Talks in mathematical physics

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Date / Time

Speaker

Title

Location

1 October 2020
15:15-16:15

Stefano D'Alesio
ETH Zurich

Event Details

Title	Derived representation schemes and Nakajima quiver varieties
Speaker, Affiliation	Stefano D'Alesio, ETH Zurich
Date, Time	1 October 2020, 15:15-16:15
Location	HG G 43
Abstract	(hybrid talk: presence and Zoom) Zoom link https://ethz.zoom.us/j/94591926812 In this talk, we introduce a family of derived representation schemes associated with quivers, which may be thought of as derived versions of Nakajima quiver varieties. We exhibit an explicit cofibrant replacement for these partial preprojective algebras as a non-commutative complete intersection so that the associated derived representation scheme is the corresponding object in the world of (commutative) geometry, the Koszul complex. By doing so we link the classical result of flatness of the moment map for representations of quivers with the vanishing condition for higher representation homologies. By considering Euler characteristics of the above-mentioned derived representation schemes we obtain some integral formulas of the same flavour of other formulas present in the mathematical and physical literature since a few years, such as Jeffrey-Kirwan's residue formulas or integral formulas for Nekrasov partition functions of supersymmetric quiver gauge theories.

Derived representation schemes and Nakajima quiver varietiesread_more

22 October 2020
15:15-16:15

Thomas Gemünden
ETH Zurich

Event Details

Title	Non-Abelian Orbifold Theory
Speaker, Affiliation	Thomas Gemünden, ETH Zurich
Date, Time	22 October 2020, 15:15-16:15
Location	Zoom
Abstract	In this talk, we will discuss the theory of holomorphic extensions of non-abelian orbifold vertex operator algebras. We will give a brief overview of the concepts and motivations of vertex operator algebras and their modules. Then we will construct the module category of non-abelian orbifold vertex operator algebras and classify their holomorphic extensions. If time permits we will prove that there exist holomorphic vertex operator algebras at central charge 72 that cannot be constructed as a holomorphic extension of a cyclic orbifold of a lattice vertex operator algebra. https://ethz.zoom.us/j/93309966252

Non-Abelian Orbifold Theoryread_more

Zoom

26 November 2020
15:15-16:15

Drazen Adamovic
University of Zagreb

Event Details

Title	Some constructions of vertex algebras and their modules in LCFT
Speaker, Affiliation	Drazen Adamovic, University of Zagreb
Date, Time	26 November 2020, 15:15-16:15
Location	Zoom
Abstract	We shall first review some basic constructions in the representation theory of C_2 cofinite VOAs in LCFT. They carry the structure of certain extensions of non-rational Virasoro vertex algebras. Next we shall discuss our recent realizations of affine vertex algebras V_k(sl(2)), and show how one can obtain realization of their logarithmic modules. We will also present a properties of a family of logarithmic VOAs, called the R^(p) algebras, present their different realizations and prove certain interesting conjectures related to them (this part is based on recent joint work with T. Creutzig, N. Genra and J. Yang). Some applications in the representation theory of affine vertex algebras will be also discussed. Zoom-Link: https://ethz.zoom.us/j/99258501511 The password is the name of the largest of the sporadic simple finite groups: Mon****

Some constructions of vertex algebras and their modules in LCFTread_more

Zoom

3 December 2020
15:15-16:15

Yi-Zhi Huang
Rutgers University

Event Details

Title	Representation theory of vertex operator algebras and orbifold conformal field theory
Speaker, Affiliation	Yi-Zhi Huang, Rutgers University
Date, Time	3 December 2020, 15:15-16:15
Location	Zoom
Abstract	In this talk, I will discuss a program to develop orbifold conformal field theory using the representation theory of vertex operator algebras. The construction and existence of twisted modules and the definition and basic properties of twisted intertwining operators will be reviewed briefly. The conjectural properties, including the associativity, commutativity and modular invariance of twisted intertwining operators will be formulated explicitly. The main conjectures in orbifold conformal field theory will be stated precisely. Some thoughts on the further development of orbifold conformal field theory will be discussed. Zoom-Link: https://ethz.zoom.us/j/91572030879 The password is the name of the largest of the sporadic simple finite groups: Mon****

Representation theory of vertex operator algebras and orbifold conformal field theoryread_more

Zoom

17 December 2020
15:15-16:15

Damien Calaque
Université de Montpellier

Event Details

Title	Moduli of quiver varieties and relative critical loci
Speaker, Affiliation	Damien Calaque, Université de Montpellier
Date, Time	17 December 2020, 15:15-16:15
Location	Zoom
Abstract	In this talk I will describe a procedure that allows to construct lagrangian subvarieties inside symplectic quiver varieties. We will see how this works on the example of the Hilbert scheme of points of the plane. I will also explain the derived geometric construction that led to this procedure, and discuss (relative) Calabi-Yau structures, as well as Ginzburg algebras, and moduli of objects. This is a joint work with Tristan Bozec and Sarah Scherotzke. https://ethz.zoom.us/j/98436949871

Moduli of quiver varieties and relative critical lociread_more

Zoom

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