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Autumn Semester 2013

Date / Time Speaker Title Location
19 September 2013
15:15-16:15 		Prof. Dr. Dror Bar-Natan
University of Toronto
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Talks in Mathematical Physics

Title Trees and Wheels and Balloons and Hoops
Speaker, Affiliation Prof. Dr. Dror Bar-Natan, University of Toronto
Date, Time 19 September 2013, 15:15-16:15
Location HG G 43
Trees and Wheels and Balloons and Hoops
HG G 43
* 20 September 2013
14:00-18:00 		Emanuele Latini
University of Zurich
Pierre Nolin
ETH
Cristian Vergu
ETH
Wendelin Werner
ETH
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Talks in Mathematical Physics

Title End of summer meeting in mathematical physics
Speaker, Affiliation Emanuele Latini, University of Zurich
Pierre Nolin, ETH
Cristian Vergu, ETH
Wendelin Werner, ETH
Date, Time 20 September 2013, 14:00-18:00
Location HG G 43
End of summer meeting in mathematical physics
HG G 43
26 September 2013
15:15-16:15 		Prof. Dr. Victor Turchin
Kansas State University
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Talks in Mathematical Physics

Title From manifold calculus to graph-complexes
Speaker, Affiliation Prof. Dr. Victor Turchin, Kansas State University
Date, Time 26 September 2013, 15:15-16:15
Location HG G 43
Abstract The manifold calculus is a machinery invented by Goodwillie and Weiss in order to understand spaces of embeddings from one manifold into another by splitting the source into smaller pieces. In my talk I will explain briefly the main concepts of the manifold calculus, its connection to the operad of little discs. At the end I will show how the latter operadic approach can be used to describe the rational homology and homotopy of spaces of long embeddings Emb(R^m,R^N), N>2m+1, as the homology of fairly explicit graph-complexes.
From manifold calculus to graph-complexesread_more
HG G 43
24 October 2013
15:15-16:15 		Dr. Giorgia Fortuna
ETH Zurich, Switzerland
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Talks in Mathematical Physics

Title Opers on X x X and spherical modules over affine Lie algebras at the critical level
Speaker, Affiliation Dr. Giorgia Fortuna, ETH Zurich, Switzerland
Date, Time 24 October 2013, 15:15-16:15
Location HG G 43
Abstract In this talk we will consider the category of modules over the Kac-Moody algebra at the critical level. It is known that the center of this category can be described as functions over a scheme Op_X. For every positive coweight \lambda, we can define a subscheme Op^{\lambda}_X of Op_X, and consider the subcategory of modules for the kac-moody algebra which are G[[t]]-integrable, and such that the action of the center factors through the algebra of functions on these sub-schemes. By a theorem of Gaitsgory and Frenkel, this category is equivalent to the category of quasi coherent sheaves on Op^{\lambda}_X. In this talk we will explain how to view the above categories as fibers at x\in X of some categories living over a smooth curve X. More generally, we will construct categories over X\times X that restrict to the above over the diagonal. In this framework, we will then explain a generalization of the above result over X^2, with particular interest on the geometry of the X^2-version of the sub-schemes Op^{\lambda}_X's. We will moreover relate the geometry of these schemes to the geometry of the stack of G-local systems on the disc viewed as a sub-functor of the stack of G-local systems on the punctured disc.
Opers on X x X and spherical modules over affine Lie algebras at the critical levelread_more
HG G 43
29 October 2013
15:00-16:00 		Dror Bar-Natan
Toronto
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Talks in Mathematical Physics

