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Autumn Semester 2015

Date / Time Speaker Title Location
17 September 2015
15:15-16:15 		Qingtao Chen
ETH Zurich
Event Details

Talks in Mathematical Physics

Title Volume Conjectures for 3-manifolds
Speaker, Affiliation Qingtao Chen, ETH Zurich
Date, Time 17 September 2015, 15:15-16:15
Location HG G 43
Abstract We will discuss volume conjectures via Turaev-Viro and Reshetikhin-Turaev invariants for 3-manifolds with or without boundaries. This is a joint work with Tian Yang.
Volume Conjectures for 3-manifoldsread_more
HG G 43
24 September 2015
15:15-16:15 		Christoph Keller
ETH Zurich
Event Details

Talks in Mathematical Physics

Title The modern conformal and modular bootstrap
Speaker, Affiliation Christoph Keller, ETH Zurich
Date, Time 24 September 2015, 15:15-16:15
Location HG G 43
Abstract The bootstrap program is the attempt to construct Conformal Field Theories from the bottom up by explicitly solving the consistency conditions that come from conformal symmetry. I will discuss recent developments in the bootstrap program and some of its applications.
The modern conformal and modular bootstrapread_more
HG G 43
* 27 October 2015
13:15-14:15 		Thomas Willwacher
Universität Zürich
Event Details

Talks in Mathematical Physics

Title Rational Homotopy Theory of the little disks operads
Speaker, Affiliation Thomas Willwacher, Universität Zürich
Date, Time 27 October 2015, 13:15-14:15
Location HG G 19.2
Abstract The little n-disks operads are classical objects in topology, introduced by Boardman-Vogt and May in the 1970's in their study of iterated loop spaces. They have since seen a wealth of applications in algebra and topology, and received much attention recently due to their appearance in the manifold calculus of Goodwillie and Weiss, and relatedly in the factorization (or topological chiral) homology by Lurie, Francis, Beilinson-Drinfeld and others. I report on recent joint work with V. Turchin and Benoit Fresse, in which we (mostly) settle the rational homotopy theory of the little n-disks operads, by showing that they are intrinsically formal for n>=3, and by computing the rational homotopy type of the function spaces between these objects. As an application we obtain complete rational invariants of long knots in codimension >=3. Non-specialists are particularly welcome to attend this seminar talk: I will invest some time to explain the relevant algebraic and topological notions, and to provide mathematical and historical context.
Rational Homotopy Theory of the little disks operadsread_more
HG G 19.2
29 October 2015
15:15-16:15 		Yi Sun
MIT
Event Details

Talks in Mathematical Physics

Title Traces of intertwiners for quantum affine sl2 and Felder-Varchenko functions
Speaker, Affiliation Yi Sun, MIT
Date, Time 29 October 2015, 15:15-16:15
Location HG G 43
Abstract This talk concerns two approaches for studying a family of special functions occurring in the study of the q-Knizhnik-Zamolodchikov-Bernard (q-KZB) equation. The philosophy of KZ-type equations predicts that it admits solutions via (1) traces of intertwining operators between representations of quantum affine algebras produced by Etingof-Schiffmann-Varchenko and (2) certain theta hypergeometric integrals we term Felder-Varchenko functions. In a series of papers in the early 2000's, Etingof-Varchenko conjectured that these families of solutions are related by a simple renormalization; in the trigonometric limit, they proved such a link and used it to study these functions. In recent work, I resolve the first case of the Etingof-Varchenko conjecture by showing that the traces of quantum affine sl_2-intertwiners of Etingof-Schiffmann-Varchenko valued in the 3-dimensional evaluation representation converge in a certain region of parameters and give a representation-theoretic construction of Felder-Varchenko functions. I will explain the two constructions of solutions, the methods used to relate them, and connections to affine Macdonald theory and the Felder-Varchenko conjecture on the q-KZB heat operator and corresponding SL(3,Z)-action. This talk is based on the preprint arXiv:1508.03918.
Traces of intertwiners for quantum affine sl2 and Felder-Varchenko functionsread_more
HG G 43
5 November 2015
14:15-15:15 		Jörg Schmiedmayer
Vienna University of Technology
Event Details

