Speaker: Sujay Nair
Title: Chiral algebras for twisted class S
Abstract: The SCFT/VOA correspondence of Beem-Lemos-Liendo-Peelaers-Rastelli-van Rees leads to a particularly rich family of vertex algebras when applied to the theories of class S. A remarkably uniform construction of these, so called, 'chiral algebras of class S' has been put forward by Arakawa in arxiv:1811.01577. This construction takes a simple Lie algebra as an input and applies equally well in the non-simply laced case. However, the non-simply laced construction does not correspond, in any clear way, to known four-dimensional theories.
Physically, the incorporation of non-simply laced symmetry algebras requires the inclusion of outer automorphism twists. I will detail an extension of Arakawa's construction to this twisted setting. The resulting novel vertex algebras possess intricate properties and I will point out some important open problems, which are of both physical and mathematical interest.
This talk is based on joint work with C. Beem.
Speaker: Naoki Genra
Title: Feigin-Semikhatov duality
Abstract: We talk about Feigin-Semikhatov duality, which is dualities between subregular W-algebras and principal W-superalgebras, super analogs of Feigin-Frenkel duality and generalizations of Kazama-Suzuki cosets correspondences. The Feigin-Semikhatov duality gives rise to correspondences of fusion rules of dual W-(super)algebras in rational cases, and the induced coset functors imply equivalences between blocks of the module categories in general levels. We will also talk about recent developments: convolutions of W-algebras and reductions by stages if time permits. This is joint work with Thomas Creutzig, Andrew Linshaw, Shigenori Nakatsuka and Ryo Sato.
Speaker: Adrea Maffei
Speaker: Juan Guzman
Title: Gluing data for factorization algebras and spaces
Abstract: Beilinson and Drinfeld have defined several geometric generalizations of the notion of vertex algebra, among which we find chiral algebras, factorization algebras and OPE algebras over smooth curves. In this talk I will introduce these notions with a special emphasis in the translation equivariant case over the affine line, where we recover the usual vertex algebras. I will also describe a way to interpret an OPE algebra as the gluing data for its associated factorization algebra, and we shall see how this interpretation can be applied to the non-linear setting of factorization spaces, thus arriving to a very concrete description of certain ind-schemes as "non-linear vertex algebras". This is joint work with C. Boyallian.
Speaker: Maxim Zabzine
(In IMPA Seminário de Geometria Simplética LINK)
Title: Shift equations for equivariant volumes
Abstract: Motivated by the study of the Donaldson-Thomas theory on toric CY 3-folds I will reconsider application of Duistermaat-Heckman formula for non-compact toric Kahler manifolds. I will review the calculation of equivariant volumes for non-compact manifolds and explain some underlying issues. I will derive the set of finite-difference equations obeyed by equivariant volumes and their quantum versions. The talk is based on my joint paper with Nikita Nekrasov and Nicolo Piazzalunga (with appendix by Michele Vergne).
Speaker: Justine Fasquel
Title: Irreducible representations of certain W-algebras associated with sp4
Abstract: W-algebras form a family of vertex algebras associated with a nilpotent element f in a simple Lie algebra and a complex parameter k. Their simple quotients have been recently proved to be rational for specific values of the pair (f, k) called admissible. The rationality means the complete reducibility of positively graded modules. In particular, it implies that rational W-algebras have finitely many irreducible positive energy representations, but in general these modules remain unknown. In this talk, we will give the classification of irreducible positive energy representations for rational W-algebras associated with subregular and minimal nilpotent elements of the Lie algebra sp4.
Speaker: Michael Lau
Title: Toda systems for Takiff algebras
Abstract: Toda systems were introduced in the late 1960s as integrable lattice models for nonlinear particle interactions. Their Hamiltonians can be reinterpreted in terms of root systems, with coadjoint orbits serving as classical phase spaces. After an introduction from first principles, we will discuss how to extend and solve such integrable systems in the context of Takiff algebras, Lie algebras of matrices with entries in a ring of (truncated) polynomials of bounded degree. Such algebras appear in jet schemes and other applications. The resulting Hamiltonians have exp-polynomial potentials governing nonsymmetric interactions. We close with some remarks on quantization to large commutative subalgebras of the corresponding universal enveloping algebras.