Title Informal Talks on the Topology, Combinatorics, and Low and High Algebra of w-Knots
Speaker, Affiliation Dror Bar-Natan, Toronto
Date, Time 29 October 2013, 15:00-16:00
Location Y03 G 95
Abstract Taylor's theorem maps smooth functions to power series. In other words, it maps the smooth to the combinatorial and algebraic, which is susceptible to an inductive degree-by-degree study. Surprisingly, there is a notion of "expansions" for topological things, which shares the spirit of the original Taylor expansion while having nothing to do with approximations of smooth functions. "w-Knots", or more generally "w-knotted objects", are knotted 2-dimensional objects in 4-dimensional space (some restrictions apply). They have a rich theory of "expansions" which takes topology into combinatorics. That combinatorics, in itself, turns out to be the combinatorics of formulas that can be written universally in arbitrary finite-dimensional Lie algebras ("low algebra"). Taylor's theorem for a certain class of w-knotted objects turns out to be equivalent to some global statements about Lie algebras and Lie groups ("Kashiwara-Vergne", "high algebra"). I will do my best to talk about all these things. "w-Knotted objects" contain the usual "u-knotted objects" (braids, knots, links, tangles, knotted graphs, etc.) and are quotients of the more general "v-knotted objects". To within reason I will also speak about the relationship of "w" with "u" and "v", where the key words are "associators" and "Lie bi-algebras", respectively. Anna asked me to talk for up to 6 hours, and that's more than I can prepare in detail in advance. Hence the adjective "informal": I have a general idea of what I want to say and much of it I've said many times before. Beyond that things will flow, if they won't stand still, chaotically and randomly.
Informal Talks on the Topology, Combinatorics, and Low and High Algebra of w-Knotsread_more
Y03 G 95
7 November 2013
15:15-16:15 		Dan Petersen
ETH Zurich
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Talks in Mathematical Physics

Title Formality of the little disk operad and the yoga of weights
Speaker, Affiliation Dan Petersen, ETH Zurich
Date, Time 7 November 2013, 15:15-16:15
Location HG G 43
Abstract I will present a short proof of a theorem of Tamarkin, that the operad of little 2-disks is formal. The proof uses the action of the Grothendieck-Teichmüller group on the chain operad of small disks, and an operadic version of a simple criterion for formality of minimal dg algebras due to Sullivan. It is inspired by the formalism of weights in the cohomology of an algebraic variety.
Formality of the little disk operad and the yoga of weightsread_more
HG G 43
13 November 2013
14:30-16:00 		Ezra Getzler
Northwestern University
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Talks in Mathematical Physics

Title Higher Lie groupoids
Speaker, Affiliation Ezra Getzler, Northwestern University
Date, Time 13 November 2013, 14:30-16:00
Location Y27 H 46
Abstract I will present my work with Kai Behrend on the construction of higher Lie groupoids in deformation theory. We show (generalizing Kuranishi) that locally, the deformations of a twisted complex of vector bundles on a compact complex manifold is represented by a higher Lie groupoid over an analytic germ. (If the complex has amplitude [a,a+n-1], it is actually a Lie n-groupoid.) Along the way, we will obtain a criterion for when a morphism of Lie n-groupoids is a weak equivalence - and show that this definition has the expected properties.
Higher Lie groupoidsread_more
Y27 H 46
14 November 2013
15:15-16:15 		Andrea Appel
Hebrew University of Jerusalem
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Talks in Mathematical Physics

Title Quasi-Coxeter structures arising from Quantum Groups
Speaker, Affiliation Andrea Appel, Hebrew University of Jerusalem
Date, Time 14 November 2013, 15:15-16:15
Location HG G 43
Abstract A quasi-Coxeter quasitriangular quasibialgebra is, informally, a bialgebra carrying actions of a given generalized braid group on its modules and Artin's braid group on their tensor product. The main example of such structure is given by Uhg the quantized universal enveloping algebra of a symmetrizable Kac-Moody algebras g, described by the universal R-matrix, the quantum Weyl group operators and their actions on integrable modules. V. Toledano Laredo proved that, for a simple complex Lie algebra g, this structure can be cohomologically transferred on Ug[[h]], the algebra of formal power series in h with coefficients in Ug. This result is a fundamental step in the proof of the monodromy conjecture, describing the quantum Weyl group operators in terms of the monodromy of the rational Casimir connection. In this talk, I will present a constructive proof, based on a modification of the Etingof-Kazhdan quantization functor, that holds for any symmetrizable Kac--Moody algebra and yields an equivalence of quasi-Coxeter categories at the level of integrable modules in category O. This talk is based on a joint work with V. Toledano Laredo (arxiv:1212.6720v2).
Quasi-Coxeter structures arising from Quantum Groupsread_more
HG G 43
21 November 2013
15:15-16:15 		Ozgur Ceyhan
University of Luxembourg
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Talks in Mathematical Physics

