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Spring Semester 2013

Date / Time Speaker Title Location
* 31 January 2013
15:15-16:15 		Robin Koytcheff
Brown university
Event Details

Talks in Mathematical Physics

Title Homotopy Bott-taubes integrals and the Milnor triple linking number
Speaker, Affiliation Robin Koytcheff, Brown university
Date, Time 31 January 2013, 15:15-16:15
Location Y27 H 12
Abstract Bott and Taubes produced knot invariants by considering a bundle over the space of knots and integrating differential forms along its fiber. Their methods were used by D. Thurston to construct all Vassiliev invariants. They were also used by Cattaneo, Cotta-Ramusino, and Longoni to construct Vassiliev-type classes, which are real cohomology classes in spaces of knots in Euclidean space of dimension at least 4. By replacing integration of forms by a Pontrjagin–Thom construction, we can produce cohomology classes with arbitrary coefficients. We recover the Milnor triple linking number for string links via this method. Along the way, we find a description of this invariant as the degree of a certain map. More generally, we should be able to produce integral multiples of all the Vassiliev-type classes, showing that these classes are rational.
Homotopy Bott-taubes integrals and the Milnor triple linking numberread_more
Y27 H 12
28 February 2013
15:15-16:15 		Michael Polyak
Technion, Haifa
Event Details

Talks in Mathematical Physics

Title Invariants of 3-manifolds via the mapping class group and flat graphs
Speaker, Affiliation Michael Polyak, Technion, Haifa
Date, Time 28 February 2013, 15:15-16:15
Location HG G 43
Invariants of 3-manifolds via the mapping class group and flat graphs
HG G 43
7 March 2013
15:15-16:15 		Emanuele Latini
University of Zurich
Event Details

Talks in Mathematical Physics

Title Conformal geometry in the bulk and holography
Speaker, Affiliation Emanuele Latini, University of Zurich
Date, Time 7 March 2013, 15:15-16:15
Location HG G 43
Abstract In this talk we present a new approach,based on a machinery called tractor calculus, to study the relation between boundary CFT and bulk geometry. The main idea is to substitute in the interior Riemannian geometry with an almost Riemannian geometry that naturally produces the conformal boundary structure. We will discuss the ambient approach to tractors calculus and, as an example, we will show how to write down Maxwell like equations within this formalism. Our main goal will be then to solve higher form Proca equation on Einstein manifold with boundary data along conformal infinity. To this aim we will first construct the exterior tractor calculus and study the cohomology of the Thomas-D operator. We will show then how to solve Laplace-type boundary problems formally, and to all orders, by constructing an operator which projects arbitrary forms to solutions.
Conformal geometry in the bulk and holographyread_more
HG G 43
21 March 2013
15:15-16:15 		Prof. Dr. Joachim Kock
Universitat Autònoma de Barcelona
Event Details

Talks in Mathematical Physics

Title Polynomial functors over groupoids, and combinatorial Dyson-Schwinger equations
Speaker, Affiliation Prof. Dr. Joachim Kock, Universitat Autònoma de Barcelona
Date, Time 21 March 2013, 15:15-16:15
Location HG G 43
Abstract Polynomial functors are essentially functors defined in terms of sums, products, and exponentiation. They can be seen as a categorification of elementary arithmetic, but they also constitute a general machinery for encoding and handling combinatorial structures and data types. Groupoid coefficients rather than set coefficients are needed to transparently handle symmetries, like those occurring in Feynman graphs. The real Dyson-Schwinger equation are the 'quantum equations of motion'. I will only talk about their combinatorial skeleton, Kreimer's combinatorial Dyson-Schwinger equations, which are fixpoint equations whose solutions are certain series of graphs or trees. I will explain how any polynomial endofunctor P generates a free monad, whose operations form a groupoid of P-trees, which is a solution to an abstract combinatorial Dyson-Schwinger equation X=1+P(X), and satisfies a Faà di Bruno formula in the Connes-Kreimer bialgebra of P-trees. Analogous results for Feynman graphs are obtained by specialising to certain endofunctors P given in terms of interaction labels and 1PI primitive graphs. Many of the ideas involved originate in the theory of inductive data types. If time permits, I may say something about that.
Polynomial functors over groupoids, and combinatorial Dyson-Schwinger equationsread_more
HG G 43
* 26 March 2013
15:15-16:15 		Dr. Alejandro Cabrera
Departamento de Matematica Aplicada, UFRJ, Rio de Janeiro, Brasil
Event Details

