Abstracts

Invited Speakers

Lino Amorim

Kansas State University



Morita Invariance of Categorical Enumerative Invariants

Caldararu-Costello-Tu defined Categorical Enumerative Invariants (CEI) as a set of invariants associated to a cyclic A-infinity category (with some extra conditions/data) that resemble the Gromov-Witten invariants in symplectic geometry. In this talk I will explain how one can define these invariants for Calabi-Yau A-infinity categories - a homotopy invariant version of cyclic - and then show the CEI are Morita invariant. This has applications to Mirror Symmetry and Algebraic Geometry.

Hülya Argüz

University of Georgia



Fock–Goncharov Dual Cluster Varieties and Gross–Siebert Mirrors

Cluster varieties come in pairs: for any X-cluster variety there is an associated Fock–Goncharov dual A-cluster variety. On the other hand, in the context of mirror symmetry, associated with any log Calabi–Yau variety is its mirror dual, which can be constructed using the enumerative geometry of rational curves in the framework of the Gross–Siebert program. I will explain how to bridge the theory of cluster varieties with this algebro-geometric framework of mirror symmetry and show that the mirror to the X-cluster variety is a degeneration of the Fock–Goncharov dual A-cluster variety. To do this, we investigate how the cluster scattering diagram of Gross–Hacking–Keel–Kontsevich compares with the canonical scattering diagram defined by Gross–Siebert to construct mirror duals in arbitrary dimensions. This is joint work with Pierrick Bousseau.

Pierrick Bousseau

University of Georgia

BPS Dendroscopy on Local P2

I will describe a one-parameter family of scattering diagrams computing Donaldson-Thomas invariants of local P2 at any point of the physical slice in the space of Bridgeland stability conditions. The scattering diagrams are made of attractor flow trees and are also projections of special Lagrangian submanifolds in the universal family of mirror curves. I will also present a connection with the scattering diagram describing Donaldson-Thomas invariants of the McKay quiver associated to local P2. This is joint work with Pierre Descombes, Bruno Le Floch and Boris Pioline (arXiv:2210.10712).

Lawrence Ein

University of Illinois at Chicago

Measures of Irrationality for Hypersurfaces and Complete Intersections

We will discuss some recent work on measures of irrationality for hypersurfaces and complete intersections.

Alex Waldron

University of Wisconsin

Harmonic Map Flow Near Holomorphic Maps

I will discuss recent work on removability of singularities for 2D harmonic map flow at finite time, and (time permitting) upcoming work on unique convergence at infinite time.

Yuanqi Wang

University of Kansas

ALG Ricci-flat Kähler 3-folds of Schwartz Decay

ALG gravitational instantons, i.e., non-compact complete hyper-Kähler surfaces asymptotic to a twisted product of the complex plane and an elliptic curve, are intensively studied. Following the classical work of Tian-Yau and Hein, etc. on Monge-Ampere methods for Ricci flat Kähler metrics on quasi-projective varieties, we provide a geometric existence theorem for generalized ALG Ricci flat Kähler 3-folds on isotrivial K3 fibrations/crepant resolutions. These metrics decay to the ALG model in any polynomial rate, and topological numbers/data can be calculated.