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Autumn Semester 2014

Date / Time Speaker Title Location
19 September 2014
14:00-18:00 		Samuel Monnier
Universität Zürich
Marcello Porta
Universität Zürich
Junliang Shen
ETH Zurich
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Talks in Mathematical Physics

Title End of summer meeting & SwissMAP presentation
Speaker, Affiliation Samuel Monnier, Universität Zürich
Marcello Porta, Universität Zürich
Junliang Shen, ETH Zurich
Date, Time 19 September 2014, 14:00-18:00
Location HG G 19.1
Abstract Programme 14:00 – 14:45 Samuel Monnier, Finite higher spin symmetries 15:00 – 15:45 Marcello Porta, Mean-field evolution of fermionic systems —Tea— 16:15 – 17:00 Junliang Shen, Cobordism invariants of the moduli space of stable pairs 17:15 – 18:00 Giovanni Felder, Presentation of SwissMAP and discussion
End of summer meeting & SwissMAP presentationread_more
HG G 19.1
9 October 2014
15:15-16:15 		Martin Lohmann
ETH Zurich, Switzerland
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Talks in Mathematical Physics

Title Cluster expansions for uncondensed many Boson systems
Speaker, Affiliation Martin Lohmann, ETH Zurich, Switzerland
Date, Time 9 October 2014, 15:15-16:15
Location HG G 43
Abstract The truncated correlation functions of a grand canonical gas of Bosons can be computed (formally and also rigorously) via so called coherent state functional integrals. We discuss how cluster expansions can be used to analyze these functional integral representations in the uncondensed phase, and how they prove exponential decay of correlations.
Cluster expansions for uncondensed many Boson systemsread_more
HG G 43
14 October 2014
15:15-17:00 		Joel Kamnitzer
University of Toronto
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Talks in Mathematical Physics

Title SwissMAP minicourse: Representation theory, geometric Langlands duality and categorification I
Speaker, Affiliation Joel Kamnitzer, University of Toronto
Date, Time 14 October 2014, 15:15-17:00
Location HG G 19.2
Abstract The representation theory of reductive groups, such as the group GL_n of invertible complex matrices, is an important topic, with applications to number theory, algebraic geometry, mathematical physics, and quantum topology. One way to study this representation theory is through the geometric Satake correspondence (also known as geometric Langlands duality). This correspondence relates the geometry of spaces called affine Grassmannians with the representation theory of reductive groups. This correspondence was originally developed from the viewpoint of the geometric Langlands program, but it has many other interesting applications. For example, this correspondence can be used to construct knot homology theories in the framework of categorification. In my lecture, I will begin by explaining the representation theory of reductive groups, using GL_n as a concrete example. I will then the explain geometric Satake correspondence. I will conclude by explaining how this can be used for the purposes of categorification. Required background: Basic graduate algebra and topology. Some knowledge of compact Lie groups or semisimple Lie algebras would be helpful, but not required. Literature: Fulton and Harris, Representation theory, a first course. J. Kamnitzer, Lectures on geometric constructions of the irreducible representations of GL_n, 0912.0569. V. Ginzburg, Perverse sheaves on a loop group and Langlands duality, alg-geom/9511007. S. Cautis and J. Kamnitzer, Knot homology via derived categories of coherent sheaves II, sl(m) case, arXiv:0710.3216.
SwissMAP minicourse: Representation theory, geometric Langlands duality and categorification Iread_more
HG G 19.2
16 October 2014
15:15-17:00 		Joel Kamnitzer
University of Toronto
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Talks in Mathematical Physics

Title Representation theory, geometric Langlands duality and categorification II
Speaker, Affiliation Joel Kamnitzer, University of Toronto
Date, Time 16 October 2014, 15:15-17:00
Location HG G 43
Representation theory, geometric Langlands duality and categorification II
HG G 43
21 October 2014
15:15-17:00 		Joel Kamnitzer
University of Toronto
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Talks in Mathematical Physics

