Topology Seminar at the University of Miami

Organizers: Ken Baker, Nikolai Saveliev, Chris Scaduto
Time: Wednesdays at 11am
Location: Ungar 506

Spring 2026 Schedule

Date	Speaker
1/28/26	Shunyu Wan (Georgia Tech)
Title: Surgeries on knots and tight contact structures Abstract: The existence and nonexistence of tight contact structures on 3-manifolds are interesting and important topics studied over the past thirty years. Etnyre-Honda found the first example of a 3-manifold that does not admit tight contact structures, and later Lisca-Stipsicz extended their result and showed that a Seifert fiber space admits a tight contact structure if and only if it is not smooth (2n-1)-surgery along the T(2,2n+1) torus knot for any positive integer n. Surprisingly, since then no other example of a 3-manifold without tight contact structures has been found. Hence, it is interesting to study if all such manifolds, except those mentioned above, admit a tight contact structure. Towards this goal, I will discuss the joint work with Zhenkun Li and Hugo Zhou about showing any negative surgeries on any knot in S^3 admit a tight contact structure.
2/4/26	Advika Rajapakse (UCLA)
Title: Space-level properties of odd Khovanov homology Abstract: Odd Khovanov homology, developed by Ozsváth-Rasmussen-Szabó, is a categorification of the Jones polynomial with suspected connections to Heegaard Floer homology. We investigate the properties of the odd Khovanov spectrum, a space-level lift of odd Khovanov homology, using the second Steenrod square. Using this square operation, we uncover unexpected results regarding the behavior of this space, and classify it for prime knots up to 11 crossings.
2/11/26	Fraser Binns (Princeton)
Title: 4-ended tangles, Heegaard Floer homology and norm detection Abstract: Link Floer homology is a powerful invariant of links due to Ozsváth and Szabó. One of its most striking properties is that it detects each link's Thurston norm, a result also due to Ozsváth and Szabó. In this talk I will discuss generalizations of this result to the context of 4-ended tangles, as well as some tangle detection results. This is joint work in progress with Subhankar Dey and Claudius Zibrowius.
2/18/26	Ali Naseri Sadr (Boston College)
Title: Periodic Inscription Problems Abstract: Periodic inscriptions are a variation of the Toeplitz square peg problem suggested by Tao in 2017. A periodic curve is an embedding of the real line in the plane that is invariant under translation by a fixed vector. We say that a pair of disjoint periodic curves inscribe a quadrilateral Q if there exist four points in the union of their images such that the quadrilateral they form is similar to Q. In this talk, I will present a proof of the existence of such inscriptions when Q is an isosceles trapezoid, using tools from symplectic geometry and Lagrangian Floer homology. If time permits, I will also discuss other modifications of the square peg problem in non-Euclidean geometries and explain how symplectic geometry can be used to establish analogous results.
2/25/26	Cancellation due to weather conditions in the Northeast

3/4/26	Nikolai Saveliev (University of Miami)
Title: Seiberg-Witten equations on Berger 3-spheres Abstract: The Seiberg-Witten equations are a system of nonlinear partial differential equations that play a central role in low-dimensional topology and differential geometry. This talk will focus on the three-dimensional theory for closed, oriented manifolds. We begin with an accessible introduction to the Seiberg-Witten equations and conclude with an explicit formula for counting their solutions on Berger 3-spheres in terms of the spectrum of the Dirac operator.
3/11/26	Spring break

3/18/26	Juan Muñoz‑Echániz (Simons Center at Stony Brook)
TBA
3/25/26

4/1/26

4/8/26

4/15/26	Alex Zupan (University of Nebraska-Lincoln)
TBA
4/22/26	Yikai Teng (Rutgers)
TBA