| Date |
Speaker |
| 1/28/26 |
Shunyu Wan (Georgia Tech) |
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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) |
|
Title: Constraints on Lefschetz fibrations with 4-dimensional fibers
Abstract: I will describe a new constraint on the topology of smooth Lefschetz fibrations with 4-dimensional fibers, arising from Seiberg--Witten theory. I will explain how it yields smooth isotopy obstructions for products of Dehn twists on self-intersection -2 spheres in 4-manifolds. As an application, we give a negative answer to a question of Donaldson asking whether, for a closed simply-connected symplectic 4-manifold, the symplectic Torelli group is generated by squared Dehn twists on Lagrangian spheres. Based on joint work with H. Konno, J. Lin, and A. Mukherjee.
|
| 3/25/26 |
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.
|
| 4/1/26 |
Steven Munoz Ruiz (University of Miami) |
|
Title: A polynomial invariant for tangles
Abstract: The Alexander Polynomial is a classical link invariant. If we realize a link as the closure of a 2-tangle, we may compute the Alexander Polynomial via Kauffman states. We will extend this idea to define a polynomial invariant for a general 2n-tangle and see several properties it shares with the Alexander Polynomial. (This is a talk surveying some work of Claudius Zibrowius.)
|
| 4/8/26 |
Shiyu Liang (UT Austin) |
|
Title: Genus 0 simple knots
Abstract: A simple knot is a knot in a lens space that decomposes into two meridional arcs. We give a complete classification of simple knots with planar rational Seifert surface. The condition of having a planar rational Seifert surface is equivalent to the knot admitting a surgery containing a non-separating 2-sphere. In particular, we classify all simple knots that admit Dehn surgery to $S^1\times S^2$. This is joint work with Josh Greene and John Luecke.
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| 4/15/26 |
Alex Zupan (University of Nebraska-Lincoln) |
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Title: Property R and its generalizations
Abstract: Gabai proved that knots have property R, meaning that the only way to obtain S^1 x S^2 by Dehn surgery on a knot in the 3-sphere is to do 0-surgery on the unknot. The generalized property R conjecture (GPRC) posits a similar situation for links, claiming that if L is an n-component link in the 3-sphere with a surgery to the connected sum of n copies of S^1 x S^2, then L must be handleslide equivalent to the unlink. While there are many potential counterexamples to the GPRC in the literature, obstructing handleslide equivalence is a tricky proposition. Thus, we further generalize the GPRC to include a mixture of geometric and homological data, and then we provide a counterexample to this broader version of the GPRC. This is joint work with Tye Lidman and Trevor Oliveira-Smith.
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| 4/22/26 |
Yikai Teng (Rutgers) |
|
Title: Khovanov homology and exotic planes
Abstract: Since the 1980s, mathematicians have discovered uncountably many "exotic" embeddings of R^2 in R^4, i.e., embeddings that are topologically but not smoothly isotopic to the standard xy-plane. However, until today, there have been no direct, computable invariants that could detect such exotic behavior (with prior results relying on indirect arguments). In this talk, we define the end Khovanov homology, which is the first known combinatorial invariant of properly embedded surfaces in R^4 up to ambient diffeomorphism. Moreover, we apply this invariant to detect new exotic planes, including the first known example of an exotic plane that is a Lagrangian submanifold of the standard symplectic R^4.
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