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Spring Semester 2018

Date / Time Speaker Title Location
22 February 2018
15:15-16:15 		Julien Ducoulombier
ETH Zurich
Event Details

Talks in Mathematical Physics

Title Swiss-Cheese operad and applications to spaces of embeddings
Speaker, Affiliation Julien Ducoulombier, ETH Zurich
Date, Time 22 February 2018, 15:15-16:15
Location HG G 43
Abstract During this talk, I would like to give an overview of the (relative) delooping theorems as well as applications to spaces of long embeddings. In particular, we show that the space of long embeddings and the space of (k)-immersions from R^d to R^m are weakly equivalent to an explicit d-iterated loop space and an explicit d-iterated relative loop space, respectively. Both of them can be expressed in term of derived mapping spaces of coloured operads. Such a pair is a typical example of Swiss-Cheese algebra.
Swiss-Cheese operad and applications to spaces of embeddingsread_more
HG G 43
1 March 2018
15:15-16:15 		Michael Ehrig
University of Sidney
Event Details

Talks in Mathematical Physics

Title Functoriality of link homologies and higher representation theory
Speaker, Affiliation Michael Ehrig, University of Sidney
Date, Time 1 March 2018, 15:15-16:15
Location HG G 43
Abstract In the talk I will discuss how to obtain functoriality for coloured Khovanov–Rozansky homology. This uses a foam category constructed via a foam evaluation by Robert–Wagner and deformation techniques. This is joint work with Daniel Tubbenhauer and Paul Wedrich.
Functoriality of link homologies and higher representation theoryread_more
HG G 43
8 March 2018
15:15-16:15 		Anton Khoroshkin
HSE Moscow
Event Details

Talks in Mathematical Physics

Title Cacti groups, real locus of Deligne-Mumford compactification Mbar_{0,n+1}
Speaker, Affiliation Anton Khoroshkin, HSE Moscow
Date, Time 8 March 2018, 15:15-16:15
Location HG G 43
Abstract The real locus of Deligne-Mumford compactification $\bar{M_{0,n+1}}(R)$ is known to be the Eilenberg-Maclane space of the so called pure cacti group. This group has a lot of common properties with pure braid group. In particular, (pure) cacti group acts naturally on tensor products of representations of quantum groups $U_q(g)$. This action has a well-defined simple combinatorial limit for $q \to 0$. I will report on old and new results on the (pure) cacti group. In particular, I will explain how the language of operads provides the description of the rational homotopy type of $\bar{M_{0,n+1}}(R)$. The talk is based on the joint work with Thomas Willwacher.
Cacti groups, real locus of Deligne-Mumford compactification Mbar_{0,n+1}read_more
HG G 43
15 March 2018
15:15-16:15 		Nikita Nikolaev
Université de Genève
Event Details

Talks in Mathematical Physics

Title Abelianisation of logarithmic connections
Speaker, Affiliation Nikita Nikolaev, Université de Genève
Date, Time 15 March 2018, 15:15-16:15
Location HG G 43
Abstract We will describe an approach to studying meromorphic connections on vector bundles of higher rank in terms of simpler objects: meromorphic connections on line bundles (aka abelian connections). Roughly speaking, given a connection on a vector bundle over a complex curve X, we extract the asymptotic information at the poles and encode it in a flat line bundle over another complex curve Σ which is an appropriate cover Σ -> X. This approach is called abelianisation, because the nonabelian holonomy data of a connection on X of higher rank is put in equivalence with abelian holonomy data of an abelian connection on Σ. We will explain how abelianisation sets up an equivalence of categories.
Abelianisation of logarithmic connectionsread_more
HG G 43
21 March 2018
13:15-15:00 		Francesco Bonechi
INFN Florence
Event Details

Talks in Mathematical Physics

Title Shifted Poisson structures on differentiable stacks
Speaker, Affiliation Francesco Bonechi, INFN Florence
Date, Time 21 March 2018, 13:15-15:00
Location Y27 H 12
Shifted Poisson structures on differentiable stacks
Y27 H 12
22 March 2018
15:15-16:15 		Domenico Fiorenza
Università di Roma
Event Details