Talks in Mathematical Physics

Title On infinite dimensional geometry and Topological Field Theories
Speaker, Affiliation Dr. Alejandro Cabrera, Departamento de Matematica Aplicada, UFRJ, Rio de Janeiro, Brasil
Date, Time 26 March 2013, 15:15-16:15
Location Y27 H 25
Abstract We shall introduce so-called Dirac structures (which generalize symplectic and Poisson structures as well as integrable distributions at once) on infinite dimensional manifolds and consider their reduction by infinite dimensional groups of symmetries. We present an application of this construction on spaces of principal connections and obtain known finite dimensional geometric structures as reductions (eg: the Cartan-Dirac structure over a Lie group, group valued moment maps). Finally, we elaborate on how to try to apply these ideas to obtain an 'extended' description of classical Chern-Simons theory.
On infinite dimensional geometry and Topological Field Theoriesread_more
Y27 H 25
11 April 2013
15:15-16:15 		Philip Boalch
ENS, Paris, France
Event Details

Talks in Mathematical Physics

Title Geometry of moduli spaces of connections on curves
Speaker, Affiliation Philip Boalch, ENS, Paris, France
Date, Time 11 April 2013, 15:15-16:15
Location HG G 43
Abstract The aim of this talk is to describe some basic situations where moduli spaces of meromorphic connections on vector bundles on complex algebraic curves arise. Subsequently it will be shown how these examples are linked together and may be generalised. The themes I hope to cover include: a) Quantum differential equations and nonlinear braid group actions in the theory of semisimple Frobenius manifolds b) Drinfeld-Jimbo quantum groups, Poisson Lie groups and the quantum Weyl group actions c) Hitchin integrable systems, their meromorphic and genus zero versions (related to work of Moser and Adams-Harnad-Hurtubise-Previato) and their deformations: isomonodromy systems If time permits I will describe some of the philosophy (and theorems) of nonabelian Hodge theory underlying this circle of ideas, and the (new) hyperkahler manifolds that arise. Main references: a) Stokes Matrices, Poisson Lie Groups and Frobenius Manifolds Invent. Math. 146, (2001) 479-506 b) Symplectic Manifolds and Isomonodromic Deformations Adv. in Math. 163, (2001) 137-205 c) Wild non-abelian Hodge theory on curves (with O. Biquard) Compos. Math. 140 (2004), no. 1, 179-204
Geometry of moduli spaces of connections on curvesread_more
HG G 43
* 12 April 2013
11:15-12:15 		Philip Boalch
ENS, Paris, France
Event Details

Talks in Mathematical Physics

Title Geometric braid group actions
Speaker, Affiliation Philip Boalch, ENS, Paris, France
Date, Time 12 April 2013, 11:15-12:15
Location HG G 43
Abstract I will explain how the well-known symplectic actions of braid and mapping class groups on character varieties (spaces of representations of the fundamental group of a Riemann surface) have a natural generalisation when one considers moduli spaces of wild/irregular connections on curves. The simplest perspective is to generalize the notion of `algebraic curve with marked points'(which appears in the usual, tame, setting) to the notion of an `irregular curve'. The "wild mapping class group" then appears as the fundamental group of the moduli space of admissible deformations of an irregular curve, generalising the usual moduli space of curves. These actions arise by integrating a natural nonlinear connection, called the (irregular) isomonodromy connection or the nonabelian Gauss-Manin connection, on a family of wild character varieties fibred over a space of admissible deformations of irregular curves. Mathematically it seems there is just one class of completely natural nonlinear flat connections, so it is not surprising that they appear in many different places. The simplest example (from 2001) explains the geometry underlying the "quantum Weyl group" action defined by generators and relations by Lusztig, Soibelman, and Kirillov-Reshetikhin. One possible way to describe these connections is via wall-crossing formulae reminiscent of those of Kontsevich-Soibelman. Main references: a) G-bundles, Isomonodromy and Quantum Weyl Groups Int. Math. Res. Not. 22, (2002) 1129-1166 (arXiv:0108152) b) Geometry and braiding of Stokes data; Fission and wild character varieties Annals of Math., to appear (arXiv:1111.6228)
Geometric braid group actionsread_more
HG G 43
* 12 April 2013
14:00-15:00 		Philip Boalch
ENS, Paris, France
Event Details

