GAUGE-TOPOLOGY-SYMPLECTIC
April 26, 2019 3:30 pmAbstract: We show that the three-dimensional homology cobordism group admits an infinite-rank summand. It was previously known that the homology cobordism group contains an infinite-rank subgroup and a Z-summand. The...
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GAUGE-TOPOLOGY-SYMPLECTIC
April 19, 2019 3:30 pmAbstract: An exotic structure on a smooth manifold X is another smooth manifold which is homeomorphic but not diffeomorphic to X. There are many closed 4-manifolds which admit exotic smooth...
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GAUGE-TOPOLOGY-SYMPLECTIC
April 12, 2019 3:30 pmAbstract: I will discuss some recent joint work with Helmut Hofer, in which we define and establish properties of a new class of pseudoholomorhic curves (feral J-curves) to study certain...
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GAUGE-TOPOLOGY-SYMPLECTIC
April 5, 2019 3:30 pmAbstract: In "The Yang-Mills equations over Riemann surfaces", Atiyah and Bott studied Yang-Mills functional over a Riemann surface from the point of view of Morse theory, and derived results on...
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GAUGE-TOPOLOGY-SYMPLECTIC
March 29, 2019 3:30 pmAbstract: 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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GAUGE-TOPOLOGY-SYMPLECTIC
March 15, 2019 3:30 pmAbstract: 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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GAUGE-TOPOLOGY-SYMPLECTIC
March 8, 2019 3:30 pmAbstract: 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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GAUGE-TOPOLOGY-SYMPLECTIC
March 1, 2019 3:30 pmAbstract: 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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GAUGE-TOPOLOGY-SYMPLECTIC
February 22, 2019 3:30 pmAbstract: 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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GAUGE-TOPOLOGY-SYMPLECTIC
February 15, 2019 3:30 pmAbstract: In joint work with Matic, Van Horn-Morris, and Wand, we seek an answer to this question. We define a refinement of the contact invariant in Heegaard Floer homology that...
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