AMS Western Sectional Meeting, October 8-9, 2016 | All talks will be held in Sturm Hall, Room 287, University of Denver |

**8:30 - 8:50 am, Oct. 8: Bojko Bakalov (NC State)**

- Title: Vertex operators in Gromov-Witten theory

**Abstract: We first review the recent notion of a twisted logarithmic module of a vertex algebra, which provides an algebraic approach to the operator product expansion in logarithmic conformal field theory. Then we present a construction that associates such a module to any semisimple Frobenius manifold. The talk is based on a joint work in progress with Todor Milanov.**

- Title: Vertex operators in Gromov-Witten theory

**9:00 - 9:20 am, Oct. 8: Tomoyuki Arakawa (RIMS Kyoto, and MIT)**

- Title: Quasi-lisse vertex algebras

**Abstract: The lisse condition, or the C2-cofiniteness condition, is an important finiteness condition of vertex algebras. Lisse vertex algebras satisfy various favorable properties including modular invariance. However, there are non-lisse vertex algebras, such as admissible affine vertex algebras, that still have some nice properties. In this talk we introduce a notion of quasi-lisse vertex algebras and explain that admissible affine vertex algebras are quasi-lisse. Moreover, we show that quasi-lisse vertex algebras satisfy a certain modular invariance property. This is a joint work with Kazuya Kawasetsu.**

- Title: Quasi-lisse vertex algebras

**9:30 - 9:50 am, Oct. 8: Fedor Malikov (USC)**

- Title: TBA

**Abstract: TBA**

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**10:30 - 10:50 am, Oct. 8: Bob Griess (Michigan)**

- Title: TBA

**Abstract: TBA**

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**3:00 - 3:20 pm, Oct. 8: Robert McRae (Vanderbilt)**

- Title: Tensor categories for vertex operator algebra extensions: Theory

**Abstract: In a recent paper, Huang, Kirillov, and Lepowsky showed that under suitable conditions, an extension of vertex operator algebras is equivalent to a commutative associative algebra in the braided tensor category of modules for the smaller vertex operator algebra. Here, we relate a certain monoidal category of representations of a commutative associative algebra in a braided tensor category constructed by Kirillov and Ostrik to Huang-Lepowsky tensor category theory for modules for a vertex operator algebra.**

- Title: Tensor categories for vertex operator algebra extensions: Theory

**3:30 - 3:50 pm, Oct. 8: Shashank Kanade (Alberta)**

- Title: Tensor categories for vertex operator algebra extensions: Applications

**Abstract: In this talk, I'll report on an ongoing joint work with Thomas Creutzig and Robert McRae, pertaining to tensor categories for vertex operator algebra extensions. I'll elucidate a few general tensor-categorical results with concrete applications regarding coset problems.**

- Title: Tensor categories for vertex operator algebra extensions: Applications

**4:00 - 4:20 pm, Oct. 8: Ching Hung Lam (Academia Sinica)**

- Title: Reverse orbifold construction and classification of holomorphic VOAs of central charge 24

**Abstract: In 1993, Schellekens determined the possible Lie algebra structures for the weight one subspaces of holomorphic vertex operator algebras of central charge 24. There are 71 cases in his list but not all cases were constructed at that time. It was also conjectured that the VOA structure of a holomorphic VOA of central charge 24 is uniquely determined by the Lie algebra structure of its weight one subspace. In this talk, we will report our recent work on the classification (with H. Shimakura, X.J. Lin and K. Kawasetsu). We will discuss the constructions of all 71 cases in Schellenkens' list. Moreover, we will show that the VOA structures of certain holomorphic VOAs of central charge 24 are uniquely determined by their weight one Lie algebras using a technique which we call "reverse orbifold construction".**

- Title: Reverse orbifold construction and classification of holomorphic VOAs of central charge 24

**4:30 - 4:50 pm, Oct. 8: Li Ren (Sichuan)**

- Title: On orbifold theory

**Abstract: This talk will report our recent work on orbifold theory. Let V be a simple vertex operator algebra and G a finite automorphism group of V such that V^G is regular. It is proved that every irreducible V^G-module occurs in an irreducible g-twisted V-module for some g in G. Moreover, the quantum dimensions of each irreducible V^G-module are determined and a global dimension formula for V in terms of twisted modules is obtained.**

- Title: On orbifold theory

**5:00 - 5:20 pm, Oct. 8: Chongying Dong (UC Santa Cruz)**

- Title: Modular framed vertex operator algebras

**Abstract: We report our recent work on framed vertex operator algebras over algebraically closed fields of finite characteristics. In particular, the irreducible modules for modular code vertex operator algebras are constructed and classified.**

- Title: Modular framed vertex operator algebras

**8:30 - 8:50 am, Oct. 9: John Duncan (Emory)**

- Title: Genus Zero Groups in Moonshine

**Abstract: Genus zero groups of isometries of the hyperbolic plane play an important role in monstrous moonshine. In this talk we describe joint work with Miranda Cheng which classifies the mock modular forms with minimal growth whose coefficients are algebraic. This reveals a fundamental role for genus zero groups in umbral moonshine, and points to new paths for the future development of the theory.**

