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Autumn Semester 2017

Date / Time Speaker Title Location
24 August 2017
15:15-16:15 		Najib Idrissi
Université de Lille
Event Details

Talks in Mathematical Physics

Title Configuration Spaces of Compact Manifolds
Speaker, Affiliation Najib Idrissi, Université de Lille
Date, Time 24 August 2017, 15:15-16:15
Location HG G 43
Abstract We study the real homotopy type of configuration spaces of smooth compact manifolds with and without boundary. We provide an explicit real model of these configuration spaces for closed manifolds and a large class of manifolds with boundary, and we show that it only depends on the real homotopy type of the manifold. We moreover study the action of the little disks operads and the Swiss-cheese operads on the configuration spaces of framed manifolds, and we prove that our model is compatible with them.
Configuration Spaces of Compact Manifoldsread_more
HG G 43
21 September 2017
15:15-16:15 		Pavel Safronov
Universität Zürich
Event Details

Talks in Mathematical Physics

Title Shifted Poisson structures with examples
Speaker, Affiliation Pavel Safronov, Universität Zürich
Date, Time 21 September 2017, 15:15-16:15
Location HG G 43
Abstract The theory of shifted Poisson structures allows one to define Poisson structures on a large class of spaces such as (derived) algebraic stacks. I will describe the basic theory and sketch some examples such as the Atiyah class of a symplectic manifold. One of the motivations for shifted Poisson structures is that they appear in categorified deformation quantization which is related to quantum groups. I will explain this connection in the second half of the talk.
Shifted Poisson structures with examplesread_more
HG G 43
5 October 2017
15:15-16:15 		Nils Carqueville
Universität Wien
Event Details

Talks in Mathematical Physics

Title Topological quantum field theories: state sums and defects
Speaker, Affiliation Nils Carqueville, Universität Wien
Date, Time 5 October 2017, 15:15-16:15
Location HG G 43
Abstract A general framework will be discussed which unifies group orbifolds and state sum models, in the context of topological quantum field theory (TQFT) in arbitrary dimension. After a review of the 2-dimensional case, I will outline general aspects of the construction and discuss examples in 3 dimensions, including surface defects in quantised Chern-Simons theory. (Based on joint work with I. Runkel and G. Schaumann.)
Topological quantum field theories: state sums and defectsread_more
HG G 43
12 October 2017
15:15-16:15 		Nezhla Aghaei
Universität Bern
Event Details

Talks in Mathematical Physics

Title Quantization of Teichmüller spaces and its generalisation
Speaker, Affiliation Nezhla Aghaei, Universität Bern
Date, Time 12 October 2017, 15:15-16:15
Location HG G 43
Abstract The quantization of the Teichmüller spaces of Riemann surfaces has found important applications to conformal field theory and $N=2$ supersymmetric gauge theories.We construct a quantization of the Teichmüller spaces of super Riemann surfaces, using coordinates associated to the ideal triangulations of super Riemann surfaces. A new feature is the non-trivial dependence on the choice of a spin structure which can be encoded combinatorially in a certain refinement of the ideal triangulation. We construct a projective unitary representation of the groupoid of changes of refined ideal triangulations. Therefore, we demonstrate that the dependence of the resulting quantum theory on the choice of a triangulation is inessential.In the quantum Teichmüller theory, it was observed that the key object defining the Teichmüller theory has a close relation to the representation theory of the Borel half of $U_q(sl(2))$. In our research we observed that the role of $U_q(sl(2))$ is taken by quantum superalgebra $U_q(osp(1|2))$. A Borel half of $U_q(osp(1|2))$ is the super quantum plane. The canonical element of the Heisenberg double of the quantum super plane is evaluated in certain infinite dimensional representations on $L^2(\mathbb{R})\otimes\mathbb{C}^{1|1}$ and compared to the flip operator from the Teichmüller theory of super Riemann surfaces.
Quantization of Teichmüller spaces and its generalisationread_more
HG G 43
19 October 2017
15:15-16:15 		Ajay Ramadoss
Indiana University
Event Details

