Tye Lidman, NC State, Spineless 4-manifolds
We construct smooth compact 4-manifolds homotopy equivalent to S^2 which do not contain nicely embedded spheres realizing the homotopy equivalence.
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Geometry and Topology Seminar
- Events
- Geometry and Topology Seminar
Curtis Porter, NC State, Spinning Black Holes and CR 3-Folds
Some physically significant solutions to Einstein's field equations are spacetimes which are foliated by a family of curves called a shear-free null geodesic congruence (SFNGC). Examples include models of gravitational…
Alex Chandler, NC State, Thin Posets and Homology Theories
Inspired by Bar-Natan's description of Khovanov homology, we discuss thin posets and their capacity to support homology and cohomology theories which categorify rank-statistic generating functions. Additionally, we present two main…
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…