Kristin DeVleming: Moduli of boundary polarized log Calabi Yau pairs

Abstract: I will discuss joint work with Kenny Ascher, Dori Bejleri, Harold Blum, Giovanni Inchiostro, Yuchen Liu, and Xiaowei Wang on construction of moduli stacks and moduli spaces of boundary polarized log Calabi Yau pairs.  Unlike moduli of canonically polarized varieties (respectively, Fano varieties) in which the moduli stack of KSB stable (respectively, K semistable) objects is bounded for fixed volume and dimension, the objects here form unbounded families.  Despite this unbounded behavior, we define the notion of asymptotically good moduli space, and, in the case of plane curve pairs (P2, C), we construct a projective good moduli space parameterizing S-equivalence classes of such pairs.  

Weite Pi: Moduli of one-dimensional sheaves on P^2: from cohomology to enumerative geometry

Abstract: The moduli spaces of one-dimensional sheaves on P^2 are first studied by Simpson and Le Potier. In recent years, they have been investigated intensively, for example, for their connections to the moduli of Higgs bundles and to curve counting invariants for local P^2. In this talk, I will explain how the cohomological and enumerative aspects of this moduli space tie closely together, and discuss some recent progress on these aspects. Based on joint work with Y. Kononov, W. Lim, M. Moreira, and J. Shen.

Carl Lian: Counting curves on P^r

Abstract: We will explain a complete solution to the following problem. If (C,p_1,…,p_n) is a general curve of genus g and x_1,…,x_n are general points on P^r, then how many degree d maps f:C\to P^r are there with f(p_i)=x_i? These are the “Tevelev degrees“ of projective space, which were previously known only when r=1, when d is large compared to g, or virtually in Gromov-Witten theory. Time-permitting, we will also discuss some partial results when the conditions f(p_i)=x_i are replaced by conditions f(p_i) \in X_i, where the X_i are linear spaces of any dimension.

Brian Lehmann: Restriction theorems for curves on Fano varieties

Abstract: Let X be a Fano variety and let E be a vector bundle on X.  A common way to analyze E is to fix a family of curves C on X and to study the restrictions of E to C.  In this talk I will give several qualitative statements describing the behavior of these restrictions.  This is joint work with Eric Riedl and Sho Tanimoto.