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Instantons and lattices of smooth 4-manifolds with boundary

GAUGE-TOPOLOGY-SYMPLECTIC

March 29, 2019      3:30 pm
Speaker: Chris Scaduto - Simons Center

Abstract: Given a 3-manifold Y, what are the possible definite intersection forms of smooth 4-manifolds with boundary Y? Donaldson's theorem says that if Y is the 3-sphere, then all such...
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Inductively collapsing Fukaya categories and flexibility

GAUGE-TOPOLOGY-SYMPLECTIC

March 15, 2019      3:30 pm
Speaker: Emmy Murphy - Northwestern

Abstract: A Weinstein manifold is a symplectic manifold which admits a Lagrangian skeleton, and associated to any Weinstein manifold is its wrapped Fukaya category, a powerful algebraic invariant. One important...
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Super-rigidity and Castelnuovo’s bound

GAUGE-TOPOLOGY-SYMPLECTIC

March 8, 2019      3:30 pm
Speaker: Thomas Walpuski - Michigan State

Abstract: Castelnuovo’s bound is a very classical result in algebraic geometry. It asserts a sharp bound on the genus of a curve of degree d in n-dimensional projective space. It...
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Computing knot Floer homology

GAUGE-TOPOLOGY-SYMPLECTIC

March 1, 2019      3:30 pm
Speaker: Peter Ozsváth - Princeton

Abstract: I will explain how to use bordered Floer homology to obtain a practical, algebraic computation of knot Floer homology. This is joint work with Zoltán Szabó.
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Instanton L-space knots

GAUGE-TOPOLOGY-SYMPLECTIC

February 22, 2019      3:30 pm
Speaker: John Baldwin - Boston College

Abstract: A 3-manifold is said to be SU(2)-abelian if all homomorphisms from its fundamental group to SU(2) factor through the first homology of the manifold. Understanding which manifolds are SU(2)-abelian...
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Algebraic methods in knot Floer homology

GAUGE-TOPOLOGY-SYMPLECTIC

February 1, 2019      3:30 pm
Speaker: Zoltán Szabó - Princeton

Abstract: The aim of this talk is to present an algebraic description of knot Floer homology, discovered in a joint work with Peter Ozsváth.
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Irreducible SL(2,C)-representations of homology-3-spheres

GAUGE-TOPOLOGY-SYMPLECTIC

December 7, 2018      3:30 pm
Speaker: Raphael Zentner - Regensburg

Abstract: We prove that the splicing of any two non-trivial knots in the 3-sphere admits an irreducible SU(2)-representation of its fundamental group. This uses instanton gauge theory, and in particular...
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Structural results in wrapped Floer theory

GAUGE-TOPOLOGY-SYMPLECTIC

November 30, 2018      3:30 pm
Speaker: John Pardon - Princeton

Abstract: I will discuss results relating different partially wrapped Fukaya categories. These include a Kunneth formula, a 'stop removal' result relating partially wrapped Fukaya categories relative to different stops, and...
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A formalism for Floer theory with coefficients

GAUGE-TOPOLOGY-SYMPLECTIC

November 9, 2018      3:30 pm
Speaker: Mohammed Abouzaid - Columbia

Abstract: I will discuss a formalism for defining (Lagrangian) Floer homology with coefficients which is a little more abstract than has been used so far in the literature, and is...
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