Organizer: Lilit Martirosyan
Fall 2025 Semester
August 29, 2025 at 3:30pm in ST2006
Speaker: Lilit Martirosyan (UNCW)
Title: Vertex algebras from the point of view of Isaac Newton.
Abstract: Vertex operator algebras (VOAs) are central objects in modern mathematics and mathematical physics, with connections to number theory, representation theory, and conformal field theory. In this lecture, I will introduce VOAs through Isaac Newton’s method of forward differences, showing how this elementary tool provides a natural doorway into the formal calculus underlying vertex algebras. Along the way, I will highlight how Newton’s perspective unexpectedly echoes modern algebraic structures, and how these ideas touch on themes that appear in current research. The talk will be accessible to graduate students and advanced undergraduates, with no prior background in VOAs assumed.
September 5, 2025 at 3:30pm in ST2006
Speaker: Corey Jones (NC State)
Title: Exotic fiber functors on Rep(SLn) in positive characteristic
Abstract: A fiber functor is an embedding of a tensor category into vector spaces. For representation categories of groups or Hopf algebras, the canonical forgetful functors are the main examples, but truly exotic examples are hard to come by. In this talk we will introduce a family of exotic fiber functors on the category of representations of SLn in positive characteristic, arising from combinatorial objects called triangle presentations associated to Bruhat-Tits buildings.
October 3, 2025 at 3:30pm in ST2006
Speaker: Elizabeth Jurisich (College of Charlston)
Title: Defining Hecke-Adams operators on certain group module pairs.
Abstract: Motivated by the special case of the Monstrous Moonshine example G= M, V=V^♮we define Hecke-Adams operators on suitable pairs of a group G and graded module V ∈ R(G)[q] with modular Thompson series characters. These operators form a Hecke algebra. This is a work in progress.
October 24, 2025 at 3:30pm in ST2006
Speaker: Darlayne Addabbo (SUNY Polytechnic Institute)
Title: Modularity of Vertex Operator Algebra Correlators with Zero Modes
Abstract: Correlation functions for modules of vertex operator algebras (VOAs) have long been known to satisfy nice modular transformation properties. A famous example of this is given by the Moonshine module, a VOA whose graded dimension is a modular function. Zhu proved that, more generally, correlation functions for modules of C_2-cofinite rational VOAs satisfy nice modular transformation properties. In this talk, we will discuss modular transformation properties of correlation functions with zero modes inserted. No prior knowledge of VOAs will be assumed. This talk is based on joint work with Christoph A. Keller.
November 14, 2025 at 3:30pm in ST2006
Speaker: Christian Budde (University of Free State, South Africa)
Title: On von Neumann algebras and non-commutative Lp-spaces
Abstract: The so-called von Neumann algebras are well-known concepts in the area of mathematical physics. They can be seen non-commutative versions of measure spaces due to the fact the abelian von Neumann algebras can be represented as a space of functions on a measure space. Also their classification is a big achievement in this research area. More recently, there has also been work on non-commutative Lp spaces that are constructed via von Neumann algebras. We will discuss those constructions and will show that they also give rise to rich structures even though there is not a notion of points but only of functions.