|
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.
|
| 2/4/25 |
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. |
| 2/18/25 |
Ali Naseri Sadr (Boston College) |
|
TBD |
| 2/25/26 |
Miriam Kuzbary (Amherst College) |
|
Title: 0-Surgeries on Links
Abstract: In work in progress with Ryan Stees, we show that every closed, oriented 3-manifold can be obtained by 0-surgery on a link. Since the 0-surgery of a link can capture the data of many of the typical isotopy and concordance invariants of a link, particularly in the pairwise linking number 0 case, this result gives us a nice lens through which to study both 3-manifolds and links. However, 0-surgery on a link is certainly not a complete link invariant, and we also give multiple constructions for non-isotopic (and even non-concordant) links with homeomorphic 0-surgeries. We further address a recently popular proposed strategy for constructing exotic 4-manifolds by finding a pair of knots (or links with the same number of components) which share 0-surgeries such that exactly one of the pair is slice.
|
| 3/4/25 |
|
|
|
| 3/11/26 |
Spring break |
|
|
| 3/18/25 |
Juan Muñoz‑Echániz (Simons Center at Stony Brook) |
|
TBD
|
| 3/25/26 |
|
|
|
| 4/1/25 |
|
|
|
| 4/8/26 |
|
|
|
| 4/15/25 |
|
|
|
| 4/22/26 |
|
|
|
|