Seminars and Colloquia by Series

Singularities of Lagrangian and Legendrian fronts

Series
Geometry Topology Seminar Pre-talk
Time
Monday, February 11, 2019 - 12:45 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Daniel Álvarez-GavelaIAS
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.

Introduction to symplectic flexibility

Series
Geometry Topology Seminar Pre-talk
Time
Monday, December 3, 2018 - 12:45 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Oleg LazarevColumbia
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.

Models of unstable motivic homotopy theory

Series
Geometry Topology Seminar Pre-talk
Time
Monday, November 12, 2018 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Tom BachmannMIT
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.

Introduction to Freedman's disk embedding conjecture

Series
Geometry Topology Seminar Pre-talk
Time
Monday, November 5, 2018 - 12:45 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Min Hoon KimKorea Institute for Advanced Study
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.

Transverse links in the tight three sphere

Series
Geometry Topology Seminar Pre-talk
Time
Monday, October 15, 2018 - 00:45 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Lev Tovstopyat-NelipBoston College
We explain the (classical) transverse Markov Theorem which relates transverse links in the tight three sphere to classical braid closures. We review an invariant of such transverse links coming from knot Floer homology and discuss some applications which appear in the literature.

Higher Order Linking Numbers

Series
Geometry Topology Seminar Pre-talk
Time
Monday, September 24, 2018 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Miriam KuzbaryRice University
In this introductory talk I will outline the general landscape of Milnor’s invariants for links. First introduced in Milnor’s master’s thesis in 1954, these invariants capture fundamental information about links and have remained a fascinating object of study throughout the past half century. In the early 80s, Turaev and Porter independently proved their long-conjectured correspondence with Massey products of the link complement and in 1990, Tim Cochran introduced a beautiful construction to compute them using intersection theory. I will give an overview of these constructions and motivate the importance of these invariants, particularly for the study of links considered up to concordance.

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