Monday, July 1st, 2024
Workshop Mini-course 1: Eleny Ionel
Time: 9:30 AM - 10:45 AM
Location: SCGP 102
Title: Moduli spaces of pseudo-holomorphic curves: a glimpse into their structure
Speaker: Eleny Ionel
Abstract: We begin with an overview of the moduli spaces of pseudo-holomorphic curves, typically used to define enumerative invariants of symplectic manifolds such as the Gromov-Witten invariants. We then focus on structure results for the Gromov-Witten invariants of symplectic 6-dimensional manifolds. We present the introductory background, some of the analytic and topological techniques involved, which will be combined into a proof outline.
Title: Moduli spaces of pseudo-holomorphic curves: a glimpse into their structure
Speaker: Eleny Ionel
Abstract: We begin with an overview of the moduli spaces of pseudo-holomorphic curves, typically used to define enumerative invariants of symplectic manifolds such as the Gromov-Witten invariants. We then focus on structure results for the Gromov-Witten invariants of symplectic 6-dimensional manifolds. We present the introductory background, some of the analytic and topological techniques involved, which will be combined into a proof outline.
Workshop Mini-course 1: John Pardon
Time: 11:30 AM - 12:45 PM
Location: SCGP 102
Title: Derived moduli spaces of pseudo-holomorphic curves
Speaker: John Pardon
Abstract: We will discuss how to construct moduli spaces of pseudo-holomorphic curves as derived log smooth manifolds using the framework of representable functors.
Title: Derived moduli spaces of pseudo-holomorphic curves
Speaker: John Pardon
Abstract: We will discuss how to construct moduli spaces of pseudo-holomorphic curves as derived log smooth manifolds using the framework of representable functors.
Tuesday, July 2nd, 2024
Workshop Mini-course 1: Chenyang Xu
Time: 9:30 AM - 10:45 AM
Location: SCGP 102
Title: K-moduli space of Fano varieties
Speaker: Chenyang Xu
Abstract: Moduli of varieties is a central topic in algebraic geometry. In the last decade, one of the most exciting stories in algebraic geometry is the observation that K-stability can be used to provide a robust moduli theory of Fano varieties, which are varieties with an ample first Chern class. Its construction uses a wide range of tools, from different subfields of algebraic geometry. In this mini-course, I will explain the notion of K-stability, sketch the construction of the K-moduli space, as well as prove its some fundamental properties.
Title: K-moduli space of Fano varieties
Speaker: Chenyang Xu
Abstract: Moduli of varieties is a central topic in algebraic geometry. In the last decade, one of the most exciting stories in algebraic geometry is the observation that K-stability can be used to provide a robust moduli theory of Fano varieties, which are varieties with an ample first Chern class. Its construction uses a wide range of tools, from different subfields of algebraic geometry. In this mini-course, I will explain the notion of K-stability, sketch the construction of the K-moduli space, as well as prove its some fundamental properties.
Workshop Mini-course 2: Eleny Ionel
Time: 11:30 AM - 12:45 PM
Location: SCGP 102
Title: Moduli spaces of pseudo-holomorphic curves: a glimpse into their structure
Speaker: Eleny Ionel
Abstract: We begin with an overview of the moduli spaces of pseudo-holomorphic curves, typically used to define enumerative invariants of symplectic manifolds such as the Gromov-Witten invariants. We then focus on structure results for the Gromov-Witten invariants of symplectic 6-dimensional manifolds. We present the introductory background, some of the analytic and topological techniques involved, which will be combined into a proof outline.
Title: Moduli spaces of pseudo-holomorphic curves: a glimpse into their structure
Speaker: Eleny Ionel
Abstract: We begin with an overview of the moduli spaces of pseudo-holomorphic curves, typically used to define enumerative invariants of symplectic manifolds such as the Gromov-Witten invariants. We then focus on structure results for the Gromov-Witten invariants of symplectic 6-dimensional manifolds. We present the introductory background, some of the analytic and topological techniques involved, which will be combined into a proof outline.
Workshop Forward-Looking Talk: Dusa McDuff
Time: 2:30 PM - 3:30 PM
Location: SCGP 102
Title: Cuspidal curves, scattering diagrams and the stabilized ellipsoidal embedding conjecture.
Speaker: Dusa McDuff
Abstract: This talk will explain how the obstructions to embedding four dimensional ellipsoids symplectically into the complex projective plane can be understood in terms of planar rational unicuspidal curves. These obstructions are stable, in that they persist after multiplying both domain and target by the complex plane, and it is easy to see that they give sharp obstructions to the corresponding stabilized embedding problem. We find necessary and sufficient conditions for such embeddings by interpreting moduli spaces of cuspidal curves in terms of scattering diagrams. This is joint work (in progress) with Kyler Siegel.
Title: Cuspidal curves, scattering diagrams and the stabilized ellipsoidal embedding conjecture.
