# Mathematical Conversations

Nov 13 2019

### Erdős distinct distances problem on the plane

Speaker: Hong Wang
6:00pm | Dilworth Room
Given $N$ distinct points on the plane, what's the minimal number, $g(N)$, of distinct distances between them? Erdős conjectured in 1946 that $g(N)\geq O(N/(log N)^{1/2})$. In 2010, Guth and Katz showed that $g(N)\geq O(N/log N)$ using the polynomial method.
Oct 30 2019

### Optimal transport and its unexpected appearances

Speaker: Maria Colombo
6:00pm | Dilworth Room
Optimal transport has been used to have new insights on a variety of mathematical questions, ranging from functional inequalities to economics. We will discuss some of the unexpected uses of optimal transport, as a simple proof of the isoperimetric inequality and a link with...
Oct 23 2019

### Khovanov homology

Speaker: Linh Truong
6:00pm | Dilworth Room
I will describe the construction and applications of Khovanov homology, a combinatorially defined invariant for knots that categorifies the Jones polynomial.
Oct 16 2019

### What is percolation?

Speaker: Stanislav Smirnov
6:00pm | Dilworth Room
Percolation is a simple model for the movement of liquid through a porous medium or the spread of a forest fire or an epidemic: the edges of some graph are declared open or closed depending on independent coin tosses, and then connected open clusters are studied. Seemingly...
Oct 09 2019

### Finite fields and the Ax-Grothendieck theorem

Speaker: Remy van Dobben de Bruyn
6:00pm | Dilworth Room
The Ax-Grothendieck theorem from the 1960s says that an injective polynomial $f : \mathbb C^n \to \mathbb C^n$ is also surjective. It is one of the first examples of the powerful technique in algebraic geometry of using finite fields to prove results over the complex numbers...
Apr 10 2019

### How do computers do arithmetic, and should we believe the answers?

Speaker: Scott Tremaine
6:00pm | Dilworth Room
When designing the first computer built at IAS, von Neumann rejected floating-point arithmetic as neither necessary nor convenient. In 1997 William Kahan at Berkeley, who designed the famously accurate algorithms on Hewlett-Packard calculators, said that "floating–point...
Apr 03 2019

### A glamorous movie star, the "bad boy" of music, and the development of spread spectrum communications

Speaker: Mark Goresky
6:00pm | Dilworth Room
An unlikely couple devised one of the first spread spectrum communication systems. Today these systems use sophisticated mathematics and are ubiquitous. This is a verbatim repeat (by popular demand) of a talk I gave about 6 years ago.
Mar 27 2019

### A curious family of curves

Speaker: Amie Wilkinson
6:00pm | Dilworth Room
I will construct a family of curves in the square that illustrates the interplay between hyperbolic dynamics and pathology.
Mar 20 2019

### from dynamics to contact topology and back

Speaker: Jo Nelson
6:00pm | White Levy Room
This is a light survey of the origins of contact topology and its applications to dynamics. We will use anecdotes and images to illustrate ideas.
Mar 13 2019

### Wiggling and wrinkling

Speaker: Daniel Álvarez-Gavela
6:00pm | Dilworth Room
The idea of corrugation goes back to Whitney, who proved that homotopy classes of immersed curves in the plane are classified by their rotation number. Generalizing this result, Smale and Hirsch proved that the space of immersions of a manifold X into a manifold Y is (weakly...