## Syntax and Semantics

Benedikt Ahrens

Universite Nice Sophia Antipolis; Member, School of Mathematics

September 25, 2012

Benedikt Ahrens

Universite Nice Sophia Antipolis; Member, School of Mathematics

September 25, 2012

Marius Beceanu

Rutgers, The State University of New Jersey; Member, School of Mathematics

September 25, 2012

Stefanos Aretakis

University of Cambridge; Member, School of Mathematics

September 25, 2012

Bhargav Bhatt

University of Michigan; Member, School of Mathematics

September 25, 2012

Jing Chen

Massachusetts Institute of Technology; Member, School of Mathematics

September 25, 2012

Tsao-Hsien Chen

Massachusetts Institute of Technology; Member, School of Mathematics

September 25, 2012

Organizers: Laszlo Lovasz, Balazs Szegedy, Kati Vesztergombi and Avi Wigderson

June 4, 2012

Joel Spencer

Courant Institute, NYU

February 21, 2012

Alberto Abbondandolo

University of Pisa, Italy

February 8, 2012

I will discuss a middle-dimensional generalization of Gromov's Non-Squeezing Theorem.

Richard Taylor

Institute for Advanced Study

February 1, 2012

One of the oldest subjects in mathematics is the study of Diophantine equations, i.e., the study of whole number (or fractional) solutions to polynomial equations. It remains one of the most active areas of mathematics today. Perhaps the most basic tool is the simple idea of “congruences,” particularly congruences modulo a prime number. In this talk, Richard Taylor, Professor in the School of Mathematics, introduces prime numbers and congruences and illustrates their connection to Diophantine equations. He also describes recent progress in this area, an application, and reciprocity laws, which lie at the heart of much recent progress on Diophantine equations, including Wiles’s proof of Fermat’s last theorem.