Speaker: Dusa McDuff
Abstract: This talk will explain how the obstructions to embedding four dimensional ellipsoids symplectically into the complex projective plane can be understood in terms of planar rational unicuspidal curves. These obstructions are stable, in that they persist after multiplying both domain and target by the complex plane, and it is easy to see that they give sharp obstructions to the corresponding stabilized embedding problem. We find necessary and sufficient conditions for such embeddings by interpreting moduli spaces of cuspidal curves in terms of scattering diagrams. This is joint work (in progress) with Kyler Siegel.
Wednesday, July 3rd, 2024
Workshop Mini-course 2: John Pardon
Time: 9:30 AM - 10:45 AM
Location: SCGP 102
Title: Derived moduli spaces of pseudo-holomorphic curves
Speaker: John Pardon
Abstract: We will discuss how to construct moduli spaces of pseudo-holomorphic curves as derived log smooth manifolds using the framework of representable functors.
Title: Derived moduli spaces of pseudo-holomorphic curves
Speaker: John Pardon
Abstract: We will discuss how to construct moduli spaces of pseudo-holomorphic curves as derived log smooth manifolds using the framework of representable functors.
Workshop Mini-course 2: Chenyang Xu
Time: 11:30 AM - 12:45 PM
Location: SCGP 102
Title: K-moduli space of Fano varieties
Speaker: Chenyang Xu
Abstract: Moduli of varieties is a central topic in algebraic geometry. In the last decade, one of the most exciting stories in algebraic geometry is the observation that K-stability can be used to provide a robust moduli theory of Fano varieties, which are varieties with an ample first Chern class. Its construction uses a wide range of tools, from different subfields of algebraic geometry. In this mini-course, I will explain the notion of K-stability, sketch the construction of the K-moduli space, as well as prove its some fundamental properties.
Title: K-moduli space of Fano varieties
Speaker: Chenyang Xu
Abstract: Moduli of varieties is a central topic in algebraic geometry. In the last decade, one of the most exciting stories in algebraic geometry is the observation that K-stability can be used to provide a robust moduli theory of Fano varieties, which are varieties with an ample first Chern class. Its construction uses a wide range of tools, from different subfields of algebraic geometry. In this mini-course, I will explain the notion of K-stability, sketch the construction of the K-moduli space, as well as prove its some fundamental properties.
Workshop Mini-course 3: Eleny Ionel
Time: 2:30 PM - 3:30 PM
Location: SCGP 102
Title: Moduli spaces of pseudo-holomorphic curves: a glimpse into their structure
Speaker: Eleny Ionel
Abstract: We begin with an overview of the moduli spaces of pseudo-holomorphic curves, typically used to define enumerative invariants of symplectic manifolds such as the Gromov-Witten invariants. We then focus on structure results for the Gromov-Witten invariants of symplectic 6-dimensional manifolds. We present the introductory background, some of the analytic and topological techniques involved, which will be combined into a proof outline.
Title: Moduli spaces of pseudo-holomorphic curves: a glimpse into their structure
Speaker: Eleny Ionel
Abstract: We begin with an overview of the moduli spaces of pseudo-holomorphic curves, typically used to define enumerative invariants of symplectic manifolds such as the Gromov-Witten invariants. We then focus on structure results for the Gromov-Witten invariants of symplectic 6-dimensional manifolds. We present the introductory background, some of the analytic and topological techniques involved, which will be combined into a proof outline.
Friday, July 5th, 2024
Workshop Mini-course 3: John Pardon
Time: 9:30 AM - 10:45 AM
Location: SCGP 102
Title: Derived moduli spaces of pseudo-holomorphic curves
Speaker: John Pardon
Abstract: We will discuss how to construct moduli spaces of pseudo-holomorphic curves as derived log smooth manifolds using the framework of representable functors.
Title: Derived moduli spaces of pseudo-holomorphic curves
Speaker: John Pardon
Abstract: We will discuss how to construct moduli spaces of pseudo-holomorphic curves as derived log smooth manifolds using the framework of representable functors.
Workshop Mini-course 3: Chenyang Xu
Time: 11:30 AM - 12:45 PM
Location: SCGP 102
Title: K-moduli space of Fano varieties
Speaker: Chenyang Xu
Abstract: Moduli of varieties is a central topic in algebraic geometry. In the last decade, one of the most exciting stories in algebraic geometry is the observation that K-stability can be used to provide a robust moduli theory of Fano varieties, which are varieties with an ample first Chern class. Its construction uses a wide range of tools, from different subfields of algebraic geometry. In this mini-course, I will explain the notion of K-stability, sketch the construction of the K-moduli space, as well as prove its some fundamental properties.
Title: K-moduli space of Fano varieties
Speaker: Chenyang Xu
Abstract: Moduli of varieties is a central topic in algebraic geometry. In the last decade, one of the most exciting stories in algebraic geometry is the observation that K-stability can be used to provide a robust moduli theory of Fano varieties, which are varieties with an ample first Chern class. Its construction uses a wide range of tools, from different subfields of algebraic geometry. In this mini-course, I will explain the notion of K-stability, sketch the construction of the K-moduli space, as well as prove its some fundamental properties.