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

Counting incompressible surfaces in 3-manifolds

Posted in
Speaker: 
Stavros Garoufalidis
Affiliation: 
MPIM
Date: 
Mon, 2019-02-04 16:30 - 18:00
Location: 
MPIM Lecture Hall
Parent event: 
MPIM Topology Seminar

A 3-manifold is small, smallish or very large if it contains no embedded incompressible surfaces (up to isotopy), finitely many, or infinitely many. We will prove a structure theorem for counting
such surfaces by Euler characteristic in a cusped hyperbolic 3-manifolds. Our proofs use PL methods (ideal triangulations, normal and almost normal surfaces), simple isotopies, hyperbolic geometry, come with a computer-implementation, illustrate phenomena for triangulated 3-manifolds with at most 18 ideal tetrahedra and connect with quantum 3-manifold invariants (the q-series of the 3D-index of Dimofte-Gaiotto-Gukov). Joint work with Nathan Dunfield and Hyam Rubinstein.

Rational homotopy theory, III

Posted in
Speaker: 
José Moreno-Fernández
Affiliation: 
Universidad de Malaga/MPIM
Date: 
Mon, 2019-01-21 14:15 - 15:45
Location: 
MPIM Lecture Hall
Parent event: 
IMPRS Minicourse

Rational homotopy theory is a branch of homotopy theory focused on the study of spaces “modulo torsion”. Roughly, this consists of two steps. First, one “kills” all torsion phenomena of a given space in a nice way – by a process called the “rationalization”, or “localization at the empty set of primes”. Second, one finds algebraic models that faithfully capture the homotopy type of this rationalization, and which are amenable to computations. 

This brief course is a very friendly and basic introduction to rational homotopy theory. 
 
Lecture 1: Rationalization. Sullivan PL-forms and minimal models.
Lecture 2. Topology of Sullivan and Quillen models. Formality and coformality.

New results in geography and geometry of moduli spaces of stable rank 2 sheaves on projective space

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Speaker: 
Alexandr Tikhomirov
Affiliation: 
HSE Moscow
Date: 
Tue, 2019-02-19 14:00 - 15:00
Location: 
MPIM Lecture Hall

In this talk, we will give an overview of recent results on the geography and geometry of the Gieseker-Maruyama
moduli scheme $M = M(c_1,c_2,c_3)$ of rank 2 stable coherent sheaves with first Chern class $c_1 = 0$ or $-1$,
second Chern class $c_2$, and third Chern class $c_3\ge0$ on the projective space $\mathbb{P}^3$.
We will enumerate all currently known irreducible components of $M$ for small values of $c_2$ and $c_3\ge0$.
We then present the constructions of new series of components of $M$ for arbitrary $c_2$. The problem of
connectedness of $M$ will be discussed. These are the resuts of several joint works of the speaker with
M.Jardim, D.Markushevich, A.Ivanov, C.Almeida and others.

Steklov problem, II

Posted in
Speaker: 
Anna Siffert
Affiliation: 
MPIM
Date: 
Mon, 2019-02-04 14:15 - 15:45
Location: 
MPIM Lecture Hall
Parent event: 
IMPRS Minicourse

In the last few years there has been growing interest in the Steklov problem - this is
an eigenvalue problem with the spectral parameter in the boundary conditions. In this
talk we will discuss some recent advances and open questions.

Steklov problem, I

Posted in
Speaker: 
Anna Siffert
Affiliation: 
MPIM
Date: 
Mon, 2019-01-28 14:15 - 15:45
Location: 
MPIM Lecture Hall
Parent event: 
IMPRS Minicourse

In the last few years there has been growing interest in the Steklov problem - this is
an eigenvalue problem with the spectral parameter in the boundary conditions. In this
talk we will discuss some recent advances and open questions.

