Events
Geometry and Topology Seminar
- Events
- Geometry and Topology Seminar
Guangbo Xu, Simons Center for Geometry and Physics, Mirror Symmetry and Gauged Linear Sigma Model
In this overview talk, I will first explain several mathematical approaches of mirror symmetry. Then I will focus on the mathematical theory of Witten's gauged linear sigma model based on the…
Alex Zupan, University of Nebraska, A special case of the Smooth 4-dimensional Poincare Conjecture
The smooth version of the 4-dimensional Poincare Conjecture (S4PC) states that every homotopy 4-sphere is diffeomorphic to the standard 4-sphere. One way to attack the S4PC is to examine a…
Juanita Pinzon Caicedo, NC State, Four–manifolds and knot concordance
SAS 4201The main goal of geometric topology is the classification of manifolds within a certain framework (topological, piecewise linear, smooth, simply-connected, symplectic, etc.). Dimension four is special, as it is the…
Yakov Berchenko-Kogan, Washington University in St. Louis, Variational numerical methods in geometric PDE
Variational methods can be used to create numerical methods that respect conservation laws. I will discuss applications to electromagnetism, the Yang-Mills equations, and mean curvature flow. I will also discuss some new ideas…
Dustin Leninger, An Introduction to Spectral Sequences
SAS 2201I will describe a homological algebra construction which is fundamental in algebraic topology, algebraic geometry, and related areas: the spectral sequence. Originally developed by Jean Leray in the 1940s, a…
Alex Chandler, NC State, Spectral Sequences Working Seminar part 3
Exact couples and the Bockstein spectral sequence.
Grant Barkley, NC State, Spectral Sequences Working Seminar part 5
Computing Tor with spectral sequences.
Jai Aslam and Ezra Nance, NC State, Spectral Sequences Working Seminar
Knot homology theories
Juanita Pinzon-Caicedo, NC State, Instanton and Heegaard Floer homologies of surgeries on torus knots
SAS 2102A Floer homology is an invariant of a closed, oriented 3-manifold Y that arises as the homology of a chain complex whose generators are either the set of solutions to…
Alex Chandler, NC State, Spectral Sequences Working Seminar
Spectral sequences in Khovanov homology.
Jonathan Hanselman, Princeton, The cosmetic surgery conjecture and Heegaard Floer homology
Duke University, Physics 119The cosmetic surgery conjecture states that no two surgeries on a given knot produce the same 3-manifold (up to orientation preserving diffeomorphism). Floer homology has proved to be a powerful…
Yuanan Diao, Department of Mathematics and Statistics, UNC Charlotte, Braid Index Bounds Ropelength From Below
For an un-oriented link K, let L(K) be the ropelength of K. It is known that in general L(K) is at least of the order O((Cr(K))3/4), and at most of the…
Krzysztof Putyra, University of Zurich, An equivalence between gl(2)-foams and Bar-Natan cobordisms
The original construction of the Khovanov homology of a link can be seen as a formal complex in the category of flat tangles and surfaces between them. There is a way to…
Irina Kogan, NC State, A Generalization of an Integrability Theorem of Darboux
SAS 4201In his monograph “Systèmes Orthogonaux” (Leçons sur les systèmes orthogonaux et les coordonnées curvilignes, Gauthier-Villars, Paris, 1910), Darboux stated three theorems providing local existence and uniqueness of solutions to first order systems of…
Tye Lidman, NC State, Homology three-spheres and SU(2) representations
One way to effectively show a group is non-trivial is to find a non-trivial representation. A major open question in low-dimensional topology is whether the fundamental group of a closed…