Talks in Mathematical Physics

Title T-duality in rational homotopy theory
Speaker, Affiliation Domenico Fiorenza, Università di Roma
Date, Time 22 March 2018, 15:15-16:15
Location HG G 43
Abstract A topological T-duality configuration is the datum of two U(1)-principal bundles P and Q over the same base B together with a trivialization of their cup product 2-gerbe. As shown by Bunke and Schick, such a configuration induces a shifted isomorphism between the twisted K-theories of the total spaces P and Q. When seen in the approximation given by rational homotopy theory, this result translates into an shifted isomorphism between twisted cohomologies of central extensions of L-infinity algebras. Remarkably, this algebraic statement can be given a very quick and simple proof, coming with an explicit Fourier-transform-type formula for translating twisted cocycles for an L-infty algebra into twisted cocycles for its T-dual. This formula was known to the string theory literature as Hori's formula. Based on joint work with Hisham Sati and Urs Schreiber.
T-duality in rational homotopy theoryread_more
HG G 43
* 12 April 2018
14:00-15:00 		Riccardo Iraso
SISSA Trieste
Event Details

Talks in Mathematical Physics

Title 2d Yang-Mills in BV-BFV formalism
Speaker, Affiliation Riccardo Iraso, SISSA Trieste
Date, Time 12 April 2018, 14:00-15:00
Location HG G 43
Abstract The BV-BFV formalism gives a general functorial approach to the quantization of gauge theories on manifolds with boundary. In this talk I will review the basics of the BV-BFV formalism and discuss its application to 2-dimensional Yang-Mills theory. The extension of the formalism to manifolds with corners allows to complete the analysis and compute the complete perturbative solution on surfaces with arbitrary genus.
2d Yang-Mills in BV-BFV formalismread_more
HG G 43
12 April 2018
15:15-16:15 		Benjamin Enriquez
Université de Strasbourg
Event Details

Talks in Mathematical Physics

Title A Betti counterpart of the harmonic coproduct (joint w. H. Furusho)
Speaker, Affiliation Benjamin Enriquez, Université de Strasbourg
Date, Time 12 April 2018, 15:15-16:15
Location HG G 43
Abstract In earlier work, we proved that Racinet's double shuffle group is the stabilizer of the harmonic coproduct defined on a subalgebra of the free algebra over two generators relative to a certain action on this algebra. This leads to the construction of a new coproduct on the same algebra. The double shuffle torsor can then be described as the set of elementstaking the harmonic coproduct to the new coproduct. We identify the new coproduct with an explicit coproduct of a suitable subalgebra of the algebra of the free group with two generators. The proof relies on an interpretationof the harmonic coproduct in terms of infinitesimal braid Lie algebras, which is implicit in the unpublished work of Deligne and Terasoma from 2005. We will try to explain how this work leads the construction of the "Betti side" of the double shuffle torsor. (Par ailleurs, notre preprint sur le sujet est disponible à https://arxiv.org/abs/1803.10151.)
A Betti counterpart of the harmonic coproduct (joint w. H. Furusho)read_more
HG G 43
19 April 2018
15:15-16:15 		Qingtao Chen
ETH Zurich
Event Details

Talks in Mathematical Physics

Title Asymptotics of quantum 6j symbols evaluated at non-conventional root of unity
Speaker, Affiliation Qingtao Chen, ETH Zurich
Date, Time 19 April 2018, 15:15-16:15
Location HG G 43
Abstract Quantum 6j symbols attract much attention in mathematical physics for the sake of their relation to quantum gravity. Previously, Woodward formulated a conjecture on quantum 6j symbols evaluated at the usual root of unity exp(2 π i/r), predicting a polynomial growth in terms of r. Inspired by the Volume Conjecture of (modified) Turaev-Viro invariants of cusped 3-manifolds (orientable or non-orientable) evaluated at non-conventional roots of unity made by T. Yang and me, it is possible to consider the asymptotics of quantum 6j symbol associated to a single tetrahedron (because the building blocks of Turaev-Viro invariants are quantum 6j-symbols). It turns out that the growth is exponential in r and we conjectured that the growth rate is proportional to the hyperbolic volume of a single tetrahedron. We proved the majority of the cases of this conjecture and also obtained secondary terms for the asymptotics of quantum 6j symbols. The very mysterious symmetric conjecture of quantum 6j symbols will also be discussed. This is a joint work with Jun Murakami.
Asymptotics of quantum 6j symbols evaluated at non-conventional root of unityread_more
HG G 43
3 May 2018
15:15-16:15 		Michael Reiterer
ETH Zürich
Event Details

