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Autumn Semester 2021

Date / Time Speaker Title Location
23 September 2021
15:15-16:15 		Kasia Rejzner
University of York
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Talks in Mathematical Physics

Title "Symmetries and Renormalization in the algebraic approach to interacting quantum field theory"
Speaker, Affiliation Kasia Rejzner, University of York
Date, Time 23 September 2021, 15:15-16:15
Location HG G 43
Abstract In 2019 Buchholz and Fredenhagen proposed a new approach to constructing interacting quantum filed theory models, based on the idea that local algebras of observables can be understood as C*-algebras generated by unitaries interpreted as local S-matrices, satisfying certain physically motivated relations. In a recent paper (2108.13336), we have formulated the notion of renormalization group in that framework, discussed symmetries and proved a result that can be seen as the quantum anomalous version of Noether's theorem. In my talk I will give the account of these findings and discuss connections to perturbation theory.
"Symmetries and Renormalization in the algebraic approach to interacting quantum field theory"read_more
HG G 43
21 October 2021
15:15-16:15 		Silvain Lacroix
ETH Institute for Theoretical Studies
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Talks in Mathematical Physics

Title Finite and affine Gaudin models and their realisations
Speaker, Affiliation Silvain Lacroix, ETH Institute for Theoretical Studies
Date, Time 21 October 2021, 15:15-16:15
Location HG G 43
Abstract In this talk, I will review some recent advances in the study of Gaudin models, which are integrable systems associated with Lie algebras, and their realisations. Finite Gaudin models correspond to finite dimensional Lie algebras, in which case the models can be interpreted as integrable spin chains or mechanical systems. In contrast, affine Gaudin models are obtained by considering affine Kac-Moody Lie algebras (which are infinite dimensional) and lead to integrable field theories. After reviewing these constructions, I will explain how various previously known integrable systems, as well as many new ones, arise as realisations of such Gaudin models, e.g. systems of Calegoro-Moser-Surtherland type in the finite case and integrable sigma-models in the affine one. This talk is mostly based on [2108.00023] and [1903.00368].
Finite and affine Gaudin models and their realisationsread_more
HG G 43
4 November 2021
15:15-16:15 		Michael Borinsky
ETH ITS
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Talks in Mathematical Physics

Title The Euler characteristic of Out(Fn) and renormalized topological field theory
Speaker, Affiliation Michael Borinsky, ETH ITS
Date, Time 4 November 2021, 15:15-16:15
Location HG G 43
Abstract I will report on ongoing joint work with Karen Vogtmann on the topology of Out(Fn) and the moduli space of graphs. The first part of this work settled a 1987 conjecture on the Euler characteristic of Out(Fn) and indicates the existence of large amounts of homology in odd dimensions. A similar study has been performed in the 1986 work of Harer and Zagier on the Euler characteristic of the mapping class group and the moduli space of curves. I will review a topological field theory proof, due to Kontsevich, of Harer and Zagier´s result and illustrate how an analogous `renormalized` topological field theory argument can be applied to Out(Fn). Moreover, I will report on very recent results on the integer Euler characteristic of Out(Fn) and its growth rate which prove the existence of large amounts of unexplained homology in odd dimensions.
The Euler characteristic of Out(Fn) and renormalized topological field theoryread_more
HG G 43
* 18 November 2021
14:45-15:45 		Rhea Palak Bakshi
ETH Institute for Theoretical Studies
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Talks in Mathematical Physics

Title Skein modules and algebras
Speaker, Affiliation Rhea Palak Bakshi , ETH Institute for Theoretical Studies
Date, Time 18 November 2021, 14:45-15:45
Location HG G 43
Abstract (NOTE UNUSUAL TIME) Skein modules are invariants of 3-manifolds which were introduced by Józef H. Przytycki in 1987 as generalisations of the Jones, HOMFLYPT, and Kauffman bracket polynomial link invariants in the 3-sphere to arbitrary 3-manifolds. Over time, skein modules have evolved into one of the most important objects in knot theory and quantum topology having strong ties with many fields of mathematics such as algebraic geometry and hyperbolic geometry via SL(2,C) character varieties and quantum Teichmüller spaces, quantum cluster algebras, the Witten-Reshetikhin-Turaev 3-manifold invariants, and Topological Quantum Field Theories, to name a few. In this talk we will give the audience a tour of the development of the various kinds of skein modules and skein algebras studied in literature, focusing primarily on the Kauffman bracket skein module which is the most extensively studied skein module of all.
Skein modules and algebrasread_more
HG G 43
2 December 2021
15:15-16:15 		Johannes Brödel
ETH Zurich
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Talks in Mathematical Physics