Talks in Mathematical Physics

Title Representation homology of spaces
Speaker, Affiliation Ajay Ramadoss, Indiana University
Date, Time 19 October 2017, 15:15-16:15
Location HG G 43
Abstract We discuss representation homology of topological spaces, which is a higher homological extension of the representation varieties of fundamental groups. We give a natural interpretation of representation homology as functor homology and relate it to other homology theories associated with spaces (such as Pontryagin algebras and S^1-equivariant homology of free loop spaces). One of our main results, which we call the Comparison Theorem, computes the representation homology of any simply connected space of finite rational homotopy type in terms of its Quillen and Sullivan models. We also compute representation homology for some interesting examples, such as spheres, Riemann surfaces, complex projective spaces and link complements in R^3. While the representation homology of spheres and complex projective spaces is related to the strong Macdonald conjecture of Feigin and Hanlon, the representation homology of link complements is a new homological link invariant similar to knot contact homology. This is joint work with Yuri Berest and Wai-Kit Yeung.
Representation homology of spacesread_more
HG G 43
26 October 2017
15:15-16:15 		Igor Kanatchikov
Event Details

Talks in Mathematical Physics

Title Quantum gravity from scratch: precanonical quantization
Speaker, Affiliation Igor Kanatchikov,
Date, Time 26 October 2017, 15:15-16:15
Location HG G 43
Abstract I will present an approach to quantization of gravity which is based on the De Donder-Weyl extension of the Hamiltonian formalism to field theory, which is known in the calculus of variations. First I describe the construction of a proper generalization of Poisson brackets to this formulation, which will lead to the Gerstenhaber algebra structure of brackets defined on differential forms. Their quantization according to the Dirac quantization rule leads to a Clifford algebraic extension of quantum mechanical formalism to field theory. Then I argue that in a certain limiting case this formulation of quantum theory of fields is able to reproduce the functional Schroedinger representation of QFT. An application to quantization of General Relativity requires a generalization of the classical formalism of De De Donder-Weyl theory to the singular (constrained) case. This is done for the Einstein-Palatini formulation of vielbein gravity. Quantization of the generalized Dirac brackets of the fundamental variables leads to the representation of vielbeins in terms of partial differential operators with respect to the spin connection coefficients and to the formulation of the covariant (precanonical) analogue of the Schroedinger equation. The resulting theory describes quantum gravity in terms of the sections of the Clifford bundle over the bundle of spin-connections over space-time. Physically it means that the quantum space-time is described by Clifford-algebra-valued probability amplitudes of observing a certain value of spin connection at some space-time point or the corresponding transition amplitudes, i.e. a spin-connection foam. I also show that the Einstein equations (in the first order vielbein formulations) can be derived from the equations derived by precanonical quantization of GR as the equations for expectation values of the corresponding operators.
Quantum gravity from scratch: precanonical quantizationread_more
HG G 43
2 November 2017
15:15-16:15 		Huafeng Zhang
University of Lille
Event Details

Talks in Mathematical Physics

Title Elliptic quantum groups and Baxter relations
Speaker, Affiliation Huafeng Zhang, University of Lille
Date, Time 2 November 2017, 15:15-16:15
Location HG G 43
Abstract Associated to an arbitrary special linear Lie algebra is Felder's face-type elliptic quantum group. We introduce a monoidal and abelian category O à la Bernstein-Gelfand-Gelfand of representations of the elliptic quantum group. We construct infinite-dimensional representations in category O, called asymptotic representations, as analytic continuation of finite-dimensional ones. Making use of asymptotic representations, we prove various identities in the Grothendieck ring of category O. These identities lead to functional relations à la Baxter for the transfer matrices of the face-type quantum integrable system.
Elliptic quantum groups and Baxter relationsread_more
HG G 43
* 7 November 2017
14:00-15:00 		Vasily Pestun
IHES
Event Details

Talks in Mathematical Physics

Title Non-simply laced q-deformed W-algebras from fractional instantons
Speaker, Affiliation Vasily Pestun, IHES
Date, Time 7 November 2017, 14:00-15:00
Location HIT E 41.1
Abstract I will discuss the construction of the generators of q-deformed W-algebra(g) for arbitrary simple Lie algebra g, including the non-simply laced cases, in terms of the geometry of the moduli spaces of fractional instantons and Coulomb branches of fractional quiver gauge theories.
Non-simply laced q-deformed W-algebras from fractional instantonsread_more
HIT E 41.1
9 November 2017
15:15-16:15 		Vasily Pestun
IHES
Event Details

