Departement Mathematik

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Frühjahrssemester 2015

Datum / Zeit Referent:in Titel Ort
19. Februar 2015
15:15-16:15 		Pavol Severa
Universität Genf
Details

Talks in Mathematical Physics

Titel Quantization of Lie bialgebras and moduli spaces of flat connections
Referent:in, Affiliation Pavol Severa, Universität Genf
Datum, Zeit 19. Februar 2015, 15:15-16:15
Ort HG G 43
Abstract I will describe a new method of quantization of Lie bialgebras, simpler than the original method of Etingof and Kazhdan. The geometric background comes from quasi-Poisson rather than from Poisson geometry, in particular from moduli spaces of flat connections on surfaces with marked points on the boundary.
Quantization of Lie bialgebras and moduli spaces of flat connectionsread_more
HG G 43
* 26. Februar 2015
14:15-15:15 		Iakovos Androulidakis
University of Athens
Details

Talks in Mathematical Physics

Titel Singular subalgebroids
Referent:in, Affiliation Iakovos Androulidakis, University of Athens
Datum, Zeit 26. Februar 2015, 14:15-15:15
Ort HG G 19.2
Abstract Recently Gualtieri and Li gave a symplectic realization for Log-symplectic manifolds by deploying the "blow-up" construction used by Melrose. In this talk we introduce singular subalgebroids and their integration. Log-symplectic manifolds are instances of singular subalgebroids, and we show that in this context the above symplectic realization is really a holonomy groupoid. The basic ingredient of our constructions is the notion of a bisubmersion. At the end of the talk we discuss how bisubmersions allow the construction of the C*-algebra of any Lie algebroid (possibly non-integrable). This is joint work with Marco Zambon (Leuven).
Singular subalgebroidsread_more
HG G 19.2
* 26. Februar 2015
15:30-16:30 		Anton Khoroshkin
HSE Moscow
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Talks in Mathematical Physics

Titel Around categorification of Macdonald polynomials
Referent:in, Affiliation Anton Khoroshkin, HSE Moscow
Datum, Zeit 26. Februar 2015, 15:30-16:30
Ort HG G 19.2
Abstract The goal of the talk is to explain an approach to the problem of categorification of Macdonald polynomials based on derived categories of modules over Lie algebras of currents and relationship of Macdonald pairing with certain Lie algebra cohomology. Unfortunately, we are not able to solve the categorification problem in the full generality, however, we can explain what kind of generalizations, limits and applications one can derive out of this approach. The talk is based on math.arxiv:1312.7053
Around categorification of Macdonald polynomialsread_more
HG G 19.2
* 5. März 2015
14:15-15:15 		Florian Schätz
University of Aarhus
Details

Talks in Mathematical Physics

Titel Flat superconnections and the loop space
Referent:in, Affiliation Florian Schätz, University of Aarhus
Datum, Zeit 5. März 2015, 14:15-15:15
Ort HG G 19.2
Abstract The holonomies of a vector bundle with connection give rise to interesting structures on the based and the free loop space, respectively. I will explain how these structures generalize to flat superconnections. The talk is based on ongoing joint work with Camilo Arias Abad (Universidad Nacional de Colombia, Medellin).
Flat superconnections and the loop spaceread_more
HG G 19.2
12. März 2015
15:15-16:15 		Saikat Chatterjee
IHES
Details

Talks in Mathematical Physics

Titel Decorated categorical principal bundles and gerbes
Referent:in, Affiliation Saikat Chatterjee, IHES
Datum, Zeit 12. März 2015, 15:15-16:15
Ort HG G 43
Abstract A (strict) categorical group is a (strict) monoidal category with an additional operation of'inversion' under monoidal product. It has an equivalent description in terms of crossed modules. I will discuss the notion of a categorical principal bundle, and prescribe a general method of constructing a categorical principal bundle over the path space groupoid of a manifold, for an arbitrary categorical group. We call it a "decorated categorical bundle". I will explain it's relation with gerbes on the underline manifold. The background motivation behind this work, is to develop a differential geometric frame work for the "higher gauge theory".
Decorated categorical principal bundles and gerbesread_more
HG G 43
19. März 2015
15:15-16:15 		Paul Wedrich
Cambridge University
Details

Talks in Mathematical Physics

Titel Deformations of link homologies
Referent:in, Affiliation Paul Wedrich, Cambridge University
Datum, Zeit 19. März 2015, 15:15-16:15
Ort HG G 43
Abstract I will start by explaining how deformations help to answer two important questions about the family of (colored) sl(N) link homology theories: What relations exist between them? What geometric information about links do they contain? I will recall Lee's deformation of Khovanov homology and sketch how it generalizes to the case of colored sl(N) link homology. The result is a decomposition theorem for deformed colored sl(N) link homologies which leads to new spectral sequences between various type A link homologies and concordance invariants in the spirit of Rasmussen's s-invariant. Joint work with David Rose.
Deformations of link homologiesread_more
HG G 43
2. April 2015
15:15-16:15 		Xiaomeng Xu
Université de Genève
Details

