Du Val surface singularities are a type of mild singularity which appear on complex surfaces. In this talk, we will compute resolutions of Du Val singularities and give many equivalent definitions. If time allows, we will define canonical singularities for normal, quasiprojective varieties over C and show that the Du Val surface singularities are canonical.

Given a vertex operator algebra V, one can attach a graded Poisson algebra called the C2-algebra. The associated Poisson variety is an important invariant for V and is known as the associated variety of V. In this talk, we will introduce the cohomological variety of a vertex operator algebra, a notion cohomologically dual to that of the associated variety. First, we will motivate and define this variety, as well as give some of its structural properties. Then we will explain how to extract information on the Yoneda algebra defining this variety. Lastly, we will apply those results to the simple vertex operator algebras constructed from the Virasoro Lie algebra and finite dimensional simple Lie algebras. This is a joint work with Cuipo Jiang (Shanghai Jiao Tong University) and Zongzhu Lin (Kansas State University)

The cohomological variety of a vertex operator algebra.

Oct. 12, 2023 3:35pm (MATH 3…

Probability

Nhan Nguyen (CU Boulder)

X

A random polynomial is a polynomial whose coefficients are random variables. A major task in the theory of random polynomials is to examine how the real roots are distributed and correlated in situations where the degree of the polynomial is large. In this talk, we examine two classes of random polynomials that have captured the attention of researchers in the fields of probability theory and mathematical physics: elliptic polynomials and generalized Kac polynomials.

Correlations between the real roots of random polynomials, part II