8/30: no meeting this day
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9/6: no meeting this day
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9/13: Prof. Marco Castronovo (Columbia U.)
Title: Introduction to symplectic topology.
Abstract: This talk will be an overview of contemporary symplectic topology, geared towards graduate students. I will start with some basic definitions and examples, then list a few representative questions. Pseudo-holomorphic curves are the main tool used to study such questions. I will explain what they are, and how they can be used to deform and categorify the invariants of classical algebraic topology.
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9/20: Prof. Semon Rezchikov (Princeton U.)
Title: Cyclotomic Structure in Symplectic Topology
Abstract: Symplectic cohomology is a fundamental invariant of a symplectic manifold M with contact type boundary that is defined in terms of dynamical information and counts of pseudoholomorphic genus zero curves, and carries algebraic structures that parallel the algebraic structures on the Hochschild (co)homology of the Fukaya category of M. We show, under natural topological assumptions, that the symplectic cohomology is the homology of a genuine p-cyclotomic spectrum in the sense of Nikolaus-Scholze. The cyclotomic structure arises geometrically from the map which sends loops in M to their p-fold iterates. The data of this refinement is expected to produce many new algebraic structures of an arithmetic nature on symplectic cohomology, analogously to the way that prismatic cohomology refines the de Rham cohomology of a variety. The methods involved use ideas from genuine equivariant stable homotopy theory to avoid the issues associated to the failure of equivariant transversality. If time permits, we will discuss some expected connections to string topology.
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9/27: Sebastian Haney (U. Columbia)
Title: Infinity inner products and open Gromov-Witten invariants.
Abstract: The open Gromov-Witten (OGW) potential is a function
defined on the Maurer-Cartan space of a closed Lagrangian submanifold
in a symplectic manifold with values in the Novikov ring. From the values
of the OGW potential, one can extract open Gromov-Witten invariants,
which count pseudoholomorphic disks with boundary on the Lagrangian.
Existing definitions of the OGW potential only allow for the
construction of OGW invariants with values in the real or complex
numbers. In this talk, we will present a construction of the OGW
potential which gives invariants valued in any field of characteristic
zero. The main algebraic input for our construction is an infinity inner
product, which comes from a proper Calabi-Yau structure on the Fukaya
category. If time permits, we will also discuss a partial extension of
our results that give OGW invariants valued in fields of positive
characteristic, and connections to homological mirror symmetry.
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10/4: no meeting (no classes at CUNY)
10/11: no meeting (no classes at CUNY)
10/18: Prof. Andrei Caldararu (U. Wisconsin)
Title: TBA
Abstract: TBA
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10/25: Prof. Ethan Addison (Stony Brook U.)
Title:
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11/1: Prof. Lucia Martin-Merchan (U. Waterloo)
Title: TBA
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11/8:
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11/15: Prof. Guangbo Xu (Rutgers U.)
Title:
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11/22: Prof. Qi Yao (Stony Brook U.)
Title:
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12/6: Prof. Janet Talvacchia (Swarthmore College)
Title: TBA
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12/13:
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