May 20 2020
Speaker: Amie Wilkinson5:30pm | Remote Access Only
In 1978, Charles Conley classified all continuous dynamical systems. His theorem, dubbed the "fundamental theorem of dynamical systems" states that the orbits of any continuous map on a compact metric space fall into two classes: gradient-like and recurrent. When the recurrent part is...
May 13 2020
Speaker: Daniel Cristofaro-Gardiner5:30pm | Remote Access Only
In the 60s and 70s, there was a flurry of activity concerning the question of whether or not various subgroups of homeomorphism groups of manifolds are simple, with beautiful contributions by Fathi, Kirby, Mather, Thurston, and many others. A funnily stubborn case that...
May 06 2020
Speaker: Daniel Spielman5:30pm | Remote Access Only
Discrepancy theory tells us that it is possible to partition vectors into sets so that each set looks surprisingly similar to every other. By "surprisingly similar" we mean much more similar than a random partition. Randomized Controlled Trials are used to test the effectiveness of...
Apr 29 2020
Musings about a 10-year collaboration with biological morphologists, or how to make biologists comfortable with fiber bundles.
Speaker: Ingrid Daubechies5:30pm | Remote Access Only
In the course of this collaboration, both sides learned about the other field; to my surprise, the biologists learned to "speak" some mathematics. Also, when they saw how we approached answering their initial questions, the questions changed. And finally, the collaboration led to interesting...
Apr 22 2020
Speaker: Richard Schwartz5:30pm | Remote Access Only
In 1976 Dennis Sullivan gave an example of a smooth vector-field on a compact (Riemannian) 5-dimensional manifold in which all the orbits are closed but for which there is no upper bound to the length of a closed orbit. (At first this doesn't even seem possible...) Sullivan explained his...
Apr 15 2020
Speaker: Jordan Ellenberg5:30pm | Remote Access Only
Through interactions with engineers and computer scientists over the years, including some current visitors at IAS, I have become pretty sold on the idea that machine learning is rich in questions which are interesting to pure mathematicians and where our insights might perhaps be useful....
Apr 09 2020
Speaker: Lai-Sang Young5:30pm | Remote Access Only
In the absence of a vaccine, isolation is about the only available means to control an epidemic. I would like to share with everyone some things I learned from a project I worked on a few years ago studying the consequences of delays and imperfect isolation. We used a toy model...
Mar 25 2020
Mar 04 2020
Speaker: Alexander Perry6:00pm | Dilworth Room
I will survey what is known about the rationality of algebraic varieties, including recent progress and open questions. There will be a surprising connection to whiskey.
Feb 26 2020
Speaker: Hyunju Kwon6:00pm | Dilworth Room
I’ll introduce the incompressible Euler equations and talk about the solution’s behavior when the vorticity has odd symmetry.