Talks in Mathematical Physics

Title Simply-laced isomonodromy systems
Speaker, Affiliation Philip Boalch, ENS, Paris, France
Date, Time 12 April 2013, 14:00-15:00
Location HG G 19.2
Abstract In this talk some of the simplest examples of (irregular) isomonodromy systems will be considered in detail (as systems of integrable nonlinear differential equations), generalising the isomonodromy system of Jimbo-Miwa-Mori-Sato (1979) that they studied in relation to the quantum nonlinear Schrodinger equation. In particular a link with Nakajima quiver varieties will be described. This leads to a precise relation between moduli spaces of connections on curves and many Kac-Moody root systems/Weyl groups. In particular it explains the Okamoto (affine Weyl group) symmetries of the fourth, fifth and sixth Painleve equations, and puts these symmetries into the larger context of Weyl groups for not-necessarily-affine Kac-Moody root systems. On one hand this explains why there are such symmetries, via the Fourier-Laplace transform, and on the other hand it shows where such exotic root systems occur in nature. The appearance of such root systems and Weyl groups, beyond the affine case, seems to distinguish this theory from earlier work on soliton equations. Such (nonlinear) isomonodromy systems often have "quantum" (or "linear") analogues. For example Schlesinger system quantizes to the KZ connection and similarly the JMMS system quantizes to the the FMTV connection, of Felder-Markov-Tarasov-Varchenko (2000). This work on simply-laced isomonodromy systems suggests there are more quantum connections generalizing the KZ and FMTV connections. Main references: a) Irregular connections and Kac-Moody root systems June 2008 (arXiv:0806.1050) b) Simply-laced isomonodromy systems Publ. Math. IHES 116, No. 1 (2012) 1-68 (arXiv:1107.0874)
Simply-laced isomonodromy systemsread_more
HG G 19.2
18 April 2013
15:15-16:15 		Anton Khoroshkin
Stony Brook
Event Details

Talks in Mathematical Physics

Title Highest weight categories and orthogonal polynomials
Speaker, Affiliation Anton Khoroshkin, Stony Brook
Date, Time 18 April 2013, 15:15-16:15
Location HG G 43
Abstract I will explain the approach to the representation theory of nonsemisimple Lie algebras with anti-involution based on the notion of highest weight categories. The classical example of a highest weight category is known as the category$\mathcal{O}$ after Bershtein-Gelfand-Gelfand. I will try to explain that certain assumptions on the weight decomposition of a given nonsemisimple  Lie algebra $a$ implies a lot of common useful properties ofthe category of $a$-modules such as BGG duality, excellent filtrations and the theory of tilting modules.As a corollary I will explain that the characters of corresponding Verma modules for current Lie algebra $g\otimes C[t]$ are specialization of MacDonald polynomials what follows the Schur positivity of these polynomials.The talk does not expect any deep background in representation theory and should be understandable for nonspecialists.
Highest weight categories and orthogonal polynomialsread_more
HG G 43
25 April 2013
15:15-16:15 		Dr. Ajay Ramadoss
ETH Zurich
Event Details

Talks in Mathematical Physics

Title Stable representation homology
Speaker, Affiliation Dr. Ajay Ramadoss, ETH Zurich
Date, Time 25 April 2013, 15:15-16:15
Location HG G 43
Abstract Recently, the derived scheme DRep_n(A) of the classical representation scheme Rep_n(A) has been studied. One of the main results in this direction has been the construction of higher trace maps HC_k(A)-->H_k(DRep_n(A))^{GL_n} extending the usual characters to higher cyclic homology. These maps define a homomorphism of graded commutative algebras Sym(Tr_n): Sym(HC(A))--->H(DRep_n(A))^{GL_n}. Given a well known theorem of Procesi, it is natural to ask whether the above homomorphism is surjective. We study this question for augmented algebras. In this case, our main result shows that on passing to the inverse limit (as n approaches infinity), Sym(Tr_n) converges to an isomorphism between Sym(HC(A)) and H(DRep^{Tr}(A)) where DRep^{Tr}(A) is a canonical dense DG subalgebra of DRep_{\infty](A)^{GL_{\infty}}. A derived version of Procesi's theorem is therefore, true in the limit. However, for finite n, there are homological obstructions to a derived Procesi theorem. Explicit examples show that these obstructions do not vanish in general. Time permitting, we will discuss how one can use our main result to obtain interesting combinatorial identites by computing Euler characteri stics on both sides... (Joint work with Yuri Berest & partly with Giovanni Felder)
Stable representation homologyread_more
HG G 43
* 21 May 2013
15:15-16:15 		Dr. Ryan Grady
Boston University
Event Details

Talks in Mathematical Physics

Title Ricci flow and the space of quantum field theories
Speaker, Affiliation Dr. Ryan Grady, Boston University
Date, Time 21 May 2013, 15:15-16:15
Location HG G 19.2
Abstract In this talk I aim to make precise the statement of Friedan (1980's) that the \beta function of the nonlinear \sigma model is given by the Ricci curvature of the target manifold. Working in Costello's approach to perturbative field theory, I will define a version of the nonlinear \sigma model, set up the machinery of the \beta function, and give a proof of Friedan's result. If time permits I will also discuss work on the observables in this nonlinear \sigma model. The talk is based on joint work with Si Li (Boston U).
Ricci flow and the space of quantum field theoriesread_more
HG G 19.2
* 22 May 2013
13:15-14:15 		Prof. Dr. Alexander Berglund
University of Copenhagen
Event Details