Title Feynman integrals, motives and periods of configuration spaces
Speaker, Affiliation Ozgur Ceyhan, University of Luxembourg
Date, Time 21 November 2013, 15:15-16:15
Location HG G 43
Abstract Mid 90's, Broadhurst and Kreimer observed that multiple zeta values persist to appear in Feynman integral computations. Following this observation, Kontsevich proposed a conceptual explanation, that is, the loci of divergence of these integrands, which are also known as graph hypersurfaces, must be mixed Tate motives. However, Belkale and Brosnan disproved this conjecture by showing that the classes of graph hypersurfaces in the Grothendieck group of varieties can be arbitrarily complicated. Since then, Aluffi, Bloch, Brown, Doryn, Esnault, Kreimer, Marcolli, Schnetz and many others collected further and counter evidences around the problem. In this talk, I will describe a way to rectify Kontsevich's proposal and show that the regularized Feynman integrals in position space setting as well as their ambiguities are given in terms of periods of suitable configuration spaces, which are mixed Tate. This talk will be based on a joint work with M. Marcolli.
Feynman integrals, motives and periods of configuration spacesread_more
HG G 43
28 November 2013
15:15-16:15 		Thomas Willwacher
Universität Zürich
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Talks in Mathematical Physics

Title The oriented graph complex
Speaker, Affiliation Thomas Willwacher, Universität Zürich
Date, Time 28 November 2013, 15:15-16:15
Location HG G 43
Abstract There exist several flavors of graph complexes in the literature, each of which controls a an algebraic deformation problem of some sort. For none of these complexes is the cohomology (the graph cohomology) known. We will see that two types of graph cohomology are identical, namely that of the oriented graph complex (defined by S. Merkulov) and that of the ordinary commutative graph complex, but in a shifted "dimension".
The oriented graph complexread_more
HG G 43
5 December 2013
15:15-16:15 		Dario Beraldo
Oxford University
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Talks in Mathematical Physics

Title Loop group actions on categories and Langlands duality
Speaker, Affiliation Dario Beraldo, Oxford University
Date, Time 5 December 2013, 15:15-16:15
Location HG G 43
Abstract In the first part of the talk, I will discuss some notions of "categorical representation theory", that is, the study of group actions on categories. Many operations in ordinary representation theory (invariants, coinvariants, duals...) still make sense in this context. In the second part, I will focus on actions by a loop group LG and introduce the concept of Whittaker invariant, which turns out to be a tool to produce Langlands dualities. For instance, the Whittaker invariant category of the affine Grassmannian for G is equivalent to the category of representations of the Langlands dual group. A factorizable generalization of this result is important for the geometric Langlands program.
Loop group actions on categories and Langlands dualityread_more
HG G 43
12 December 2013
15:15-16:15 		Daniele Valeri
SISSA, Trieste
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Talks in Mathematical Physics

Title Classical W-algebras and applications
Speaker, Affiliation Daniele Valeri, SISSA, Trieste
Date, Time 12 December 2013, 15:15-16:15
Location HG G 43
Abstract To the four fundamental physics theories: Classical Mechanics, Quantum Mechanics, Classical Field Theory and Quantum Field Theory there are corresponding algebraic structures on the space of the observables. Respectively, they are: Poisson Algebras, Associative Algebras, Poisson Vertex Algebras and Vertex Algebras. W-algebras provide a very rich family of examples, parametrized by a simple Lie algebra g and a nilpotent element f in g, which appear in all the four fundamental algebraic structures. At the classical level, they were introduced, for a principal nilpotent element f, by Drinfeld and Sokolov, in 1985, as Poisson algebras of functions on an infinite dimensional Poisson manifold, and they were used to study KdV-type integrable bi-Hamiltonian hierarchies of PDEs, known as Drinfeld-Sokolov hierarchies. In this talk I want to describe classical W-algebras as Poisson Vertex Algebras. This allows to generalize the original construction of Drinfeld and Sokolov to arbitrary nilpotent elements f and to formalize the theory of Drinfeld-Sokolov hierarchies in a rigorous and complete way.
Classical W-algebras and applicationsread_more
HG G 43
19 December 2013
15:15-16:15 		Lisa Lamberti
University of Oxford
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Talks in Mathematical Physics

Title Cluster combinatorics of type E6
Speaker, Affiliation Lisa Lamberti, University of Oxford
Date, Time 19 December 2013, 15:15-16:15
Location HG G 43
Abstract In this talk I will explain some aspects of the combinatorics appearing in cluster algebras and cluster categories associated to a Dynkin diagram of type E_6.
Cluster combinatorics of type E6read_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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