Talks in Mathematical Physics

Title On "solving" a quantum many body problem by experiment
Speaker, Affiliation Jörg Schmiedmayer, Vienna University of Technology
Date, Time 5 November 2015, 14:15-15:15
Location HG G 19.1
Abstract The knowledge of all correlation functions of a system is equivalent to solving the corresponding quantum many-body problem. If one can identify the relevant degrees of freedom, the knowledge of a finite set of correlation functions is in many cases sufficient to determine a sufficiently accurate solution of the corresponding field theory. Complete factorization is equivalent to identifying the relevant degrees of freedom where the Hamiltonian becomes diagonal. I will give examples how one can apply this powerful theoretical concept in experiment. Interference in a pair of tunnel-coupled one-dimensional atomic super-fluids, which realize the quantum Sine-Gordon / massive Thirring models, allows us to study if, and under which conditions the higher correlation functions factorize [1]. This allowed us to characterize the essential features of the model solely from our experimental measurements: detecting the relevant quasi-particles, their interactions and the different topologically distinct vacuum-states the quasi-particles live in. The experiment thus provides a comprehensive insights into the components needed to solve a non-trivial quantum field theory. Our examples establish a general method to analyse quantum systems through experiments. It thus represents a crucial ingredient towards the implementation and verification of quantum simulators. Work performed in collaboration with E.Demler (Harvard), Th. Gasenzer und J. Berges (Heidelberg). Supported by the Wittgenstein Prize, the Austrian Science Foundation (FWF): SFB FoQuS: F40-P10 and the EU: ERC-AdG QuantumRelax [1] T. Schweigler et al., arXiv:1505.03126
On "solving" a quantum many body problem by experimentread_more
HG G 19.1
6 November 2015
15:15-16:15 		Urs Schreiber
University of Prague
Event Details

Talks in Mathematical Physics

Title Prequantum field theory
Speaker, Affiliation Urs Schreiber, University of Prague
Date, Time 6 November 2015, 15:15-16:15
Location Y27 H 28
Abstract Classical field theory is traditionally formulated in terms of a globally defined horizontal p+1-form on the jet bundle of the field bundle. However, for interesting classes of field theories,there is no globally defined Lagrangian form, instead there is a horizontal p-gerbe with connection which constitutes a prequantization of the Euler-Lagrange form in analogy to Kostant-Souriau geometric prequantization. I discuss the general formulation and some applications of such "prequantum field theory".
Prequantum field theoryread_more
Y27 H 28
19 November 2015
15:15-16:15 		Jonathan Lorand
University of Zurich
Event Details

Talks in Mathematical Physics

Title Subspace pairs and linear relations in presymplectic and Poisson linear algebra
Speaker, Affiliation Jonathan Lorand, University of Zurich
Date, Time 19 November 2015, 15:15-16:15
Location HG G 43
Abstract We will discuss the classification of the following two kinds of objects, considering their "isotropic versions" in (finite-dimensional) presymplectic vector spaces. A corresponding classification of their "coisotropic counterparts" in Poisson vector spaces is obtained via a simple duality argument. The objects are: 1) ordered pairs of (co)isotropic linear subspaces of presymplectic/Poisson vector spaces, 2) (co)isotropic linear relations between presymplectic/Poisson vector spaces. We identify 10 indecomposable isomorphism classes in the first case, and 13 indecomposable isomorphism classes in the second case. In each case, we show that each object decomposes as a direct sum of multiples of indecomposables and we give a vector of invariants which is related to the vector of multiplicities by a matrix which is invertible over the integers. This is joint work with Alan Weinstein.
Subspace pairs and linear relations in presymplectic and Poisson linear algebraread_more
HG G 43
26 November 2015
15:15-16:15 		Joanna Kania-Bartoszynska
NSF, Arlington
Event Details

Talks in Mathematical Physics

Title Structure of the Kauffman bracket skein algebra of a surface
Speaker, Affiliation Joanna Kania-Bartoszynska, NSF, Arlington
Date, Time 26 November 2015, 15:15-16:15
Location HG G 43
Abstract Kauffman bracket skein algebra of a surface is formed by taking linear combinations of isotopy classes of framed links in a cylinder of the surface and dividing by the relation which defines the Kauffman bracket. Multiplication comes from stacking one link over the other. Kauffman bracket skein algebras are related to the SL(2,C) characters of the fundamental group of the surface. They are used in skein theoretic constructions of topological quantum field theories. It turns out that those algebras are integral domains, and that they are Frobenius when localized over non-zero characters.
Structure of the Kauffman bracket skein algebra of a surfaceread_more
HG G 43
* 1 December 2015
11:15-12:15 		Francesco Vaccarino
Politecnico di Torino
Event Details

