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Talk

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

tba

Posted in
Speaker: 
Wenzhi Luo
Zugehörigkeit: 
The Ohio State University
Datum: 
Die, 2019-08-06 11:15 - 12:15
Location: 
MPIM Lecture Hall
Parent event: 
Number theory lunch seminar

Rationality of Fano 3-folds over nonclosed fields

Posted in
Speaker: 
Yuri Prokhorov
Zugehörigkeit: 
Steklov Mathematical Institute, Moscow/MPIM
Datum: 
Die, 2019-08-27 14:00 - 15:00
Location: 
MPIM Lecture Hall

The rationality problem for smooth Fano threefolds over algebraically closed fields is basically solved.
In this talk I will discuss rationality  of forms of these  Fanos over nonclosed fields of characteristic 0.
I will concentrate on the case where the  Picard number  equals 1.

The talk is based on joint work with Alexander Kuznetsov (in progress).

Harmonic analysis on GLn over finite fields

Posted in
Speaker: 
Shamgar Gurevich
Zugehörigkeit: 
University of Wisconsin-Madison/MPIM
Datum: 
Die, 2019-08-20 14:00 - 15:00
Location: 
MPIM Lecture Hall

There are many formulas that express interesting properties of a finite group G in terms of sums over its characters. For evaluating or estimating these sums, one of the most salient quantities to understand is the character ratio:

Deformations of Abelian categories in algebra, geometry & physics

Posted in
Speaker: 
Severin Barmeier
Zugehörigkeit: 
Universität Münster/MPIM
Datum: 
Die, 2019-08-13 14:00 - 15:00
Location: 
MPIM Lecture Hall

W. Lowen and M. Van den Bergh developed a deformation theory for Abelian categories, such that deformations of the category of (quasi)coherent sheaves on an affine variety Spec A correspond to deformations of the algebra A, which in turn are controlled by the Hochschild cochain complex equipped with the Gerstenhaber bracket.

Some topics in Kobayashi--Hitchin correspondences

Posted in
Speaker: 
Takuro Mochizuki
Zugehörigkeit: 
RIMS Kyoto
Datum: 
Mit, 2019-07-31 11:30 - 12:30
Location: 
MPIM Lecture Hall

Recently, we studied the Kobayashi--Hitchin correspondences for monopoles and harmonic bundles. In this talk,
we would like to discuss some related topics. We plan to explain equivalences between twisted monopoles and twisted difference modules, generalizing the equivalences in the untwisted case. We also plan to discuss some examples of Higgs bundles to which we may apply our equivalences.

Special values of Asai L-functions

Posted in
Speaker: 
Baskar Balasubramanyam
Zugehörigkeit: 
IISER Puner
Datum: 
Don, 2019-07-18 15:00 - 16:00
Location: 
MPIM Lecture Hall
Parent event: 
MPI-Oberseminar

Unoriented topological field theory in low dimensions, II

Posted in
Speaker: 
Matthew Young
Zugehörigkeit: 
MPIM
Datum: 
Mon, 2019-07-22 16:30 - 17:30
Location: 
MPIM Lecture Hall
Parent event: 
MPIM Topology Seminar

This talk is an introduction to unoriented topological field theory. I will give an overview of known examples and highlight some open problems. I will also describe a new class of examples, namely unoriented extensions of twisted Dijkgraaf-Witten theory, and the resulting topological interpretation of the character theory of categorical representations.

Quantum theta functions and signal analysis

Posted in
Speaker: 
Yuri Manin
Zugehörigkeit: 
MPIM
Datum: 
Die, 2019-07-30 15:00 - 16:00
Location: 
MPIM Lecture Hall

Representations of the celebrated Heisenberg commutation relations and their exponentiated versions form the starting point for a number of basic constructions, both in mathematics and mathematical physics (geometric quantization, quantum tori, classical and quantum theta functions) and signal analysis (Gabor analysis).  In this talk I explain how Heisenberg relations bridge the noncommutative geometry and signal analysis.  After providing a brief comparative dictionary of the two languages, I will show e.g.

Knots and q-series, II

Posted in
Speaker: 
Don Zagier
Zugehörigkeit: 
MPIM
Datum: 
Fre, 2019-08-02 10:30 - 11:30
Location: 
MPIM Lecture Hall

Knots and q-series, I

Posted in
Speaker: 
Stavros Garoufalidis
Zugehörigkeit: 
MPIM
Datum: 
Fre, 2019-08-02 09:00 - 10:00
Location: 
MPIM Lecture Hall

Relative shifted symplectic structures

Posted in
Speaker: 
Tony Pantev
Zugehörigkeit: 
University of Pennsylvania
Datum: 
Don, 2019-08-01 17:30 - 18:30
Location: 
MPIM Lecture Hall

I will discuss the notion of relative shifted symplectic structures on sheaves of derived stacks over locally compact Hausdorff topological spaces. I will describe a general pushforward construction of relative symplectic forms and in the constructible case will
explain explicit techniques for computing such forms. As applications I will discuss a relative lift of recent results of Shende--Takeda on topological Fukaya categories, and a universal construction of symplectic structures on derived irregular character varieties. This
is a joint work with Dima Arinkin and Bertrand Toen.

