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Speaker:   Etienne Mann
Title:   Reduced Gromov--Witten invariants via desingularization of sheaves
Abstract:   In this talk, I will explain how the technical constructions illustrated in Talk 2 allow us to define virtual fundamental classes supported on (unions of) components of various moduli spaces. The class supported on the main component is our proposed definition of reduced Gromov--Witten invariants.
I will construct reduced invariants for complete intersections in various GIT quotients. In the case of a complete intersection projective variety, reduced GW invariants satisfy the Quantum--Lefschetz formula of Kim--Kresch--Pantev component-wise.
I will discuss to what extent these constructions are independent of the choices involved (e.g. of the desingularization, or of projective embeddings of the target variety). Owing to the universal properties discussed in the previous talk, our constructions satisfy some minimality properties which allow us to relate our definition of reduced GW invariants to previous ones. I will compare the various constructions in genus 1, here the work of Hu--Li gives us explicit local equations for the moduli spaces.

Title:   The Dehn twist on a connected sum of two homology tori
Speaker:   Haochen Qiu [Brandeis University]

Abstract:   Kronheimer-Mrowka showed that the Dehn twist along a 3-sphere in the neck of the connected sum of two K3 surfaces is not smoothly isotopic to the identity. Their result requires that the manifolds are simply connected and the signature of one of them is 16 (mod 32). We generalize the Pin(2)-equivariant family Bauer-Furuta invariant to nonsimply connected manifolds, and construct a refinement of this invariant. We use it to show that, if X_1, X_2 are two homology tori such that their determinants r_1, r_2 are odd, then the Dehn twist along a 3-sphere in the neck of X_1 # X_2 is not smoothly isotopic to the identity.
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Title:   Interactions of waves from distant gravitating sources
Speaker:   John Anderson [Stony Brook University]

Abstract:   Abstract:   Asymptotically flat spacetimes arise naturally in general relativity when trying to model isolated astrophysical systems. In this talk, I hope to describe some problems and results in the simplest setting which models interactions between several "almost isolated" systems. One result involves studying stability for nonlinear wave equations similar to the Einstein vacuum equations in such a setting. The proof requires analyzing the spacetime geometry of the interaction of waves emanating from distant sources. Another result concerns the construction of data which are appropriate for studying this problem in the case of the Einstein vacuum equations. Here, a gluing construction is used with the Brill--Lindquist metric as a template. This includes joint work with Justin Corvino and Federico Pasqualotto.
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Speaker:   Cristina Manolache
Title:   Strategy for the absolute vs reduced GW Conjecture for 3-folds
Abstract:   In this talk, I will arch back to some of the conjectures on recursion for reduced Gromov--Witten invariants which were mentioned in Talk 1. I will discuss some of the strategies that have been employed to prove them. In particular, I will be discussing the approach taken by Chang--Li in genus 1 and how this may be generalized.

Title:   Remodeling Conjecture with Descendants
Speaker:   Chiu-Chu Melissa Liu [Columbia University]

Abstract:   The Remodeling Conjecture proposed by Bouchard-Klemm-Mariño-Pasquetti relates all-genus open Gromov-Witten invariants and primary Gromov-Witten invariants of a semi-projective toric Calabi-Yau 3-manifold/3-orbifold to invariants of its mirror curve defined by Chekhov-Eynard-Orantin topological recursion. In this talk, I will describe an extension of this conjecture to equivariant descendant Gromov-Witten invariants based on joint work with Bohan Fang, Song Yu, and Zhengyu Zong.
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Title:   Passive tracers advected by 2D Navier–Stokes equations with degenerate stochastic forcing
Speaker:   Keefer Rowan [New York University]

Abstract:   I provide a high-level discussion of recent work with William Cooperman in which we prove the presence of various passive tracer phenomena in the physical model of a fluid with large-scale stirring given by the 2D Navier--Stokes equations with a degenerate stochastic forcing. This model was considered in the groundbreaking work of Hairer and Mattingly \'06. The passive tracer phenomena were proved for the case of non-degenerate forcing by Bedrossian, Blumenthal, and Punshon-Smith \'21, \'22, \'22. Our work can be viewed as a union of these frameworks.
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Title:   Chaotic almost minimal systems
Speaker:   Scott Schmieding [Penn State University]

Abstract:   A classical theorem of Furstenberg states that the only proper closed subsets of the circle which are invariant under multiplication by both two and three are finite. Several generalizations of this result have been proven since then. First I will give some background, and then discuss a class of systems motivated by this, called chaotic almost minimal systems. I\'ll present some results joint with Kra and Cyr about such systems, including the existence of Z^d-actions which are chaotic almost minimal and possess multiple non-atomic ergodic measures for d>=1. Time permitting, I will list some more recent work, joint with Kra, about some related results.
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