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Talk

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

Abstract motivic homotopy theory

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Speaker: 
Peter Arndt
Affiliation: 
Universität Düsseldorf
Date: 
Wed, 2019-02-20 16:30 - 18:00
Location: 
MPIM Lecture Hall
Parent event: 
Extra talk
Parent event: 
MPIM Topology Seminar

Motivic homotopy theory is a fusion of homotopy theory and algebraic 

Grothendieck ring of varieties and motivic measures

Posted in
Speaker: 
Valery Lunts
Affiliation: 
Indiana University, Bloomington/MPIM
Date: 
Tue, 2019-02-26 14:00 - 15:00
Location: 
MPIM Lecture Hall

This will be mostly a survey talk of the subject. I will discuss some interesting measures that can be used to study the Grothendieck ring of varieties. Applications to rationality of the motivic zeta function will be explained.

Isocrystals associated to Arithmetic Jet Spaces

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Speaker: 
Arbab Saha
Affiliation: 
ANU, Canberra/MPIM
Date: 
Wed, 2019-02-20 14:30 - 15:30
Location: 
MPIM Lecture Hall
Parent event: 
Number theory lunch seminar

The aim of the talk is to discuss the construction of an isocrystal associated to abelian schemes over p-adic fields using the arithmetic jet space theory. Isocrystals are objects in p-adic Hodge theory that lead to Galois representations. A well-known example of isocrystals coming from geometry are the ones obtained from the de Rham cohomology of the scheme. We will also talk about the interaction of our object with the first deRham cohomology of the abelian scheme. This is a joint work with Jim Borger.

 

tba

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Speaker: 
Leonid Potyagailo
Affiliation: 
Université de Lille 1/MPIM
Date: 
Thu, 2019-03-14 16:30 - 17:30
Location: 
MPIM Lecture Hall

Twisted Blanchfield pairings and Casson-Gordon invariants

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Speaker: 
Anthony Conway
Affiliation: 
Durham University
Date: 
Mon, 2019-02-18 16:30 - 18:00
Location: 
MPIM Lecture Hall
Parent event: 
MPIM Topology Seminar

In the late seventies, Casson and Gordon developed several knot invariants that obstruct a knot from being slice, i.e. from bounding a disc in the 4-ball. In this talk, we use twisted Blanchfield pairings to define twisted signature functions for knots, and describe their relation to the Casson-Gordon invariants. If time permits, we will describe how this can be used to obstruct the sliceness of some algebraic knots. This is joint work with Maciej Borodzik and Wojciech Politarczyk.

 

What is 3-dimensional hyperbolic geometry?

Posted in
Speaker: 
Stavros Garoufalidis
Affiliation: 
Georgia Institute of Technology/MPIM
Date: 
Thu, 2019-02-21 15:00 - 16:00
Location: 
MPIM Lecture Hall
Parent event: 
Colloquium
Parent event: 
MPI-Oberseminar

3-dimensional hyperbolic geometry is a classical subject.
We will give an introduction emphasizing concrete questions,
computations and answers, as well as hints to quantum aspects
of this beautiful theory. Please bring concrete questions and you may be
lucky and get some answers.

Demazure flags: A combinatorial journey

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Speaker: 
Rekha Biswal
Affiliation: 
U. du Quebec à Montréal/MPIM
Date: 
Thu, 2019-02-14 15:00 - 16:00
Location: 
MPIM Lecture Hall
Parent event: 
MPI-Oberseminar

In this talk, we will briefly review the theory of characters of Demazure modules which are modules for the standard maximal parabolic subalgebra of an affine Lie algebra. The discussion will be followed by some connections that I have discovered(with collaborators) in my own research between algebraic combinatorics and other areas of mathematics such as representation theory and number theory. For instance, we show that the graded multiplicities of higher level Demazure modules in Demazure flags can be expressed in terms Dyck paths.

Descartes, Newton and hyperfields

Posted in
Speaker: 
Oliver Lorscheid
Affiliation: 
IMPA, Rio de Janeiro/MPIM
Date: 
Wed, 2019-02-13 11:15 - 12:15
Location: 
MPIM Lecture Hall
Parent event: 
Number theory lunch seminar

Descartes bounds the number of positive roots of a polynomial with real coefficients by the number of sign changes in the coefficients, Newton bounds the number of roots of a polynomial over a nonarchimedean field in terms of its Newton polygon.

In this talk, we review these two clasical theorems and explain how they follow by the same principle from assertions about roots of polynomials over the hyperfield of signs and the tropical hyperfield, respectively. This is joint work with Matthew Baker.

Talks in the Seminar on Topological insulators

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Date: 
Wed, 2019-02-13 14:00 - 18:00
Location: 
MPIM Lecture Hall

Additive combinatorial problems of Number Theory

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Speaker: 
Ilya D. Shkredov
Affiliation: 
Steklov Mathematical Institute, Moscow
Date: 
Tue, 2019-02-12 16:30 - 17:30
Location: 
MPIM Lecture Hall

We give a survey on problems from Number Theory that can be solved or were solved by the methods of Additive
Combinatorics such as Green--Tao theorem, Ostmann conjecture, the distribution of Fermat quotients, exponential sums over multiplicative subgroups, combinatorial problems with continued fractions and so on.

