Topology
Organizers: Ciprian Manolescu & Gary Guth
Upcoming Events
Abstract: The Khovanov skein lasagna module S(X;L) is a smooth invariant of a 4-manifold X with link L in its boundary. In this talk I will outline the construction of Khovanov skein lasagna modules, as well as new computations and applications including the …
Abstract: Using a long-standing conjecture from combinatorial group theory, we explore, from multiple perspectives, the challenges of finding rare instances carrying disproportionately high rewards. Based on lessons learned in the context defined by the Andrews-Curtis conjecture, we propose…
Abstract: There has been a great deal of interest in understanding which knots are characterized by which of their Dehn surgeries. We study a 4-dimensional version of this question: which knots are determined by which of their traces? We prove several results that are in stark contrast with what…
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Past Events
Abstract: A topological model for a knot invariant is a realization of the invariant as graded intersection pairings on coverings of configuration spaces. In this talk I will describe a topological model for the HOMFLY-PT polynomial. I plan to discuss the motivation from previous work by…
Abstract: Instanton Floer homology is usually studied for SU(2) or SO(3) but admits generalization to other compact Lie groups. It also admits generalizations to linksand even trivalent graphs (webs) in three manifolds decorated with certain homogenous spacesof the Lie group. Some…
Abstract: In dimension four, there exist manifolds which are h-cobordant but not diffeomorphic. Using these cobordisms, it is known that exotic smooth structures on simply connected 4-manifolds can be localized to certain contractible submanifolds called corks. In this talk, I will discuss an…
Abstract: In this talk, I will present recent advancements in the study of smooth mapping class groups of 4-manifolds. Our work focuses on diffeomorphisms arising from Dehn twists along embedded 3-manifolds and their interaction with Seiberg-Witten theory. These investigations have led to…
Abstract: Given any smooth 4-manifold bounding a Seifert manifold, the Seifert action on its boundary can be used to define their boundary Dehn twists. If the given 4-manifold is simply-connected, this Dehn twist is always topologically isotopic to the identity, but usually not smoothly isotopic…
Abstract: In this talk I will give an introductory lecture on constructing Topological Quantum Field Theories (TQFTs) from non-semisimple categories. The main goal of the talk is to give a hint of what is needed to extend the Turaev-Viro and Crane-Yetter TQFTs from the useful setting of…
I will survey what we currently know about the relationship between T(2)-local spectra and K(2)-local spectra and what this tells us about the stable homotopy groups of spheres.
This talk is based on projects joint with Carmeli, Clausen, Hahn, Levy, Schlank and Yanovski.
Abstract: We will discuss problems of finding quadrilaterals inscribed on planar curves, such as the inscribed square problem, the inscribed rectangle problem, and the periodic square peg problem. We will examine the effectiveness and limitations of various techniques, from intersection theory…
Abstract: Khovanov homology is a combinatorially-defined invariant which has proved to contain a wealth of geometric information. In 2006 Seidel and Smith introduced a candidate analog of the theory in Lagrangian Floer analog cohomology, which has been shown by Abouzaid and Smith to be…
Abstract: I compute the knot Floer complex for the regular fiber of \Sigma(2,3,7), and I show that its Seifert genus and genus in a self homology cobordism agree. The key step in this result was providing upgrades to the surgery formula for knot lattice homotopy. Ozsv\'ath, Stipsicz, and…