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Herbstsemester 2018

Datum / Zeit Referent:in Titel Ort
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 Workshop

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Talks in Mathematical Physics

Titel Recent progress in mathematics of topological insulators
Referent:in, Affiliation Workshop ,
Datum, Zeit NaN. undefined NaN,
Ort HIT E 51
Abstract From the perspective of mathematical physics, there have been in the recent years several significant advances in the description of topologically ordered phases of matter. In particular symmetry-protected, disordered, interacting and driven systems have been intensively studied. The definition of new topological indices, their classification and the transport properties of these systems has involved the development of new techniques from functional analysis to K-theory passing by quantum field theory. The aim of this workshop is to bring together researchers in the field to get an overview of these results and see the new perspectives they open.
Recent progress in mathematics of topological insulatorsread_more
HIT E 51
4. September 2018
15:00-17:00 		Ezra Getzler
Northwestern University
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Talks in Mathematical Physics

Titel General covariance in the Batalin-Vilkovisky formalism
Referent:in, Affiliation Ezra Getzler, Northwestern University
Datum, Zeit 4. September 2018, 15:00-17:00
Ort Y27 H 14
Abstract The Batalin-Vilkovisky classical and quantum master equations are examples of Maurer-Cartan equations. In this talk, I explain how to incorporate the action of the diffeomorphism group on the world-sheet (i.e. general covariance of the theory) into this formalism. Our approach involves the introduction of curvature in the Maurer-Cartan equation. In the absence of boundary, the curvature is central, but in the presence of boundary, this is no longer the case. As examples, I will discuss the relativistic particle, which turns out to be an AKSZ model, and the superparticle (joint work with Sean Pohorence).
General covariance in the Batalin-Vilkovisky formalismread_more
Y27 H 14
20. September 2018
15:15-16:15 		Sylvain Lavau
Max Planck Institut, Bonn
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Talks in Mathematical Physics

Titel The Universal Lie infinity-algebroid of a singular foliation
Referent:in, Affiliation Sylvain Lavau, Max Planck Institut, Bonn
Datum, Zeit 20. September 2018, 15:15-16:15
Ort HG G 43
Max Planck Institut, Boon
Abstract Any regular foliation canonically induces a 'foliation' Lie algebroid, whose anchor map is injective. What is the similar structure for a singular foliation? We show that the natural candidate would be a Lie infinity-algebroid resolving the singular foliation. We show that such a Lie infinity-algebroid structure can be defined on any resolution of the singular foliation. This Lie infinity-algebroid is universal in thesense that any two such structures are equivalent up to homotopy. In particular this implies that their cohomologies are canonically isomorphic. Then we might have some time to discuss possible applications.
The Universal Lie infinity-algebroid of a singular foliationread_more
HG G 43
Max Planck Institut, Boon
27. September 2018
15:15-16:15 		Gabriele Rembado
ETH Zurich
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Talks in Mathematical Physics

Titel Quantisation of isomonodromy systems
Referent:in, Affiliation Gabriele Rembado, ETH Zurich
Datum, Zeit 27. September 2018, 15:15-16:15
Ort HG G 43
Abstract Given a meromorphic connection on a vector bundle over a Riemann surface, it is important to study deformations of its coefficients that do not vary the (extended) monodromy data of the connection, i.e. isomonodromic deformations. Isomonodromic families define the leaves of an Ehresmann connection on a symplectic bundle of moduli spaces of meromorphic connections (over the base space of deformation parameters), and in some cases it is possible to integrate this isomonodromy connection to a time-dependent Hamiltonian system: an historical example is the Schlesinger system, which controls isomonodromic deformations of connections with simple poles on the Riemann sphere. It has been shown by Reshetikhin and Harnad that a natural deformation quantisation of the Schlesinger system yields the Knizhnik-Zamolodchikov connection of Conformal Field Theory, and in this talk we will explain how to generalise this quantisation procedure to a class of connections with higher order poles on the sphere. The result is a new family of flat (quantum) connections generalising KZ, and including the dynamical connection of Felder-Markov-Tarasov-Varchenko.
Quantisation of isomonodromy systemsread_more
HG G 43
18. Oktober 2018
15:15-16:15 		Daniel Tubbenhauer
University of Zurich
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Talks in Mathematical Physics

Titel 2-representation theory in a nutshell
Referent:in, Affiliation Daniel Tubbenhauer, University of Zurich
Datum, Zeit 18. Oktober 2018, 15:15-16:15
Ort HG G 43
Abstract This talk is an example-based introduction to the main ideas of 2-represenation theory. I will also summarize some of the latest results.
2-representation theory in a nutshellread_more
HG G 43
1. November 2018
15:15-16:15 		Pavel Safronov
Universität Zürich
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Talks in Mathematical Physics