Talks in Mathematical Physics

Title Towards oscillatory singularities in general relativity
Speaker, Affiliation Michael Reiterer, ETH Zürich
Date, Time 3 May 2018, 15:15-16:15
Location HG G 43
Abstract How singularities form in general relativity in vacuum remains an open problem. I will review the original BKL proposal and related results, assuming no prior exposure to this topic. The (inhomogeneous) BKL proposal has so far defeated proper formulation and proof. A recent result (joint with Eugene Trubowitz) is the existence of formal power series solutions, in external parameters, for one BKL bounce, which is a building block for the BKL proposal. It is based on rewriting the Einstein equations as a Maurer Cartan equation in a graded Lie algebra; recognizing that the algebraic content of the BKL proposal is captured by a certain filtration; identifying suitable MC elements to perturb about; and proving the absence of obstructions using a spectral sequence calculation. I will also indicate a plan for moving forward with these results. The techniques that are employed here are not limited to the BKL proposal, the new perspective is that general relativity is a subject of both analysis (PDE) and homological algebra (gauge freedom) and that any sufficiently complicated problem, such as the BKL proposal, requires a framework that accommodates both aspects.
Towards oscillatory singularities in general relativityread_more
HG G 43
* 11 May 2018
10:15-11:15 		Marco Mackaay
Universidade do Algarve
Event Details

Talks in Mathematical Physics

Title Trihedral Hecke algebras and their categorification
Speaker, Affiliation Marco Mackaay, Universidade do Algarve
Date, Time 11 May 2018, 10:15-11:15
Location HG G 19.1
Abstract Coxeter groups of rank two are dihedral groups, whose group algebras can be deformed to give the dihedral Hecke algebras. These algebras have explicit Kazhdan-Lusztig bases, which give rise to interesting non-negative integral representations associated to ADE type Dynkin diagrams. As I will recall in my talk, the dihedral Soergel bimodules categorify the dihedral Hecke algebras and, in a certain sense, explain the integral properties of the KL bases and the representations. The so called quantum Satake correspondence, due to Elias, gives a precise relation between the above story and the quantum enveloping algebra of sl(2) at roots of unity, which I will recall too. Mazorchuk, Miemietz and Tubbenhauer and I generalized the above results to Coxeter rank 3, where a new sort of algebra shows up: the trihedral Hecke algebra. Again, there are explicit KL bases, interesting non-negative integral representations associated to certain generalized ADE type Dynkin diagrams, and trihedral Soergel bimodules. And there is a precise relation with the quantum enveloping algebra of sl(3), again via the quantum Satake correspondence, due to Elias. These results are the main topic of my talk.
Trihedral Hecke algebras and their categorificationread_more
HG G 19.1
* 22 May 2018
15:15-16:15 		Kasia Rejzner
University of York
Event Details

Talks in Mathematical Physics

Title BV quantization in perturbative algebraic quantum field theory: recent results and perspectives
Speaker, Affiliation Kasia Rejzner, University of York
Date, Time 22 May 2018, 15:15-16:15
Location Y03 G 91
Abstract In this talk I will explain how the BV quantization can be used in constructing models in perturbative algebraic quantum field theory (pAQFT). In particular, it can be applied to gauge theories and effective quantum gravity. Recently it was also shown how BV in the pAQFT framework (which works on Lorentzian manifolds) is related to the version of the BV formalism used by Costello and Gwilliam in the context of Euclidean quantum field theory.
BV quantization in perturbative algebraic quantum field theory: recent results and perspectivesread_more
Y03 G 91
25 May 2018
10:15-11:15 		Barry Simon
California Institute of Technology
Event Details

Talks in Mathematical Physics

Title Tales of Our Forefathers
Speaker, Affiliation Barry Simon, California Institute of Technology
Date, Time 25 May 2018, 10:15-11:15
Location HG G 19.1
Abstract This is not a mathematics talk but it is a talk for mathematicians. Too often, we think of historical mathematicians as only names assigned to theorems. With vignettes and anecdotes, I'll convince you they were also human beings and that, as the Chinese say, "May you live in interesting times" really is a curse.
Tales of Our Forefathersread_more
HG G 19.1
31 May 2018
15:15-16:15 		Nicolò Sibilla
University of Kent
Event Details

Talks in Mathematical Physics

Title Log schemes, root stacks and parabolic bundles
Speaker, Affiliation Nicolò Sibilla, University of Kent
Date, Time 31 May 2018, 15:15-16:15
Location HG G 43
Abstract Log schemes are an enlargement of the category of schemes that was introduced by Deligne, Faltings, Illlusie and Kato, and has applications to moduli theory and deformation problems. Log schemes play a central role in the Gross-Siebert program in mirror symmetry. In this talk I will introduce log schemes and then explain recent work joint with D. Carchedi, S. Scherotzke, and M. Talpo on various aspects of their geometry. I will discuss a comparison result between two different ways of associating to a log scheme its etale homotopy type, respectively via root stacks and the Kato-Nakayama space. Our main result is a new categorified excision result for parabolic sheaves, which relies on the technology of root stacks. I will let algebraic geometers know about the seminar as they might also be interested.
Log schemes, root stacks and parabolic bundlesread_more
HG G 43

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

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