Title Representation theory, geometric Langlands duality and categorification III
Speaker, Affiliation Joel Kamnitzer, University of Toronto
Date, Time 21 October 2014, 15:15-17:00
Location HG G 19.2
Representation theory, geometric Langlands duality and categorification III
HG G 19.2
23 October 2014
15:15-17:00 		Joel Kamnitzer
University of Toronto
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Talks in Mathematical Physics

Title Representation theory, geometric Langlands duality and categorification IV
Speaker, Affiliation Joel Kamnitzer, University of Toronto
Date, Time 23 October 2014, 15:15-17:00
Location HG G 43
Representation theory, geometric Langlands duality and categorification IV
HG G 43
* 6 November 2014
14:15-15:15 		Joan Millès
Université de Toulouse
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Talks in Mathematical Physics

Title Complex manifolds as homotopy algebras
Speaker, Affiliation Joan Millès, Université de Toulouse
Date, Time 6 November 2014, 14:15-15:15
Location HG G 19.2
Abstract A complex structure is an almost complex structure which is integrable. A local description of such a structure reveals a lot of algebraic equations. Sergei Merkulov has studied the Nijenhuis integrability condition and he has proposed a simple interpretation of the equations characterizing Nijenhuis structures in terms of homotopy algebras. Following this attempt to define "homotopy geometry", we make use of the curved Koszul duality and of a hint of differential geometry to describe complex manifolds as homotopy algebras.
Complex manifolds as homotopy algebrasread_more
HG G 19.2
12 November 2014
13:15-15:00 		Ivan Cherednik
UNC Chapel Hill
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Talks in Mathematical Physics

Title DAHA superpolynomials of iterated torus knots
Speaker, Affiliation Ivan Cherednik, UNC Chapel Hill
Date, Time 12 November 2014, 13:15-15:00
Location HG G 43
Abstract The DAHA-Jones polynomials (refined, with an extra parameter) of iterated torus knots, including all algebraic knots, will be defined for any root systems and weights. Conjecturally, they generalize the Jones-WRT invariants based on Quantum Groups, which was checked for torus knots in types A-C. For A_n, the DAHA-Jones polynomials can be combined in one superpolynomial, presumably coinciding with the stable Khovanov-Rozansky one for sl(n+1) of the corresponding knot and superpolynomials via the M5 theory (the BPS states, String Theory); the latter approach is not mathematically rigorous. The DAHA-superpolynomials match the superpolynomials obtained from perfect modules of rational DAHA (Gorsky, Oblomkov, Rasmussen, Shende), though using rational DAHA is restricted to the torus knots and (so far) only to the unclored polynomials. Conjecturally, DAHA provides the formulas for Betti numbers of Jacobian factors of plane singularities, which are very difficult to calculate in algebraic geometry. This is a great test of the maturity of the new theory, closely related to the Oblomkov-Rasmussen-Shende conjecture.
DAHA superpolynomials of iterated torus knotsread_more
HG G 43
13 November 2014
15:15-16:30 		Ivan Cherednik
UNC Chapel Hill
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Talks in Mathematical Physics

Title Global hypergeometric and Whittaker functions
Speaker, Affiliation Ivan Cherednik, UNC Chapel Hill
Date, Time 13 November 2014, 15:15-16:30
Location HG G 43
Abstract The lecture will be devoted to the new theory of global difference hypergeometric and Whittaker functions, one of the major applications of the double affine Hecke algebras and a breakthrough in the classical harmonic analysis. They integrate the Ruijsenaars-Macdonald difference QMBP and "q-Toda" (any root systems), and are analytic everywhere ("global") with superb asymptotic behavior. The definition of the global functions was suggested about 14 years ago; it is conceptually different from the definition Heine gave in 1846, which remained unchanged and unchallenged since then. The analytic theory of these functions was completed only recently (the speaker and J. Stokman). If time permits, the connection of the Harish-Chandra theory of global q-Whittaker functions will be discussed with the Givental-Lee formula (Gromov-Witten K-theoretic invariants of flag varieties) and that due to Braverman and Finkelberg (affine flag varieties).
Global hypergeometric and Whittaker functionsread_more
HG G 43
27 November 2014
15:15-16:15 		Alessandro Valentino
Hamburg
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Talks in Mathematical Physics