Titel Twists of supersymmetric field theories.
Referent:in, Affiliation Pavel Safronov, Universität Zürich
Datum, Zeit 1. November 2018, 15:15-16:15
Ort HG G 19.2
Abstract In this talk I will describe the notion of twisting of supersymmetric field theories defined by Witten. This is a procedure which takes a quantum field theory and deforms it to a simpler theory which might be holomorphic or topological. I will give some examples related to 2d and 3d mirror symmetry. At the end I will also mention the formalism for twisting supergravity theories and give an example of such.
Twists of supersymmetric field theories.read_more
HG G 19.2
8. November 2018
15:15-16:15 		Leonardo Aguirre
ETH Zürich
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Talks in Mathematical Physics

Titel Finitary process evolution
Referent:in, Affiliation Leonardo Aguirre, ETH Zürich
Datum, Zeit 8. November 2018, 15:15-16:15
Ort HG G 43
Abstract Causal-State Machines form a particular class of hidden Markov models, originally introduced in the 80s for the purpose of attractor reconstruction in chaotic dynamical systems, and have since proved to be an interesting topic in their own right with regards to the information theory of stationary stochastic processes. After giving a brief overview of basic concepts, I will show how the space of (finite-state) CSMs can be equipped with a certain information-geometric structure which is tied to the problem of inferring models from finite datasets. The subject is approached by framing the inference problem in the context of artificial evolution. Leveraging insights from mathematical biology, the respective evolution superprocess is shown to exhibit a scaling limit as a generalized Kimura diffusion whose infinitesimal generator introduces a Riemannian metric on the space of CSMs through its principal symbol. The metric tensor in fact turns out to describe the local asymptotics of the relative entropy rate between output-processes of infinitesimally close CSMs. It will be discussed how these results may serve to generalize well-known phenomena from population genetics to the realm of stochastic process inference.
Finitary process evolutionread_more
HG G 43
15. November 2018
15:15-16:15 		Léa Bittmann
Université Paris Diderot
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Talks in Mathematical Physics

Titel Quantum Grothendieck rings for quantum affine algebras
Referent:in, Affiliation Léa Bittmann, Université Paris Diderot
Datum, Zeit 15. November 2018, 15:15-16:15
Ort HG G 43
Abstract Certain Grothendieck rings of categories of finite dimensional representations admit remarkable non-commutative t-deformations, which are linked to quiver varieties. These deformations are very useful to compute characters, via Kazhdan–Lusztig type decompositions. In this talk, I will present a natural t-deformation of the Grothendieck ring of a category O of representations of quantum affine algebras. Our approach is based on quantum cluster algebras.
Quantum Grothendieck rings for quantum affine algebrasread_more
HG G 43
22. November 2018
15:15-16:15 		Alessandro Malusà
University of Saskatchewan
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Talks in Mathematical Physics

Titel Hitchin-Witten connection and asymptotic expansion
Referent:in, Affiliation Alessandro Malusà, University of Saskatchewan
Datum, Zeit 22. November 2018, 15:15-16:15
Ort HG G 43
Abstract Some interesting aspects of the SU(2)-Chern-Simons theory arose from the study of its asymptotic properties in the semiclassical limit. For instance, Berezin-Toeplitz theory defines for a closed, oriented, smooth surface a family of deformations of the Poisson algebra of its moduli space of flat SU(2)-connections, parametrised by the Teichmüller space. The dependence on the parameter can be measured via the Hitchin connection, by defining a formal version of it by means of an asymptotic expansion in the mentioned limit. This presentation will focus on the problem of finding an analogue of this formal connection for the situation of SL(2,C), together with a trivialisation thereof. Although the Hitchin-Witten connection, analogous in this situation to the Hitchin connection, admits an immediate asymptotic expansion in the full (complex!) quantum parameter, the existence of a trivialisation for the corresponding formal connection has a non-vanishing cohomological obstruction. Said obstruction, however, disappears if one considers asymptotic expansions only in the imaginary part of the quantum parameter. Moreover, in the particular case of a surface of genus one, an explicit trivialisation can be found, which can also be related to an exact trivialisation of the Hitchin-Witten connection exhibited by Witten in this special case. The content of the presentation is a joint work with Jørgen Ellegaard Andersen.
Hitchin-Witten connection and asymptotic expansionread_more
HG G 43
29. November 2018
15:15-16:15 		William Petersen
Aarhuus University
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Talks in Mathematical Physics

