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Title:   Symplectic pushforwards and DT theory
Speaker:   Hyeonjun Park
Abstract:   I will introduce how to pushforward shifted symplectic fibrations along base changes. This yields an étale local structure theorem for shifted symplectic derived Artin stacks via Hamiltonian reduction. One application is a construction of cohomological Hall algebras for Calabi-Yau 3-folds, which is joint work with Tasuki Kinjo and Pavel Safronov. Another application is deformation invariance of Donaldson-Thomas invariants for Calabi-Yau 4-folds.
Hashtag: #workshop

Title:   The quantum spectrum and Gamma structure for standard flips
Speaker:   Yefeng Shen
Abstract:   In this talk, we investigate the quantum spectrum and Gamma structure for projective bundles, blow-ups, and standard flips in a particular setup. By restricting the quantum cohomology to a fiber curve direction, both quantum spectrum and asymptotic behavior become computable. Using a sequence of reductions and asymptotic expansions of Meijer G-functions, we obtain a decomposition of the cohomology of standard flips into asymptotic Gamma classes. This decomposition is compatible with the semi-orthogonal decomposition for standard flips constructed in the work of Bondal-Orlov and Belmans-Fu-Raedschelders. The talk is based on work joint with Mark Shoemaker.
Hashtag: #workshop

Title:   Introduction to Rational Dynamics in Dimension 2
Speaker:   Eric Bedford [Stony Brook University]

Abstract:  
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Public holiday

Title:   Higher genus enumerative invariants from Calabi-Yau categories (1) -- Introduction to categorical invariants: definitions
Speaker:   Andrei Căldăraru
Abstract:   I will present the construction of categorical enumerative invariants (CEI) associated to a Calabi-Yau category and a splitting of its Hodge filtration. Computed in families, these CEI give analogs of higher genus Gromov-Witten potentials. My talk will have two parts. In the first part I will discuss recent results of Deshmukh giving a conceptual understanding of the construction of CEI. In the second part I will present an effectively computable definition of CEI (joint with Costello and Tu). Throughout the talk I will emphasize the connections with topological field theory

Title:   Framed real monopole Floer homology
Speaker:   Jiakai Li [Harvard University]

Abstract:   Seiberg-Witten theory has an analogue for 3- and 4-manifolds with involutions called real Seiberg-Witten theory. This theory can be used to construct invariants of links and embedded surfaces by passing to double branched covers. This talk will focus on a framed version of real Seiberg-Witten-Floer homology. It turns out this invariant of links has rather surprising properties not seen in ordinary Seiberg-Witten theory. I will explain why it is special and how it is related to some recent developments.
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Title:   Higher genus enumerative invariants from Calabi-Yau categories (2) -- Introduction to categorical invariants: computations
Speaker:   Andrei Căldăraru
Abstract:   In this talk I will review known results and computations of CEI in various settings:
1) for a point (results of Tu);
2) for the universal family of elliptic curves, expanded around either the large volume limit (with Tu) or around the orbifold point (with He and Huang);
3) for categories of A_n singularities (joint with Li and Tu);
I will also discuss the open problem of extending CEI computations for elliptic curves to the cusp, leading into open problems about derived categories in logarithmic geometry.

Title:   Higher genus enumerative invariants from Calabi-Yau categories (3)
Speaker:   Junwu Tu
Abstract:   In this talk, we consider categorical enumerative invariants associated with derived categories of coherent sheaves on smooth and projective Calabi-Yau 3-folds. We shall sketch a proof that these invariants satisfy Bershadsky-Cecotti-Ooguri-Vafa's holomorphic anomaly equation for a given miniversal family. Along the way, we discuss analogues of the dilaton, string and divisor equations in this context. The talk is based on a joint work with Yefeng Shen.

Title:   Variable separated correspondences
Speaker:   Vanessa Matus de la Parra [Stony Brook University]

Abstract:   We review part of Ingram's paper "Critical dynamics of variable-separated affine correspondences", in particular the boundedness locus of the family of correspondences $\{ y^2=x^3+c \}$.
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Title:   Hurwitz-Brill-Noether, K3 surfaces and stability conditions
Speaker:   Andres Rojas [Humboldt University]

Abstract:   Brill-Noether loci for general curves are described by a
collection of theorems dating back to the 70s and 80s. A remarkable
proof of one of these results, the Gieseker-Petri theorem, was given by
Lazarsfeld by specializing to curves on suitable K3 surfaces. This
provided concrete examples of Brill-Noether general curves.
On the other hand, Brill-Noether theory for curves of a fixed gonality k
has not been understood until recent times, when analogues of the
classic theorems have been obtained by several authors.
In this talk I will explain how, by using Bridgeland stability on K3
surfaces with an elliptic pencil, one can find concrete examples of
k-gonal curves which behave generically from this
"Hurwitz-Brill-Noether" perspective, thus establishing a parallel to
Lazarsfeld's approach. This is a joint work with G. Farkas and S.
Feyzbakhsh.
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Title:   Higher genus enumerative invariants from Calabi-Yau categories (4)
Speaker:   Junwu Tu
Abstract:   In this talk, we discuss the problem of extracting geometric structures on moduli spaces of Calabi-Yau 3-folds from the B-model categorical enumerative invariants. Roughly speaking, we shall see that the genus zero part is essentially the underlying variation of Hodge structures; the genus one part may be packaged as a holomorphic connection on the canonical bundle of the Calabi-Yau moduli space; while the higher genus part yields a D-module structure on the square root canonical bundle. Such structures were previously proposed by Costello, Kontsevich-Soibelman, both inspired by Witten’s interpretation of the holomorphic anomaly equation.

Title:   TAB
Speaker:   Chao Li [New York University]

Abstract:  
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Title:   Towards Open Categorical Enumerative Invariants
Speaker:   Lino Amorim
Abstract:   I will report on ongoing work with Junwu Tu aiming at defining a categorical analogue of open Gromov-Witten invariants. I will describe the first step in this project: an open-closed version of the Sen-Zwiebach DGLA and its resolution by a L-infinity algebra. I will then explain how to extract enumerative invariants from this setup in genus zero and then discuss the higher genus situation.

Title:   Introduction to Rational Dynamics in Dimension 2
Speaker:   Eric Bedford [Stony Brook University]

Abstract:  
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