Gauge Theory and Topology Seminar, SEMINARS
November 4, 2022 3:30 pmBordered Floer homology is an extension of Heegaard Floer homology to manifolds with parametrized boundary, and in the case of manifolds with torus boundary knot Floer homology gives another such extension. In...
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Gauge Theory and Topology Seminar, SEMINARS
October 14, 2022 3:30 pmRepresentations of 3-manifold groups into groups such as SU(2) and SL(2,C) have been actively studied for decades. Many topological invariants are defined by considering these representations, such as the Casson...
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Gauge Theory and Topology Seminar, SEMINARS
October 7, 2022 3:30 pmWe will talk about our recent construction of the smallest closed exotic 4-manifolds with signature zero known to date. Our novel examples are derived from fairly special small Lefschetz fibrations...
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Gauge Theory and Topology Seminar, SEMINARS
September 30, 2022 3:30 pmIn this talk, we will discuss bordered aspects of the Heegaard Floer surgery formulas of Ozsvath--Szabo and Manolescu--Ozsvath. In particular, we will explain how their theories naturally define bordered invariants...
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Gauge Theory and Topology Seminar, SEMINARS
September 23, 2022 3:30 pmThis talk is on work in preparation with Ali Daemi. I will explain why Kim Froyshov's mod 2 instanton invariant q_3 gives information about indefinite 4-manifolds: if H_1(W;Z/2) = 0...
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Gauge Theory and Topology Seminar, SEMINARS
September 15, 2022 3:00 pmInstanton homology was first introduced by Floer in 1980s. It has many important applications in the study of 3-manifolds and knots, especially in studying the SU(2) representations of fundamental groups....
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SEMINARS, GAUGE-TOPOLOGY-SYMPLECTIC
May 6, 2022 3:30 pmI'll recall the braid-theoretic characterization of knots in the 3-sphere bounding complex curves in the 4-ball due to Rudolph and Boileau-Orevkov, discuss generalizations to other 3-manifolds and fillings, a conjectural...
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SEMINARS, GAUGE-TOPOLOGY-SYMPLECTIC
April 29, 2022 3:30 pmThis event has been cancelled for today, April 29, 2022. I will talk about joint work with Andrew Lobb related to Toeplitz's square peg problem, which asks whether every (continuous)...
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Gauge Theory and Topology Seminar, SEMINARS
April 8, 2022 3:30 pmIn this talk I will discuss work in progress in which we classify topological 4-manifolds with boundary and fundamental group Z, under some mild assumptions on the boundary. We apply...
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SEMINARS, GAUGE-TOPOLOGY-SYMPLECTIC
March 4, 2022 3:30 pmIt is well-known that for any finite group G, there exists a closed 3-manifold M with G as a quotient of pi_1(M). However, we can ask more detailed questions about the possible...
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