Talks in mathematical physics

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Date / Time

Speaker

Title

Location

19 February 2024
13:15-14:15

Nezhla Aghaei
SDU, U. Geneva

Details

Title	Combinatorial quantization of Chern Simons theory for gl(1\|1)
Speaker, Affiliation	Nezhla Aghaei, SDU, U. Geneva
Date, Time	19 February 2024, 13:15-14:15
Location	HG G 43
Abstract	Chern-Simons theories with gauge supergroups appear naturally in string theory and they possess interesting applications in mathematics, e.g. for the construction of knot and link invariants. In this talk we explain the combinatorial quantisation of Chern-Simons theories and also the GL(1\|1) generalisation of it, for punctured Riemann surfaces of arbitrary genus. We construct the algebra of observables, and study their representations and applications to the construction of 3-manifold invariants. This is based on the joint work https://arxiv.org/abs/1811.09123 and part 2 in progress with A. Gainutdinov, M. Pawelkiewicz, V Schomerus.

Combinatorial quantization of Chern Simons theory for gl(1|1)read_more

25 March 2024
13:15-14:15

Vladimir Dotsenko
Université de Strasbourg

Details

Title	Lie algebra homology and wheeled operads
Speaker, Affiliation	Vladimir Dotsenko, Université de Strasbourg
Date, Time	25 March 2024, 13:15-14:15
Location	HG G 43
Abstract	I shall recall the definition of a wheeled operad (introduced by Merkulov about 15 years ago) and explain how homotopy invariants of wheeled operads appear naturally when computing stable homology of Lie algebras of derivations of free algebras. This a common generalization of the Loday-Quillen-Tsygan theorem on additive K-theory of an associative algebra, and the Fuchs' stability theorem for homology of the Lie algebra of vector fields.

Lie algebra homology and wheeled operadsread_more

8 April 2024
13:15-14:15

Alexander Veselov
University of Loughborough

Details

Title	Burau representation and q-rationals
Speaker, Affiliation	Alexander Veselov, University of Loughborough
Date, Time	8 April 2024, 13:15-14:15
Location	HG G 43
Abstract	Few years ago, Morier-Genoud and Ovsienko introduced a new interesting “quantisation” of the real numbers generalising the classical q-version of integers due to Euler and Gauss. I will explain a link between the corresponding q-deformed rational numbers and the classical Burau representation of the braid group B_3. This will be applied to the open problem of classification of faithful complex specializations of this representation. The talk is based on a joint work with Sophie Morier-Genoud and Valentin Ovsienko.

Burau representation and q-rationalsread_more

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