Abstract: 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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Abstract: 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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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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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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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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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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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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Abstract: 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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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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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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