Departement Mathematik

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Frühjahrssemester 2020

Datum / Zeit Referent:in Titel Ort
30. Januar 2020
15:15-16:15 		Ezra Getzler
Northwestern University
Details

Talks in Mathematical Physics

Titel Generalized gauge-conditions in the Batalin-Vilkovisky formalism and the Gribov ambiguity
Referent:in, Affiliation Ezra Getzler, Northwestern University
Datum, Zeit 30. Januar 2020, 15:15-16:15
Ort HG G 43
Abstract In the Batalin-Vilkovisky formalism, gauge conditions are expressed as Lagrangian submanifolds in the space of fields and antifields. We discuss a way of patching together gauge conditions over different parts of the space of fields, and apply this method to the light-cone gauge for the superparticle.
Generalized gauge-conditions in the Batalin-Vilkovisky formalism and the Gribov ambiguityread_more
HG G 43
13. Februar 2020
15:15-16:15 		Emily Norton
MPI Bonn
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Talks in Mathematical Physics

Titel Generalized Mullineux involution and perverse equivalences
Referent:in, Affiliation Emily Norton, MPI Bonn
Datum, Zeit 13. Februar 2020, 15:15-16:15
Ort HG G 43
Abstract The Mullineux involution on p-regular partitions describes the result of tensoring an irreducible representation of the symmetric group with the sign representation in characteristic p. More generally, we may work in the setting of Hecke algebras at an e'th root of unity (e not necessarily prime). An algorithm for computing the Mullineux involution using colored directed graphs was discovered by Kleshchev in 1995. Building on this crystal perspective, we generalize the definition of Mullineux involution to all charged multipartitions. The generalized Mullineux involution arises naturally in representation theory as the combinatorial shadow of certain derived equivalences on module categories. This is joint work with Thomas Gerber and Nicolas Jacon.
Generalized Mullineux involution and perverse equivalencesread_more
HG G 43
20. Februar 2020
15:15-16:15 		Chenchang Zhu
University of Göttingen
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Talks in Mathematical Physics

Titel Category of fibrant objects for higher Lie groupoids
Referent:in, Affiliation Chenchang Zhu, University of Göttingen
Datum, Zeit 20. Februar 2020, 15:15-16:15
Ort HG G 43
Abstract Category of fibrant objects is like a "nice coordinate" to generate a higher category. Higher Lie groupoids present higher differential stacks, which in turn are geometric objects to handle certain singularities. For example, take a BRST complex, it can be understand as the infinitesimal of a derived higher stack. A nice foundation should be paved, namely how to build up a nice world to handle all these objects? This will be the discussed in the talk, which is based on a joint work with Chris Rogers. In fact, the title is sort of cheating: it is not category of fibrant objects (CFO) that is easy to build, but a weaker one, which we call an incomplete CFO (ICFO). Nevertheless, we are still lucky enough that ICFO still generate higher category in the same way.
Category of fibrant objects for higher Lie groupoidsread_more
HG G 43
26. Februar 2020
13:00-14:30 		Simone Speziale
Université de Marseille
Details

Talks in Mathematical Physics

Titel Noether theorem and surface charges in general relativity
Referent:in, Affiliation Simone Speziale, Université de Marseille
Datum, Zeit 26. Februar 2020, 13:00-14:30
Ort Y03 G 91
Abstract I will review the application of Noether's theorem in general relativity, and how it leads to the first law of black hole mechanics, or balance laws at future null infinity, which are relevant to the interpretation of the LIGO/Virgo data. The emphasis will be on theoretical aspects and covariant phase space methods. I will then discuss some of the current challenges.
Noether theorem and surface charges in general relativityread_more
Y03 G 91
* 23. März 2020
14:00-16:00 		Maxim Zabzine
Uppsala
Details

Talks in Mathematical Physics

Titel Introduction to equivariant localization in quantum field theory I
Referent:in, Affiliation Maxim Zabzine, Uppsala
Datum, Zeit 23. März 2020, 14:00-16:00
Ort Zoom
Abstract (Zoom hosted by the University of Geneva) In these lectures I will introduce the main ideas behind the Atyah-Bott theorem which is mathematical statement about the situation when a semi-classical approximation for an integral is exact. I will explain the finite dimensional proof of this theorem using ideas from supergeometry and supersymmetry. The second part of the lectures will be devoted to the infinite dimensional application of the Atyah-Bott theorem in the context of quantum field theory. I will consider the Chern-Simons theory on three dimensional manifolds with an isometry. On the way I will review some basic stuff about the Faddeev-Popov ghosts and the cohomological field theory associate to the Chern-Simons theory. If time allows, I will make some general comments about further applications of equivariant localization in QFT.
Introduction to equivariant localization in quantum field theory Iread_more
Zoom
26. März 2020
14:00-16:00 		Maxim Zabzine
Uppsala
Details

