Mathematical Conversations

May 20 2020

Conley's fundamental theorem of dynamical systems

Speaker: Amie Wilkinson
5:30pm | 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

The Simplicity Conjecture

Speaker: Daniel Cristofaro-Gardiner
5:30pm | 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

Discrepancy Theory and Randomized Controlled Trials

Speaker: Daniel Spielman
5:30pm | 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 Daubechies
5:30pm | 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

Sullivan's Clock: Dennis Sullivan's counter-example to the periodic orbit conjecture

Speaker: Richard Schwartz
5:30pm | 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

Vignettes about pure mathematics and machine learning

Speaker: Jordan Ellenberg
5:30pm | 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

Consequences of delays and imperfect isolation in epidemic control

Speaker: Lai-Sang Young
5:30pm | 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

Rationality of algebraic varieties

Speaker: Alexander Perry
6:00pm | 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

Euler flow with odd symmetry

Speaker: Hyunju Kwon
6:00pm | Dilworth Room
I’ll introduce the incompressible Euler equations and talk about the solution’s behavior when the vorticity has odd symmetry.