Title Boundary conditions for extended TQFTs, anomalies and representations of the mapping class group
Speaker, Affiliation Alessandro Valentino, Hamburg
Date, Time 27 November 2014, 15:15-16:15
Location HG G 43
Abstract In this talk I will present a recent work together with Domenico Fiorenza on topological quantum field theories on manifolds with boundaries. Using infinity-category theory, we develop a formalism to relate extended TQFTs with boundary conditions to lower dimensional theories with anomalies, which in specific situations give rise to projective representations of the mapping class group of surfaces. This involves a higher categorical generalisation of the notion of a group character. Time permitting, I will also argue that in the fully extended case the converse holds, i.e. an anomalous theory contains the right amount of information to obtain a fully extended theory in higher dimensions equipped with boundary conditions.
Boundary conditions for extended TQFTs, anomalies and representations of the mapping class groupread_more
HG G 43
4 December 2014
15:15-16:15 		Kasia Rejzner
University of York
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Talks in Mathematical Physics

Title Renormalized quantum BV formalism in the Epstein-Glaser framework
Speaker, Affiliation Kasia Rejzner, University of York
Date, Time 4 December 2014, 15:15-16:15
Location HG G 43
Abstract The causal perturbation theory approach to renormalization, based on the seminal paper of Epstein and Glaser from 1973, is a mathematically rigorous framework which allows to study foundations of perturbative QFT. In this talk I will explain how to incorporate the BV formalism into this framework and derive rigorously the renormalized Quantum Master Equation.
Renormalized quantum BV formalism in the Epstein-Glaser frameworkread_more
HG G 43
11 December 2014
14:15-15:15 		Marco Zambon
University of Madrid
Details

Talks in Mathematical Physics

Title Equivalences of coisotropic submanifolds
Speaker, Affiliation Marco Zambon, University of Madrid
Date, Time 11 December 2014, 14:15-15:15
Location HG G 19.2
Abstract Fix a coisotropic submanifold C in a symplectic manifold. We consider the space of coisotropic submanifolds nearby C. A natural geometric notion of equivalence there is given by Hamiltonian equivalence. On the other hand, there is algebraic characterization of the coisotropic submanifolds near C, as Maurer-Cartan elements of a certain L-infinity algebra introduced by Oh-Park in 2003, which gives rise to an algebraic equivalence. We show that both notions of equivalence agree. Further, we carry out an analog discussion for the equivalence by symplectomorphisms, and present examples. This is joint work in progress with Florian Schätz (QGM Aarhus).
Equivalences of coisotropic submanifoldsread_more
HG G 19.2
18 December 2014
15:15-16:15 		Sara Pasquetti
University of Surrey
Details

Talks in Mathematical Physics

Title Holomorphic Blocks and q-deformed correlators
Speaker, Affiliation Sara Pasquetti, University of Surrey
Date, Time 18 December 2014, 15:15-16:15
Location HG G 43
Abstract In this talk I will discuss how supersymmetric partition functions on various compact manifolds in two, three, four and five dimensions can be expressed in terms of a universal set of building blocks, the holomorphic blocks. Two and four dimensional holomorphic blocks can be reinterpreted as conformal blocks in Liouville theory through the Alday-Gaiotto-Tachikawa correspondence. I will provide a similar realisation of three and five dimensional holomorphic blocks in a q-deformed version of Liouville theory where the Virasoro algebra is replaced by the q-deformed Virasoro algebra.
Holomorphic Blocks and q-deformed correlatorsread_more
HG G 43

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

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

Archive: AS 24 SS 24 AS 23 SS 23 AS 22 SS 22 AS 21 SS 21 AS 20 SS 20 AS 19 SS 19 AS 18 SS 18 AS 17 SS 17 AS 16 SS 16 AS 15 SS 15 AS 14 SS 14 AS 13 SS 13 AS 12 SS 12 AS 11

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