Talks in Mathematical Physics

Titel Introduction to equivariant localization in quantum field theory II
Referent:in, Affiliation Maxim Zabzine, Uppsala
Datum, Zeit 26. März 2020, 14:00-16:00
Ort Zoom
Introduction to equivariant localization in quantum field theory II
Zoom
27. März 2020
10:15-12:15 		Xiaomeng Xu
ETH Zurich
Details

Talks in Mathematical Physics

Titel Minicourse: Stokes phenomenon, WKB analysis and Gelfand-Zeitlin cones I
Referent:in, Affiliation Xiaomeng Xu, ETH Zurich
Datum, Zeit 27. März 2020, 10:15-12:15
Ort Zoom
Abstract Stokes phenomenon reflects the fact that a solution of a meromorphic ODE, near an irregular singularity, in different sectors of the complex plane in general shows different asymptotic behavior. The difference is measured by the Stokes matrices. The first part of the course will give an introduction to the Stokes phenomenon of meromorphic ODEs. The second part, based on a joint work with A. Alekseev, will explore the WKB analysis of Stokes matrices, and its relation with Gelfand-Zeitlin systems, cactus group actions and so on.
Minicourse: Stokes phenomenon, WKB analysis and Gelfand-Zeitlin cones Iread_more
Zoom
3. April 2020
10:15-12:15 		Xiaomeng Xu
ETH Zurich
Details

Talks in Mathematical Physics

Titel Minicourse: Stokes phenomenon, WKB analysis and Gelfand-Zeitlin cone II
Referent:in, Affiliation Xiaomeng Xu, ETH Zurich
Datum, Zeit 3. April 2020, 10:15-12:15
Ort Zoom
Minicourse: Stokes phenomenon, WKB analysis and Gelfand-Zeitlin cone II
Zoom
23. April 2020
15:15-17:15 		Andrey Smirnov
UNC Chapel Hill
Details

Talks in Mathematical Physics

Titel Difference equations and stable envelopes I
Referent:in, Affiliation Andrey Smirnov, UNC Chapel Hill
Datum, Zeit 23. April 2020, 15:15-17:15
Ort Zoom recording
Abstract Meeting ID: 234 036 453 Generating functions counting quasimaps from P1 to quiver varieties satisfy certain q-difference equations (qde). At the same time, K-theoretic stable envelopes equip K-theories of these variates with natural action of quantum loop groups. In this talk I explain how the representation theory of these algebras can be utilized to obtain explicit description of qde's. As an application of the general theory I consider example of a quiver variety given by the Hilbert scheme of points in complex plane. In this case we obtain explicit formula for qde in terms of the Hall algebra of elliptic curve. This formula generalizes the result of Okounkov-Pandharipande arXiv:0906.3587 to the level of equivariant K-theory. The talk is based on joint work with A. Okounkov arXiv:1602.09007.
Difference equations and stable envelopes Iread_more
Zoom recording
30. April 2020
15:15-17:15 		Andrey Smirnov
UNC Chapel Hill
Details

Talks in Mathematical Physics

Titel Difference equations and stable envelopes II
Referent:in, Affiliation Andrey Smirnov, UNC Chapel Hill
Datum, Zeit 30. April 2020, 15:15-17:15
Ort Zoom recording
Abstract The monodromy of the quantum difference equations can be described in purely geometric terms by the "elliptic stable envelope" introduced recently by Aganagic-Okounkov. In this talk I explain how the qde's themselves can be reconstructed from the monodromy and certain symmetries of the elliptic stable envelopes known as 3d-mirror symmetry (symplectic duality). As an example, the qde for the Hilbert scheme of points in the complex plane discussed in the Talk 1 will be revisited in this light.
Difference equations and stable envelopes IIread_more
Zoom recording
14. Mai 2020
15:15-16:15 		Alisa Knizel
Columbia University
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Talks in Mathematical Physics

Titel Gaussian asymptotics via discrete loop equations
Referent:in, Affiliation Alisa Knizel, Columbia University
Datum, Zeit 14. Mai 2020, 15:15-16:15
Ort Zoom recording
Abstract We introduce and study a class of discrete particle ensembles. They naturally arise in connection with classical random matrix ensembles and Jack polynomials. Under technical assumptions on a general analytic potential we prove the Law of Large Numbers and Central Limit Theorem for linear statistics. Our main tools are certain novel algebraic identities that are multi-level analogues of the discrete loop equations. Based on joint work with Evgeni Dimitrov (Columbia University)
Gaussian asymptotics via discrete loop equationsread_more
Zoom recording

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