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Topology Seminar at the University of Miami
Organizers: Ken Baker, Nikolai Saveliev, Chris Scaduto
Time: Wednesdays 10:30am-11:30am
Location: Ungar 411
Fall 2026 Schedule
| Date |
Speaker |
| 9/9/26 |
Ken Baker (University of Miami) |
| Title: Rational genus 0 knots with tunnel number 1 in lens spaces are simple.
Abstract: Forthcoming work of Greene-Liang-Luecke classifies the simple knots in lens spaces that have rational genus 0. Together with work of Moriah-Pinsky, this enables a classification of tunnel number 1 knots in lens spaces admitting a Dehn surgery to $(S^1 \times S^2) \# N$ where $N \not \cong S^3$.
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| 9/16/26 |
Chris Scaduto (University of Miami) |
| Title: Symplectic aspects of SU(2) character varieties of punctured surfaces
Abstract: The moduli space of flat SU(2) connections on a Riemann surface with an odd number of punctures, with traceless holonomy around punctures, has a natural symplectic structure. This moduli space has been studied in many contexts; it may be described in terms of conjugacy classes of homomorphisms from the fundamental group of the surface to SU(2), and also in terms of rank two stable holomorphic bundles over the surface. I will explain how tools from instanton Floer theory and 3-manifold topology can be used to study this symplectic manifold. As an application, I'll give some new classification results about Lagrangian spheres in a particular symplectic 4-manifold. This is joint work with Ali Daemi.
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| 9/23/26 |
Scott Taylor (Colby College) |
| Title: 1-tangles and sutured manifold theory
Abstract: A 1-tangle is a properly embedded arc in an unknotted solid torus in $S^3$. It is essential if the arc is not boundary-parallel. By attaching another arc outside the solid torus, the arc may be completed to a knot in $S^3$. Given an essential 1-tangle, how many ways are there to complete it to the unknot? I will outline a proof using results from sutured manifold theory that there are at most two such ways. I’ll also describe an adaptation that shows that the Krebes 1-tangle admits no unknot closure. No previous knowledge of sutured manifold theory will be required.
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| 9/30/26 |
Tye Lidman (North Carolina State University) |
| Title: Exotic four-manifolds using Floer homology
Abstract: We use the TQFT structure of Floer homology to study how a certain surgery operation changes the Seiberg-Witten invariants of a four-manifold. This can be used to produce exotic smooth structures on four-manifolds. This is joint work with Lisa Piccirillo.
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| 10/7/26 |
Mohamed Ghoneim (University of Miami) |
| TBA
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| 10/14/26 |
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| 10/21/26 |
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| 10/28/26 |
Ollie Thakar (Harvard University) |
| TBA
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| 11/4/26 |
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| 11/11/26 |
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| 11/18/26 |
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| 11/25/26 |
Thanksgiving Recess |
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| 12/2/26 |
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Past Seminar Schedules
Spring 2026
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