Title Recursions on Riemann surfaces with marked points: string-theoretic applications at genus zero and genus one.
Speaker, Affiliation Johannes Brödel, ETH Zurich
Date, Time 2 December 2021, 15:15-16:15
Location HG G 43
Abstract Scattering amplitudes in string theories can be formulated as iterated integrals on Riemann surfaces of various genera. Based on a recursion for Selberg integrals pioneered by Aomoto and Terasoma, all (open) scattering amplitudes at genus zero can be calculated recursively employing simple matrix operations. After briefly reviewing the genus-zero approach, I am going to discuss a suitable generalisation to genus one: the corresponding algorithm allows calculation of all (open) one-loop amplitudes by relating them to genus-zero amplitudes with two additional insertion points. The approach is based on facilitating the elliptic KZB associator in solving a differential equation for an auxiliary marked point, which interpolates between two geometries.
Recursions on Riemann surfaces with marked points: string-theoretic applications at genus zero and genus one.read_more
HG G 43
9 December 2021
15:15-16:15 		Per Moosavi
ETH Zurich
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Talks in Mathematical Physics

Title A geometric approach to driven inhomogeneous conformal field theory
Speaker, Affiliation Per Moosavi, ETH Zurich
Date, Time 9 December 2021, 15:15-16:15
Location HG G 43
Abstract Conformal field theory (CFT) in 1+1 dimensions is routinely used to effectively describe quantum many-body systems in equilibrium. Recently, CFT has been used to study such systems out of equilibrium, and, more recently, even with smooth inhomogeneities, such as for gapless spin chains with uniformly and smoothly spatially-varying couplings between adjacent lattice sites. The resulting effective description is an inhomogeneous CFT where the velocity is given by a smooth position-dependent function. In this talk, I will present an approach to study such CFTs by exact analytical means based on projective unitary representations of circle diffeomorphisms. I will show that this can be used to construct a geometric approach to driven inhomogeneous CFT that establishes a correspondence with classical dynamical systems on the circle. Our approach allows one to construct phase diagrams with heating/nonheating phases characterized by the presence/absence of periodic points of diffeomorphisms encoding the time evolution and to study phase transitions between them. This generalizes previous results for a small subfamily of similar systems that used only a finite-dimensional subalgebra to general smooth inhomogeneities that require the full (infinite-dimensional) Virasoro algebra.
A geometric approach to driven inhomogeneous conformal field theoryread_more
HG G 43
16 December 2021
15:15-16:15 		Tommaso Macrelli
ETH Zürich
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Talks in Mathematical Physics

Title Colour-kinematic duality, double copy and homotopy algebras
Speaker, Affiliation Tommaso Macrelli, ETH Zürich
Date, Time 16 December 2021, 15:15-16:15
Location HG G 43
Abstract Live stream: https://video.ethz.ch/live-hidden/live-10.html Colour-kinematics (CK) duality has been the source of many exciting developments in quantum field theory and gravity recently. It states that gauge theory scattering amplitudes can be re-organised so that the kinematic factors of the integrand numerator mirror the algebraic properties of the colour factors. A far-reaching ramification of this duality is the so-called double copy: when substituting a copy of colour factors of a gauge theory amplitude for CK-compliant kinematic factors, one obtains a scattering amplitude for gravity! While CK duality and the double copy are well established at the tree level, their loop-level generalisation has remained open until now. By lifting the on-shell, scattering amplitude-based description to an action-based approach, we show that a theory that exhibits tree-level CK duality can be reformulated so that its loop integrands manifest CK duality. With Yang-Mills theory as the prime example, we provide a theoretical toolkit for systematically generating an action with manifest loop-level CK duality from a theory with CK-dual tree-level scattering amplitudes. We also interpretate CK duality and the double copy in language of homotopy algebras. This talk is based on arXiv:2007.13803, arXiv:2102.11390, and arXiv:2108.03030.
Colour-kinematic duality, double copy and homotopy algebrasread_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.

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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