Talks in Mathematical Physics

Titel Irregular Riemann-Hilbert correspondence and Alekseev-Meinrenken dynamical r-matrix
Referent:in, Affiliation Xiaomeng Xu, Université de Genève
Datum, Zeit 2. April 2015, 15:15-16:15
Ort HG G 43
Abstract In 2004, Enriquez-Etingof-Marshall suggested a new approach to the Ginzburg-Weinstein linearization theorem. This approach is based on solving a system of PDEs for a gauge transformation between the standard classical r-matrix and the Alekseev-Meinrenken dynamical r-matrix. In the talk, we explain that this gauge transformation can be constructed as a monodromy (connection matrix) for a certain irregular Riemann-Hilbert problem. Geometrically, this leads to a symplectic neighborhood version of the Ginzburg-Weinstein linearization theorem. Our construction is based on earlier works by Boalch. As an application, we give a new description of the Lu-Weinstein symplectic double.
Irregular Riemann-Hilbert correspondence and Alekseev-Meinrenken dynamical r-matrixread_more
HG G 43
16. April 2015
15:15-16:15 		Roman Riser
University of Leuven
Details

Talks in Mathematical Physics

Titel Fine Asymptotic Behavior in Eigenvalues of Random Normal Matrices
Referent:in, Affiliation Roman Riser, University of Leuven
Datum, Zeit 16. April 2015, 15:15-16:15
Ort HG G 43
Abstract We will show that there is a Christoffel-Darboux like formula for the normal matrix model which can be used to study the asymptotics of the average density of eigenvalues. We will give a description of the density including subleading corrections which hold uniformly in the complex plane. At the boundary, the subleading correction has an universal behavior only depending on the curvature. We will also show a formula for the correlation kernel. Finally we will discuss some applications of our results.
Fine Asymptotic Behavior in Eigenvalues of Random Normal Matricesread_more
HG G 43
7. Mai 2015
15:15-16:15 		Clément Dupont
MPIM Bonn
Details

Talks in Mathematical Physics

Titel The Hopf algebra of dissection polylogarithms
Referent:in, Affiliation Clément Dupont, MPIM Bonn
Datum, Zeit 7. Mai 2015, 15:15-16:15
Ort HG G 43
Abstract Periods are the complex numbers which may be defined by integrals of algebraic functions (with rational coefficients) over domains defined by algebraic inequalities (with rational coefficients). They include all algebraic numbers. The philosophy of motives predicts that classical Galois theory for algebraic numbers is a special case of a Galois theory for periods. In this talk we will introduce a family of periods, called dissection polylogarithms, indexed by some combinatorial objects, called dissection diagrams, and show that their Galois theory is encoded in a combinatorial Hopf algebra. This generalizes Goncharov’s work on (generic) iterated integrals on the punctured complex line. No a priori knowledge of the theory of motives is required.
The Hopf algebra of dissection polylogarithmsread_more
HG G 43
* 21. Mai 2015
14:15-15:15 		Scott Carter
University of South Alabama
Details

Talks in Mathematical Physics

Titel Homology for Quandles with Partial Group Operations
Referent:in, Affiliation Scott Carter, University of South Alabama
Datum, Zeit 21. Mai 2015, 14:15-15:15
Ort HG G 19.2
Abstract In this talk, I'll introduce multiple conjugation quandles and show how their axiomatization corresponds to coloring handlebody knots. Then I'll develop a formalism that unifies group and quandle homology.
Homology for Quandles with Partial Group Operationsread_more
HG G 19.2
28. Mai 2015
15:15-16:15 		Huafeng Zhang
Uiversité Paris 7
Details

Talks in Mathematical Physics

Titel Asymptotic representations of quantum affine superalgebras
Referent:in, Affiliation Huafeng Zhang, Uiversité Paris 7
Datum, Zeit 28. Mai 2015, 15:15-16:15
Ort HG G 43
Abstract We study representations of quantum affine superalgebras associated to general linear Lie superalgebras. An analog of Baxter T-Q relations in the spirit of Frenkel- Hernandez is proposed where T stands for finite-dimensional representations and Q asymptotic representations.
Asymptotic representations of quantum affine superalgebrasread_more
HG G 43

Hinweise: mit einem Stern gekennzeichnete Ereignisse (*) zeigen an, dass die Zeit und/oder der Ort von der üblichen Zeit und/oder dem üblichen Ort abweichen.

Organisatoren:innen: Anna Beliakova, Alberto Cattaneo, Giovanni Felder, Matthias Gaberdiel, Gian Michele Graf, Horst Knörrer, Thomas Hans Willwacher

Archiv: HS 24 FS 24 HS 23 FS 23 HS 22 FS 22 HS 21 FS 21 HS 20 FS 20 HS 19 FS 19 HS 18 FS 18 HS 17 FS 17 HS 16 FS 16 HS 15 FS 15 HS 14 FS 14 HS 13 FS 13 HS 12 FS 12 HS 11

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