- Title: Genus Zero Groups in Moonshine

**9:00 - 9:20 am, Oct. 9: Jinwei Yang (Notre Dame)**

- Title: Twisted representations of vertex operator algebras associated to the affine Lie algebras

**Abstract: We prove that the categories of lower bounded twisted modules of positive integer levels for simple vertex operator algebras associated with affine Lie algebras and general automorphisms are semisimple, using the twisted generalization of Zhu's algebra for these vertex operator algebras, constructed by Y.-Z. Huang and myself. We also show that the category of lower bounded twisted modules for a general automorphism is equivalent to the category of lower bounded twisted modules for the corresponding diagram automorphism.**

- Title: Twisted representations of vertex operator algebras associated to the affine Lie algebras

**9:30 - 9:50 am, Oct. 9: Gerald Hoehn (Kansas)**

- Title: Fixed-point lattices of the Leech lattice and applications

**Abstract: I will first describe joint work with Geoffrey Mason on the classification of fixed-point lattices of the Leech lattice. I will then discuss applications to the classification of vertex operator algebras, symplectic automorphisms of hyperkahler manifolds and symmetries of K3-sigma models.**

- Title: Fixed-point lattices of the Leech lattice and applications

**10:30 - 10:50 am, Oct. 9: Antun Milas (Albany)**

- Title: Unrolled quantum groups and vertex algebras

**Abstract: We first introduce unrolled quantum groups and discuss a conjectural correspondence between them and certain vertex subalgebras of the Heisenberg vertex algebra. Then we focus on the simplest unrolled quantum group, U_q^H(sl_2), q = e^{πi/p}, and the corresponding vertex algebra, called the (1,p)-singlet algebra. We show how to use deformable families of modules to efficiently compute tangle invariants colored with projective U_q^H(sl_2)-modules. We also discuss logarithmic open Hopf link invariants in connection to asymptotic (or quantum) dimensions of the singlet vertex algebra. In the last part, we present evidence for higher rank generalization of these results. This talk is based on a joint project with T. Creutzig and, in part, also jointly with M. Rupert.**

- Title: Unrolled quantum groups and vertex algebras

**2:00 - 2:20 pm, Oct. 9: Geoffrey Mason (UC Santa Cruz)**

- Title: Pierce bundles of vertex rings

**Abstract: Pierce sheaves and their corresponding etale bundles are special kinds of geometric structures over a Boolean base space that have proved useful for studying certain classes of associative rings. Pierce introduced and used them to study commutative von Neumann regular rings (vNr). We show that this theory extends to the category of vertex rings. For example, there is an equivalence of categories that says that every vertex ring is the space of global sections of a certain type of etale bundle over a Boolean base space. We define and characterize von Neumann regular vertex rings, which correspond to etale bundles of simple vertex rings. This generalizes Pierce's original theorem, which is the case when the vertex ring is a commutative vNr and the bundle is a bundle of fields.**

- Title: Pierce bundles of vertex rings

**2:30 - 2:50 pm, Oct. 9: Michael Penn (Colorado College)**

- Title: Principal Subspaces of Twisted Modules of Lattice Vertex Operator Algebras

**Abstract: Given an even lattice, L, with a certain positivity condition, and an automorphism that fixes the principal subalgebra W_L of the lattice vertex algebra V_L, we explore the principal subspace of the associated twisted V_L-module. We describe this twisted module in terms of the quotient of a polynomial algebra by an ideal generated by certain quadratic relations. In addition, the graded dimensions are found.**

- Title: Principal Subspaces of Twisted Modules of Lattice Vertex Operator Algebras

**3:00 - 3:20 pm, Oct. 9: Christopher Sadowski (Ursinus College)**

- Title: Vertex-algebraic structure of principal subspaces of basic modules
for twisted affine Lie algebras of type A_{2n+1}^{(2)}, D_n^{(2)}, E_6^{(2)}

**Abstract: Principal subspaces of standard modules for untwisted affine Lie algebras were introduced by Feigin and Stoyanovsky, and have since been further studied by many authors. In this talk, we discuss the vertex-algebraic structure of principal subspaces of basic modules for twisted affine Lie algebras of type A_{2n+1}^{(2)}, D_n^{(2)}, E_6^{(2)}. In particular, we use exact sequences to derive recursions satisfied by the multigraded dimensions of these principal subspaces. Solving these recursions, we obtain the multigraded dimensions of these principal subspaces.**

- Title: Vertex-algebraic structure of principal subspaces of basic modules
for twisted affine Lie algebras of type A_{2n+1}^{(2)}, D_n^{(2)}, E_6^{(2)}

**3:30 - 3:50 pm, Oct. 9: McKay Sullivan (NC State)**

- Title: Twisted Logarithmic Modules of Free Field and Lattice Vertex Algebras

**Abstract: We will discuss the recently defined notion of twisted logarithmic modules of vertex algebras. In particular, we will consider twisted logarithmic modules of free field algebras. Explicit examples of such modules are obtainable as highest weight representations on a certain Fock space. We will use the symplectic fermions (odd super bosons) to demonstrate this construction. We will also briefly discuss our progress on the construction of twisted logarithmic modules of lattice vertex algebras.**

- Title: Twisted Logarithmic Modules of Free Field and Lattice Vertex Algebras