MPIM Lecture Hall

Dwork crystals and related congruences

Posted in
Speaker: 
Masha Vlasenko
Affiliation: 
The Polish Academy of Sciences, Warsaw/MPIM
Date: 
Tue, 2018-01-23 14:00 - 15:00
Location: 
MPIM Lecture Hall

In the talk I will describe a realization of the p-adic cohomology of an affine toric hypersurface which originates in
Dwork's work and give an explicit description of the unit-root subcrystal based on certain congruences for the coeficient
of powers of a Laurent polynomial. This is joint work with Frits Beukers. The formulas for the Frobenius and connection
on the unit-root subcrystal that we give were conjectured in my preprint ``Higher Hasse--Witt matrices'' (arXiv:1605.06440).

Backström algebras, Backström curves and their Auslander envelopes

Posted in
Speaker: 
Yuriy Drozd
Affiliation: 
National Academy of Sciences of Ukraine, Kiev/MPIM
Date: 
Thu, 2018-01-18 15:00 - 16:00
Location: 
MPIM Lecture Hall
Parent event: 
MPI-Oberseminar

From Projective Resolutions to Stable Derivators

Posted in
Speaker: 
Tobias Lenz
Affiliation: 
MPIM
Date: 
Wed, 2018-01-17 16:30 - 18:00
Location: 
MPIM Seminar Room
Parent event: 
IMPRS seminar

Exotic smooth structures on R^4, II

Posted in
Speaker: 
Arunima Ray
Affiliation: 
MPIM
Date: 
Mon, 2018-01-15 14:15 - 15:45
Location: 
MPIM Lecture Hall
Parent event: 
IMPRS Minicourse

Bridging the algebraic and analytic theory of the representation problem for quadratic polynomials

Posted in
Speaker: 
Anna Haensch
Affiliation: 
Duquesne University/MPIM
Date: 
Wed, 2018-01-17 14:30 - 15:30
Location: 
MPIM Lecture Hall
Parent event: 
Number theory lunch seminar

Given a polynomial f(x) of several variables with rational coefficients and an integer n, we say that f represents n if the equation f(x)=n is solvable in the integers.  One might ask, is it possible to effectively determine the set of integers represented by f? This so-called representation problem for quadratic polynomials is one of the classical problems in number theory.  The negative answer to Hilbert's 10th problem tells us that in general, there is no finite algorithm to decide whether a solution exists.

Tilting modules for reductive groups and the Hecke category, I

Posted in
Speaker: 
Geordie Williamson
Organiser(s): 
C. Stroppel
Affiliation: 
University of Sydney
Date: 
Tue, 2018-01-23 16:15 - 18:15
Location: 
MPIM Lecture Hall

Determining the characters of indecomposable tilting modules for reductive groups is one of the most fundamental
open problems in modular representation theory. A solution for GL_n would answer the question of the dimensions
of the simple modules for the symmetric group in characteristic p.
It is related to (but almost certainly harder than) the determination of the simple characters. I will  describe a new
algorithm (based on a long and ongoing series of work with Elias, Riche, Libedinsky, Achar-Makisumi-Riche)

Integral points on generalised affine Châtelet surfaces

Posted in
Speaker: 
Vladimir Mitankin
Affiliation: 
Universidade Federal do Rio de Janeiro
Date: 
Wed, 2018-01-10 14:30 - 15:30
Location: 
MPIM Lecture Hall
Parent event: 
Number theory lunch seminar

Building up on the work of Colliot-Thélène and Sansuc which
suggests the use of Schinzel's hypothesis we show that the integral
Brauer-Manin obstruction is the only obstruction to the integral Hasse
principle for an infinite family of generalised affine Châtelet surfaces.
Moreover, we show that the set of integral points on any surface in this
family for which there is no integral Brauer-Manin obstruction satisfies a
strong approximation property away from infinity. We do so by exploiting
the conic bundle structure of such surfaces over the affine line. A

New guests at the MPIM

Posted in
Speaker: 
Rosie Laking, Katie Gittins, Eva Hoening
Date: 
Thu, 2018-01-11 15:00 - 16:00
Location: 
MPIM Lecture Hall
Parent event: 
MPI-Oberseminar

Loop groups, Fusion product and the Freed-Hopkins-Teleman Theorem

Posted in
Speaker: 
Bertram Arnold
Affiliation: 
MPIM
Date: 
Wed, 2018-01-10 16:30 - 18:00
Location: 
MPIM Seminar Room
Parent event: 
IMPRS seminar

Exotic smooth structures on R^4

Posted in
Speaker: 
Arunima Ray
Affiliation: 
MPIM
Date: 
Mon, 2018-01-08 14:15 - 15:45
Location: 
MPIM Lecture Hall
Parent event: 
IMPRS Minicourse
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