Seminars and Colloquia by Series
Monday, February 11, 2019 - 12:45 , Location: Skiles 006 , Daniel Álvarez-Gavela , IAS , Organizer: John Etnyre
The semi-cubical cusp which is formed in the bottom of a mug when you shine a light on it is an everyday example of a caustic. In this talk we will become familiar with the singularities of Lagrangian and Legendrian fronts, also known as caustics in the mathematics literature, which have played an important role in symplectic and contact topology since the work of Arnold and his collaborators. For this purpose we will discuss some basic singularity theory, the method of generating families in cotangent bundles, the geometry of the front projection, the Legendrian Reidemeister theorem, and draw many pictures of the simplest examples.
Monday, December 3, 2018 - 12:45 , Location: Skiles 006 , Oleg Lazarev , Columbia , Organizer: John Etnyre
I will describe the h-principle philosophy and explain some recent developments on the flexible side of symplectic topology, including Murphy's h-principle for loose Legendrians and Cieliebak and Eliashberg's construction of flexible symplectic manifolds in high-dimensions.
Monday, November 12, 2018 - 13:00 , Location: Skiles 006 , Tom Bachmann , MIT , Organizer: Kirsten Wickelgren
I will review various ways of modeling the homotopy theory of spaces: several model categories of simplicial sheaves and simplicial presheaves, and related infinity categorical constructions.
Monday, November 5, 2018 - 12:45 , Location: Skiles 006 , Min Hoon Kim , Korea Institute for Advanced Study , Organizer: Jennifer Hom
In 1982, by using his celebrated disk embedding theorem, Freedman classified simply connected topological 4-manifolds up to homeomorphism. The disk embedding conjecture says that the disk embedding theorem holds for general 4-manifolds with arbitrary fundamental groups. The conjecture is a central open question in 4-manifold topology. In this introductory survey talk, I will briefly discuss Freedman's disk embedding conjecture and some related conjectures (the topological 4-dimensional surgery conjecture and the s-cobordism conjecture). I will also explain why the disk embedding conjecture implies that all good boundary links are freely slice.