Asymptotics and lower bounds for complex and real counts of singular surfaces in $\mathbb{P}^3$

Posted in
Speaker: 
Hannah Markwig
Organiser(s): 
Universität Tübingen
Datum: 
Don, 2019-08-01 16:30 - 17:20
Location: 
MPIM Lecture Hall

We use tropical geometry and floor decomposed tropical surfaces to study the asymptotics of counts of singular surfaces in $\mathbb{P}^3$ satisfying point conditions. In the real case, we give a lower bound for the number of real singular surfaces satisfying point conditions. This is joint work with Thomas Markwig, Kristin Shaw, Eugenii Shustin.

Aspects of non compact Gromov--Witten--Floer theory

Posted in
Speaker: 
Kenji Fukaya
Zugehörigkeit: 
Stony Brook
Datum: 
Don, 2019-08-01 15:00 - 15:50
Location: 
MPIM Lecture Hall

Gromov-Witten invariants and Lagrangian Floer theory for compact symplectic manifolds are now very much established as far as general theory concerns. In symplectic geometry, non-compact symplectic manifolds (such as the cotangent bundle) are as important as compact ones. There are many versions and variants for non-compact Gromov--Witten--Floer theory and many of them are still not yet completely established. In this talk, I want to explain some of such versions and issues to study them.

Motivic Donaldson--Thomas invariants of the moduli stacks of parabolic Higgs bundles and bundles with connections

Posted in
Speaker: 
Yan Soibelman
Zugehörigkeit: 
Kansas State University
Datum: 
Die, 2019-07-30 10:00 - 11:00
Location: 
MPIM Lecture Hall

Using the ideas of motivic integration I will explain how to compute the ``number'' of semistable Higgs bundles  (maybe with parabolic structure) of fixed rank and degree on a smooth complex curve. Based on that result I am going to discuss a similar problem in the case of bundles with connections. If time permits, I will explain open questions, including a conjectural relation to Satake correspondence for affine Grassmannians over 2-dimensional local rings. This is a joint project with Roman Fedorov and Alexander Soibelman.

Very stable Higgs bundles, the nilpotent cone and mirror symmetry

Posted in
Speaker: 
Tamas Hausel
Zugehörigkeit: 
IST Austria
Datum: 
Don, 2019-08-01 10:00 - 11:00
Location: 
MPIM Lecture Hall

I will discuss the existence of very stable Higgs bundles how it implies a precise formula for the multiplicity of the components of the nilpotent cone and its relationship to mirror symmetry. Joint project with Nigel Hitchin.

From the Hitchin component to opers

Posted in
Speaker: 
Laura Fredrickson
Organiser(s): 
Stanford
Datum: 
Mit, 2019-07-31 16:30 - 17:20
Location: 
MPIM Lecture Hall

Let $C$ be a compact Riemann surface.  A holomorphic quadratic differential on $C$ determines a spectral curve $\Sigma$ over $C$.  Given a holomorphic quadratic differential, we can associate two types of differential operators.   One is an oper on $C$, also known as a holomorphic Schr\"{o}dinger operator. The other is a family of first-order differential equations related to Teichm\"uller theory, which appear in the study of Hitchin's integrable system.  Recently, Gaiotto conjectured a

Weil--Petersson geometry and the BGW KdV tau function

Posted in
Speaker: 
Paul Norbury
Zugehörigkeit: 
University of Melbourne
Datum: 
Mit, 2019-07-31 15:00 - 15:50
Location: 
MPIM Lecture Hall

It was conjectured by Witten and proven by Kontsevich that a generating function for intersection numbers on the moduli space of curves is a tau function of the KdV hierarchy, now known as the Kontsevich--Witten tau function.  Mirzakhani reproved this theorem via the study of Weil-Petersson volumes of moduli spaces of hyperbolic surfaces.  In this lecture I will describe another collection of intersection numbers on the moduli space of curves whose generating function is a tau function of the KdV hierarchy, known as the Brezin--Gross--Witten tau function.  The proof uses Weil

Lagrangians within Higgs bundles and hyperpolygons

Posted in
Speaker: 
Laura Schaposnik
Zugehörigkeit: 
University of Illinois at Chicago
Datum: 
Mit, 2019-07-31 10:00 - 11:00
Location: 
MPIM Lecture Hall

Through different group actions, we will construct Lagrangian submanifolds of the moduli space of principal Higgs bundles contained over the singular locus of the Hitchin fibration, as well as of the space of hyperpolygons. As an application, we will consider correspondences between these spaces coming from mirror symmetry as well from other dualities and correspondences. The talk is based on different pieces of work in progress with Steve Rayan, Sebastian Heller, Indranil Biswas, Steve Bradlow and Lucas Branco.

tba

Posted in
Speaker: 
Albrecht Klemm
Zugehörigkeit: 
Universität Bonn, BCTP
Datum: 
Die, 2019-07-30 17:30 - 18:30
Location: 
MPIM Lecture Hall

POSTER SESSION

Posted in
Speaker: 
Severin Barmeier (MPIM); Alessandro Giacchetto (MPIM); Evgeniy Glukhov (Landau Institute for Theoretical Physics); Pengfei Huang (Université de Nice; Hélder Larraguível and Dmitry Noshchenko (University of Warsaw); Hsaio-Fan Liu (Taiwan National University); Nikita Nikolaev (Université de Genève); Kento Osuga (University of Edmonton/University of Sheffield); Blazej Ruba (Institute of Physics, Jagiellonian University; Zhaoting Wei (University of Pennsylvania); Campbell Wheeler (MPIM)
Datum: 
Die, 2019-07-30 16:30 - 17:20

For titles and abstracts of the posters, please see the attached pdf.

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