Talks in Mathematical Physics

Title Rational homotopy theory of automorphisms of highly connected manifolds
Speaker, Affiliation Prof. Dr. Alexander Berglund, University of Copenhagen
Date, Time 22 May 2013, 13:15-14:15
Location HG G 43
Abstract I will talk about joint work with Ib Madsen on the cohomology of automorphism groups of high dimensional manifolds, and on the rational homotopy types of their classifying spaces. We prove an analog of Harer's stability theorem for a family of highly connected manifolds. When calculating the stable cohomology of their homotopy automorphisms, certain Lie algebras of symplectic derivations show up that have appeared before in Kontsevich's work on the homology of outer automorphism groups of free groups.
Rational homotopy theory of automorphisms of highly connected manifoldsread_more
HG G 43
23 May 2013
15:15-16:15 		Matthias Christandl
ETH Zurich
Event Details

Talks in Mathematical Physics

Title From Pauli's Principle to Fermionic Entanglement
Speaker, Affiliation Matthias Christandl, ETH Zurich
Date, Time 23 May 2013, 15:15-16:15
Location HG G 43
Abstract The Pauli exclusion principle is a constraint on the natural occupation numbers of fermionic states. It has been suspected for decades, and only proved very recently, that there is a multitude of further constraints on these numbers, generalizing the Pauli principle. Surprisingly, these constraints are linear: they cut out a geometric object known as a polytope. This is a beautiful mathematical result, but are there systems whose physics is governed by these constraints? In order to address this question, we studied a system of a few fermions connected by springs. As we varied the spring constant, the occupation numbers moved within the polytope. The path they traced hugs very close to the boundary of the polytope, suggesting that the generalized constraints affect the system. I will mention the implications of these findings for the structure of few-fermion ground states and then discuss the relation between the geometry of the polytope and different types of fermionic entanglement.
From Pauli's Principle to Fermionic Entanglementread_more
HG G 43
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Event Details

Talks in Mathematical Physics

Title Workshop on Analytical Aspects of Mathematical Physics
Speaker, Affiliation
Date, Time NaN undefined NaN,
Location HIT E 51
Abstract Speakers include: Yosi Avron (Haifa) Sven Bachmann (Davis) Detlev Buchholz (Goettingen) Ivan Corwin (Cambridge) Wojciech DeRoeck (Heidelberg) Jon Dimock (Buffalo) Hugo Duminil-Copin (Geneva) Bertrand Duplantier (Saclay) Alessandro Giuliani (Rome) John Imbrie (Charlottesville) Christian Jäkel (Sao Paulo) Ivo Kälin (Zürich) Roy Kerr (Christchurch) Antti Knowles (New York) Joachim Krieger (Lausanne) Mathieu Lewin (Cergy-Pontoise) Vieri Mastropietro (Milano) Michael Reiterer (Zürich) Benjamin Schlein (Bonn) Stanislav Smirnov (Geneva) Thomas Spencer (Princeton) Simone Warzel (Munich) Thomas Willwacher (Zürich) Horng-Tzer Yau (Cambridge) Jakob Yngvason (Vienna)
Workshop on Analytical Aspects of Mathematical Physicsread_more
HIT E 51
30 May 2013
15:15-16:15 		Dr. Bruno Vallette
Université de Nice
Event Details

Talks in Mathematical Physics

Title Givental action is homotopy gauge symmetry
Speaker, Affiliation Dr. Bruno Vallette, Université de Nice
Date, Time 30 May 2013, 15:15-16:15
Location HG G 43
Abstract I will prove that the Givental action on genus zero cohomological field theories, also known as hypercommutative algebras, is equal to the gauge symmetry action on Maurer-Cartan elements of the homotopy Lie algebra encoding homotopy Batalin-Vilkovisky algebras. This equivalent description allows us to extend the Givental action to homotopy hypercommutative algebras, i.e. from the homology level to the chain level. [Joint work with Vladimir Dotsenko and Sergei Shadrin. Reference: arxiv.org/1304.3343]
Givental action is homotopy gauge symmetryread_more
HG G 43
6 June 2013
15:15-16:15 		Jose Antonio de la Peña
Guanajuato, México
Event Details

Talks in Mathematical Physics

Title Tame and wild algebras
Speaker, Affiliation Jose Antonio de la Peña, Guanajuato, México
Date, Time 6 June 2013, 15:15-16:15
Location HG G 43
Abstract We shall discuss tameness and wildness of finite dimensional algebras (associative, with identity) over an algebraically closed field, with respect to the complexity of their finite dimensional representations (modules). We will devote special attention to combinatorial and geometric criteria allowing to decide the tameness of distinguished classes of finite dimensional algebras, as well as describe their indecomposable finite dimensional representations. A prominent role will be played by bound quiver presentations of finite dimensional algebras and the associated Tits quadratic forms.
Tame and wild algebrasread_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.

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

Archive: 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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