Gorenstein duality for topological modular forms with level structure

Posted in
Speaker: 
Dimitar Kodjabachev
Affiliation: 
University of Sheffield
Date: 
Mon, 2019-01-21 16:30 - 18:00
Location: 
MPIM Lecture Hall
Parent event: 
MPIM Topology Seminar

The notion of Gorenstein duality introduced by Dwyer, Greenlees and Iyengar
allows one to view a number of dualities such as Poincaré duality for manifolds,
Gorenstein duality for commutative rings and Benson-Carlson duality for
cohomology rings of finite groups as instances of a single phenomenon. In this
talk I will set up an equivariant generalization of the framework and look at
examples coming from derived algebraic geometry, namely - the ring spectra of
topological modular forms with level structure.

tba

Posted in
Speaker: 
Joel Villatoro
Affiliation: 
KU Leuven
Date: 
Wed, 2019-02-27 10:30 - 12:00
Location: 
MPIM Lecture Hall

Higher-rank Bohr sets and multiplicative diophantine approximation

Posted in
Speaker: 
Niclas Technau
Affiliation: 
University of Graz
Date: 
Wed, 2019-01-23 14:30 - 15:30
Location: 
MPIM Lecture Hall
Parent event: 
Number theory lunch seminar

Gallagher’s theorem is a sharpening and extension of the Littlewood conjecture that holds for almost all tuples of real numbers. This talk is about joint work with Sam Chow where we provide a fibre refinement, solving a problem posed by Beresnevich, Haynes and Velani in 2015. Hitherto, this was only known in the plane, as previous approaches relied heavily on the theory of continued fractions. Using reduced successive minima in lieu of continued fractions, we develop the structural theory of Bohr sets of arbitrary rank, in the context of diophantine approximation.

Regular, Quasi-regular and Induced representations of infinite-dimensional groups

Posted in
Speaker: 
Alexander Kosyak
Affiliation: 
Institute of Mathematics of NAS of Ukraine, Kiev/MPIM
Date: 
Tue, 2019-02-12 14:00 - 15:00
Location: 
MPIM Lecture Hall

Almost all harmonic analysis on locally compact groups is based on the existence (and uniqueness)
of the Haar measure. If the group is not locally compact there is no Haar measure on it. The  aim
of the talk is
to give a systematic development, by example, of noncommutative harmonic 
analysis on infinite-dimensional (non-locally compact) matrix groups.

We generalize the notion of regular, quasi-regular and induced
representations to arbitrary
infinite-dimensional groups. In order to do  so,  we replace the non-existing Haar measure on an 
infinite-dimensional group by a suitable quasi-invariant measure on an appropriate completion
of the initial group or on the completion of a homogeneous space.

tba

Posted in
Speaker: 
Rui Fernandes
Affiliation: 
University of Illinois, Urbana Champaign
Date: 
Wed, 2019-06-12 10:30 - 12:00
Location: 
MPIM Lecture Hall

New guests at the MPIM

Posted in
Speaker: 
Hongyi Chu, Vladimir Mitankin, Dinh Tuan Huynh
Date: 
Thu, 2019-01-17 15:00 - 16:00
Location: 
MPIM Lecture Hall
Parent event: 
MPI-Oberseminar

The algebraic index theorem

Posted in
Speaker: 
Bertram Arnold
Affiliation: 
MPIM
Date: 
Wed, 2019-01-16 16:30 - 18:00
Location: 
MPIM Seminar Room
Parent event: 
IMPRS seminar

Comodule-Contramodule Correspondence, Higher Geometry Viewpoint

Posted in
Speaker: 
Dmitry Rumynin
Affiliation: 
Warwick / MPIM
Date: 
Wed, 2019-02-06 10:30 - 12:00
Location: 
MPIM Lecture Hall

Both comodules and contramodules were introduced in 1960-s by Eilenberg and Moore. While the comodules spread widely, the contramodules remained a poor cousin. The numbers of MathSciNet hits for them are 1327 and 14 correspondingly. In fact, the contramodules do not appear in the literature at all between 1970 and 2007, when Positselski resurrected interest to them by discovering what is now known as Comodule-Contramodule Correspondence but should probably be called Positselski Duality. It seems to underline some seemingly unrelated duality phenomena: Matlis Duality and Riemann-Hilbert Correspondence are examples. In the first half of the talk we will review Comodule-Contramodule Correspondence on a cakewalk example of a DG-coalgebra. In the second half we will discuss an approach to it from the viewpoint of model categories, It is a work in progress, joint with K. Hristova and J. D, S, Jones.