Talks in Mathematical Physics

Title Higher Persistence: from Topological Data Analysis to BF theories via Batalin-Vilkovisky algebras
Speaker, Affiliation Francesco Vaccarino, Politecnico di Torino
Date, Time 1 December 2015, 11:15-12:15
Location Y27 H 28
Abstract We will extend the usual approach of persistent (co-)homology by considering diagrams of incidence algebras of finite posets. Then, we will show that the associated cohomology is a Batalin-Vilkovisky algebra, having as anti-laplacian a suitable dual of the Alain Connes' B operator. This technical result paves the way to build on the top of reasonable data (e.g. weighted networks) abstract BF-theories, thus connecting seemingly uncorrelated research areas as topological data analysis and topological quantum field theory.
Higher Persistence: from Topological Data Analysis to BF theories via Batalin-Vilkovisky algebrasread_more
Y27 H 28
3 December 2015
15:15-16:15 		Hanno Becker
Bonn
Event Details

Talks in Mathematical Physics

Title "Homotopy-theoretic studies of Khovanov-Rozansky Homology"
Speaker, Affiliation Hanno Becker, Bonn
Date, Time 3 December 2015, 15:15-16:15
Location HG G 43
Abstract "This talk is a summary of the results of my PhD project (written at the University of Bonn under supervision of Catharina Stroppel) the aim of which was to use homotopy theoretic methods to understand better Khovanov-Rozansky homology, a categorification of the quantum sl(k) link invariant constructed using categories of matrix factorizations. I will start by recalling the relevant definitions for matrix factorizations and the original construction of KR homology. Afterwards, I will explain a notion of weak equivalences for matrix factorizations (for which no notion of homology is available) such that with respect to this, the complexes assigned to braids in Khovanov-Rozansky homology are component-wise weakly equivalent to the respective Rouquier complexes of Soergel bimodules. In particular, we get a description of KR homology as stable Hochschild homology of Rouquier complexes, parallel to Khovanov's description of triply graded KR homology via ordinary Hochschild homology. As another application, I will define a combinatorial cut-and-join formalism - similar to the one used in the construction of Khovanov homology - computing an approximation of KR homology, allowing to calculate KR homology in simple cases."
"Homotopy-theoretic studies of Khovanov-Rozansky Homology"read_more
HG G 43
* 14 December 2015
15:15-16:15 		Terry Gannon
University of Alberta
Event Details

Talks in Mathematical Physics

Title Modular forms and Grothendieck, or swatting mosquitos with a battle-axe
Speaker, Affiliation Terry Gannon, University of Alberta
Date, Time 14 December 2015, 15:15-16:15
Location HG G 19.2
Abstract Modular forms for congruence subgroups have integer coefficients. The converse is a conjecture due to Atkin-Swinnerton-Dyer. In my talk I'll explain how Grothendieck's p-curvature conjecture, and Katz' proof of it for rigid systems, supports this. Katz' work is very deep, so it looks like overkill, but it gets results that seem hard to get in more standard ways.
Modular forms and Grothendieck, or swatting mosquitos with a battle-axeread_more
HG G 19.2
17 December 2015
15:15-16:15 		Jasper Stokman
University of Amsterdam
Event Details

Talks in Mathematical Physics

Title Elliptic solutions of dynamical Yang-Baxter equations arising from connection problems
Speaker, Affiliation Jasper Stokman, University of Amsterdam
Date, Time 17 December 2015, 15:15-16:15
Location HG G 43
Abstract Cherednik attached to a representation M of the affine Hecke algebra a consistent system of difference equations, the quantum affine Knizhnik-Zamolodchikov (KZ) equations. If M is a spin representation, i.e. of the form M=V^{\otimes n} with the generators of the affine Hecke algebra acting locally on neighbouring tensor legs, then the quantum affine KZ equations are expected to give the consistency conditions of correlation functions for the integrable spin chain associated to M. I will discuss the solution of the connection problem for quantum affine KZ equations associated to principal series representations. I will explain how this result can be used to solve the connection problem for quantum affine KZ equations associated to spin representations. As an example I will apply the theory to the Perk-Schultz integrable model. The solution of the connection problem is then expressed in terms of a new elliptic solution of the dynamical Yang-Baxter equation. The second part of the talk is joint work with Wellington Galleas.
Elliptic solutions of dynamical Yang-Baxter equations arising from connection problemsread_more
HG G 43

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