Talks in Mathematical Physics

Title Periodic monopoles and q-Opers
Speaker, Affiliation Vasily Pestun, IHES
Date, Time 9 November 2017, 15:15-16:15
Location HG G 43
Abstract I will discuss geometric realization of categorical q-geometricLanglands correspondence in terms of quantized algebraic integrable system of group valued Higgs bundles on a curve, or, quantized integrable system of periodic monopoles, with particular details on construction of q-oper lagrangian in the special coordinates.
Periodic monopoles and q-Opersread_more
HG G 43
23 November 2017
15:15-16:15 		Azad Gainutdinov
Université de Tours
Event Details

Talks in Mathematical Physics

Title Modified trace is a symmetrised integral
Speaker, Affiliation Azad Gainutdinov, Université de Tours
Date, Time 23 November 2017, 15:15-16:15
Location HG G 43
Abstract A modified trace for a pivotal Hopf algebra H is a family of linear functionals on endomorphism spaces of projective H-modules which has cyclicity property and satisfies the so-called partial trace condition defined by the pivotal structure. We show that giving a modified trace is equivalent to Calabi-Yau structure on the category of projective H-modules and this structure is compatible with the duality. The modified traces provide a meaningful generalization of the categorical trace to non-semisimple categories and allow to construct interesting topological invariants. Our main theorem says that a modified trace is determined by a symmetric linear form constructed from an integral on the Hopf algebra. More precisely, we prove that for any finite dimensional unimodular pivotal Hopf algebra, shifting with the pivotal element defines an isomorphism between the space of right integrals, which is known to be 1-dimensional, and the space of modified traces. This is a joint work with Anna Beliakova and Christian Blanchet.
Modified trace is a symmetrised integralread_more
HG G 43
7 December 2017
15:15-16:15 		Iuliya Beloshapka
ETH Zurich
Event Details

Talks in Mathematical Physics

Title Twistor approach to harmonic 2-spheres in the loop space
Speaker, Affiliation Iuliya Beloshapka, ETH Zurich
Date, Time 7 December 2017, 15:15-16:15
Location HG G 43
Abstract Atiyah's theorem establishes a bijection between the modulispace of G-instantons on R4 and the space of based holomorphic 2-spheres in the loop space Ω G of a gauge group G. There is a conjecture (due to A. Sergeev) which asserts that there should exist a bijection between the moduli space of general Yang--Mills G-fields on R4/sup> and the space of based harmonic 2-spheres in the loop space $\Omega G$. In this talk we will discuss this conjecture and a twistor approach to harmonic 2-spheres in the loop space ΩG.
Twistor approach to harmonic 2-spheres in the loop spaceread_more
HG G 43
14 December 2017
15:15-16:15 		Pavel Mnev
University of Notre Dame, Indiana, USA
Event Details

Talks in Mathematical Physics

Title Abelian 2-dimensional BF theory as a twisted N=(2,2) superconformal field theory
Speaker, Affiliation Pavel Mnev, University of Notre Dame, Indiana, USA
Date, Time 14 December 2017, 15:15-16:15
Location HG G 43
Abstract We will discuss the two-dimensional topological abelian BF theory in Lorenz gauge as a conformal field theory. In particular, the objects of interest are the stress-energy tensor T and its BRST-primitive G; the latter can be used to construct Witten's descent for observables. The theory contains a conserved U(1)-current which allows one to obtain the theory as Witten's twist of type B of an N=(2,2)-superconformal field theory - an analog of Landau-Ginzburg theory with odd target - with central charge c=-3. We will also discuss the BV algebra structure (with BV Laplacian of degree -1) on the reduced space of states (space of 0-observables), constructed via descent, and the corresponding "cochain-level" framed E_2 algebra structure on composite fields (non-reduced states). We will also explain the descent in terms of AKSZ construction and will give a preliminary discussion of deformations of abelian BF theory by 2-observables, where the main examples are the non-abelian deformation and the "superpotential deformation". This is a joint work in progress with Andrey Losev and Donald Youmans.
Abelian 2-dimensional BF theory as a twisted N=(2,2) superconformal field theoryread_more
HG G 43

Note: events marked with an asterisk (*) indicate that the time and/or location are different from the usual time and/or location.

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