Mixed derived category on affine Grassmannians and coherent sheaves on Springer resolution

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Speaker: 
Nicholas Cooney
Affiliation: 
MPIM
Date: 
Mon, 2019-02-11 15:00 - 17:00
Location: 
MPIM Seminar Room

Computing p-canonical bases

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Speaker: 
Hankyung Ko
Affiliation: 
MPIM
Date: 
Fri, 2019-02-08 15:15 - 17:00
Location: 
MPIM Seminar Room

We discuss a diagrammatic presentation of the Hecke category and its cellular structure. Using this, we will compute decomposition numbers in Hecke categories and hence determine some tilting characters.

Topological Hopf algebra of Feynman graphons and its application to Quantum Field Theory, III

Posted in
Speaker: 
Ali Shojaei-Fard
Affiliation: 
MPIM
Date: 
Mon, 2019-02-25 14:15 - 15:45
Location: 
MPIM Lecture Hall
Parent event: 
IMPRS Minicourse

This mini-course is on the basis of the speaker's monograph "a mathematical perspective on the phenomenology of non-perturbative Quantum Field Theory" (The MPIM-preprint series 2018-65). I plan to explain the construction of a new Hopf algebraic formalism on graphons derived from the Kreimer's renormalization coproduct. Then I will show the application of this new mathematical object in dealing with non-perturbative parameters.
 

Topological Hopf algebra of Feynman graphons and its application to Quantum Field Theory, II

Posted in
Speaker: 
Ali Shojaei-Fard
Affiliation: 
MPIM
Date: 
Mon, 2019-02-18 14:15 - 15:45
Location: 
MPIM Lecture Hall
Parent event: 
IMPRS Minicourse

This mini-course is on the basis of the speaker's monograph "a mathematical perspective on the phenomenology of non-perturbative Quantum Field Theory" (The MPIM-preprint series 2018-65). I plan to explain the construction of a new Hopf algebraic formalism on graphons derived from the Kreimer's renormalization coproduct. Then I will show the application of this new mathematical object in dealing with non-perturbative parameters.
 

Topological Hopf algebra of Feynman graphons and its application to Quantum Field Theory, I

Posted in
Speaker: 
Ali Shojaei-Fard
Affiliation: 
MPIM
Date: 
Mon, 2019-02-11 14:15 - 15:45
Location: 
MPIM Lecture Hall
Parent event: 
IMPRS Minicourse

This mini-course is on the basis of the speaker's monograph "a mathematical perspective on the phenomenology of non-perturbative Quantum Field Theory" (The MPIM-preprint series 2018-65). I plan to explain the construction of a new Hopf algebraic formalism on graphons derived from the Kreimer's renormalization coproduct. Then I will show the application of this new mathematical object in dealing with non-perturbative parameters.
 

New guests at the MPIM

Posted in
Speaker: 
Pablo Mauricio Zadunaisky, Rouven Frassek, Felix Wierstra
Date: 
Thu, 2019-02-07 15:00 - 16:00
Location: 
MPIM Lecture Hall
Parent event: 
MPI-Oberseminar

Preprojective cohomological Hall algebras and Yangians

Posted in
Speaker: 
Tomasz Przezdziecki
Affiliation: 
MPIM
Date: 
Wed, 2019-02-06 16:30 - 18:00
Location: 
MPIM Seminar Room
Parent event: 
IMPRS seminar

Khovanov homotopy types

Posted in
Speaker: 
Tyler Lawson
Affiliation: 
University of Minnesota/MPIM
Date: 
Mon, 2019-02-11 16:30 - 18:00
Location: 
MPIM Lecture Hall
Parent event: 
MPIM Topology Seminar

I'll begin by discussing the construction of the Khovanov
homology groups from a link. I'll then discuss a framework that allows
the construction of similar objects in many contexts, in particular
recovering Lipshitz and Sarkar's refinement to an object in stable
homotopy whose homology groups recover Khovanov homology.

Elliptic analogues of cyclotomic multiple zeta values

Posted in
Speaker: 
Nils Matthes
Affiliation: 
University of Oxford
Date: 
Wed, 2019-02-06 14:30 - 15:30
Location: 
MPIM Lecture Hall
Parent event: 
Number theory lunch seminar

We will report on ongoing joint work with Martin Gonzalez (MPIM) about analogues of cyclotomic multiple zeta values for complex elliptic curves with level structure. These are holomorphic functions on the upper half plane which degenerate to cyclotomic multiple zeta values at cusps. One of the motivations for their study is the existence of several modular phenomena for cyclotomic multiple zeta values.

An algebraic characterization of the Kronecker function

Posted in
Speaker: 
Nils Matthes
Affiliation: 
University of Oxford
Date: 
Tue, 2019-02-05 14:00 - 15:00
Location: 
MPIM Lecture Hall

The Kronecker function is a kind of generalization of the classical Eisenstein series which lies at the heart of Kronecker's theory of elliptic functions. Nowadays the Kronecker function is also known to play important roles in the geometry of configuration spaces of elliptic curves as well as periods of modular forms for PSL2(Z). In both of these contexts a key role is played by a certain three-term functional equation satisfied by the Kronecker function, the Fay identity.

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