Titel Quantum Invariants: Asymptotics and Resurgence
Referent:in, Affiliation William Petersen, Aarhuus University
Datum, Zeit 29. November 2018, 15:15-16:15
Ort HG G 43
Abstract The quantum invariant associated to a closed oriented three manifold by the Reshetikhin-Turaev TQFT, is motivated by Witten's study of quantum Chern-Simons theory and the Jones polynomial. The quantum invariant is widely believed to be a mathematical model of the partition function of Chern-Simons theory with compact gauge group. In this talk, we will briefly introduce the notion of a TQFT, and discuss the asymptotic expansion conjecture for quantum invariants. We will also discuss how resurgence analysis motivates a remarkable connection between TQFT with compact gauge group and Chern-Simons theory for the complexified gauge group. The talk is based on joint work with J.E. Andersen.
Quantum Invariants: Asymptotics and Resurgenceread_more
HG G 43
5. Dezember 2018
13:00-14:00 		Iakovos Androulidakis
Athens
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Talks in Mathematical Physics

Titel "Riemannian metrics and Laplacians for generalised smooth distributions"
Referent:in, Affiliation Iakovos Androulidakis, Athens
Datum, Zeit 5. Dezember 2018, 13:00-14:00
Ort Y27 H 26
Abstract Distributions (not necessarily integrable), possibly with singularities (generalised), appear in several geometric situations, particularly in sub-Riemannian geometry. The existence of a hypoelliptic Laplacian for such a distribution, plays a very important role in representation theory (e.g. the work of Bismut). In this lecture we discuss the geometric construction of a Laplace operator for any generalised smooth distribution and the proof of its self-adjointness and hypoellipticity. This Laplacian is geometric because it arises from our construction of a smooth Riemannian metric for any distribution as such. The latter has independent interest. This is joint work with Yuri Kordyukov.
"Riemannian metrics and Laplacians for generalised smooth distributions"read_more
Y27 H 26
6. Dezember 2018
15:15-16:15 		Iakovos Androulidakis
University of Athens
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Talks in Mathematical Physics

Titel A Baum-Connes conjecture for singular foliations and its use
Referent:in, Affiliation Iakovos Androulidakis, University of Athens
Datum, Zeit 6. Dezember 2018, 15:15-16:15
Ort HG G 43
Abstract The Baum-Connes assembly map (BC) is a far-reaching evolution of index theory. Its behaviour has deep implications in several fields, for instance topology and representation theory. In this lecture we discuss the construction of a map as such for singular foliations. It is an isomorphism under certain amenability assumptions. The construction of the map is possible due to a "nice" decomposition of the manifold in terms of dimension associated with the foliation. As such, it leads to explicit calculations which provide the "shape"' of the K-theory associated with the foliation. This information is necessary for the detection of spectral gaps of the longitudinal Laplacian. This is joint work with Georges Skandalis.
A Baum-Connes conjecture for singular foliations and its useread_more
HG G 43
* 10. Januar 2019
15:15-16:15 		Ismar Volic
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Talks in Mathematical Physics

Titel Cohomology of braids, graph complexes, and configuration space integrals
Referent:in, Affiliation Ismar Volic,
Datum, Zeit 10. Januar 2019, 15:15-16:15
Ort HG G 19.1
Abstract I will explain how three integration techniques for producing cohomology classes — Chen integrals for loop spaces, Bott-Taubes integrals for knots and links, and Kontsevich integrals for configuration spaces — come together in the computation of the cohomology of spaces of braids. The relationship between various integrals is encoded by certain graph complexes. I will also talk about the generalizations to other spaces of maps into configuration spaces (of which braids are an example). This will lead to connections to spaces of link maps and, from there, to other topics such as rope length, manifold calculus of functors, and a conjecture of Koschorke, all of which I will touch upon briefly. This is joint work with Rafal Komendarczyk and Robin Koytcheff.
Cohomology of braids, graph complexes, and configuration space integralsread_more
HG G 19.1
17. Januar 2019
15:15-16:15 		Miquel Cueca Ten
IMPA
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Talks in Mathematical Physics

Titel Applications of graded manifolds to Poisson Geometry
Referent:in, Affiliation Miquel Cueca Ten, IMPA
Datum, Zeit 17. Januar 2019, 15:15-16:15
Ort HG G 43
Abstract Since the works of Vaintrob, Severa and Roytenberg it is well known that many geometric structures that naturally arise in Poisson geometry are conveniently described in terms of graded manifolds. In this talk, I will present a characterization of positively graded manifolds and related objects (submanifolds etc) in classical geometric terms. We will then discuss various applications, such as the infinitesimal description of multiplicative Dirac structures and the relation between Lagrangian Q-submanifolds of $T^*[k+1]T[1]M$ and higher Dirac structures. Time permitting, I will mention other applications and relations with TQFT.
Applications of graded manifolds to Poisson Geometryread_more
HG G 43

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