Signatures of Lefschetz fibrations

Posted in
Speaker: 
Cagri Karakurt
Affiliation: 
Bogazici University
Date: 
Mon, 2019-01-14 16:30 - 18:00
Location: 
MPIM Lecture Hall
Parent event: 
MPIM Topology Seminar

In his Ph. D. thesis, Burak Ozbagci described an algorithm computing signatures of Lefschetz fibrations where the input is a factorization of the monodromy into a product of Dehn twists. I will talk about a reformulation  of Ozbagci's algorithm which becomes much easier to implement. Our  main tool  will be Wall's non-additivity formula applied to what I call partial fiber sum decomposition of a Lefschetz fibrations over disk. This is a joint work with A. Cengel.  

 

 

A noncommutative geometry model for Dyson--Schwinger equations

Posted in
Speaker: 
Ali Shojaei-Fard
Affiliation: 
MPIM
Date: 
Tue, 2019-01-29 14:00 - 15:00
Location: 
MPIM Lecture Hall

In this talk I plan to show the importance of Noncommutative Geometry to mathematically describe quantum motions in Quantum Field Theory. At the first step, I explain the construction of a new class of spectral triples with respect to the information of Dyson--Schwinger equations. At the second step, I explain the structure of a new noncommutative differential geometry machinery derived from the BPHZ renormalization of Dyson--Schwinger equations.

Ribbon graph complexes, the Grothendieck-Teichmueller group and Goldman-Turaev Lie bialgebra

Posted in
Speaker: 
Sergei Merkulov
Affiliation: 
Universität Luxemburg/MPIM
Date: 
Mon, 2019-01-28 13:00 - 14:00
Location: 
MPIM Lecture Hall

Using recent results of Chan-Galatius-Payne “Tropical curves, graph complexes, and top weight cohomology of $cM_g$” (preprint arXiv:1805.10186) it is not hard to show that the Grothendieck-Teichmueller Lie algebra grt injects into the cohomology Lie algebra of the ribbon graph complex introduced in the paper of Merkulov-Willwacher “Props of ribbon graphs, involutive Lie bialgebras and moduli spaces of curves”  (preprint  arXiv:1511.07808) in the context of a study of the totality of cohomology groups  of moduli spaces of algebraic curves with (skewsymmetrized) punctures.

In my talk I explain that the latter ribbon graph complex controls also universal deformations of the Goldman-Turaev Lie bialgebra structure on the free loop space of a genus g Rieman surface with n+1 boundaries. Hence every element of grt
gives us a universal and highly non-trivial deformation of the  latter.

The construction can be made rather transparent.  We show explicitly the first non-trivial contribution to the standard
Goldman-Turaev bracket and co-bracket coming from Kontsevich’s tetrahedron class in grt.

The talk is based on a work in progress.

New guests at the MPIM

Posted in
Speaker: 
Hisatoshi Kodani, Panagiotis Polymerakis, Ögmundur Eiriksson
Affiliation: 
MPIM
Date: 
Thu, 2019-01-10 15:00 - 16:00
Location: 
MPIM Lecture Hall
Parent event: 
MPI-Oberseminar

Extending commutative multiplications and André-Quillen cohomology

Posted in
Speaker: 
Michael Stahlhauer
Affiliation: 
MPIM
Date: 
Wed, 2019-01-09 16:30 - 18:00
Location: 
MPIM Seminar Room
Parent event: 
IMPRS seminar

Vorlesung Topology of 4-Manifolds

Posted in
Speaker: 
Arunima Ray
Affiliation: 
MPIM
Date: 
Thu, 2019-01-24 13:15 - 15:00
Location: 
MPIM Lecture Hall

Vorlesung Topology of 4-Manifolds

Posted in
Speaker: 
Arunima Ray
Affiliation: 
MPIM
Date: 
Thu, 2019-01-17 13:15 - 15:00
Location: 
MPIM Lecture Hall
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