## Automorphic Cohomology I (General Theory)

These two talks will be about automorphic cohomology in the non-classical

case.

Phillip Griffiths

Institute for Advanced Study

February 16, 2011

These two talks will be about automorphic cohomology in the non-classical

case.

Vladimir Voevodsky

Institute for Advanced Study

December 10, 2010

The correspondence between homotopy types and higher categorical analogs of groupoids which was first conjectured by Alexander Grothendieck naturally leads to a view of mathematics where sets are used to parametrize collections of objects without "internal structure" while collections of objects with "internal structure" are parametrized by more general homotopy types. Univalent Foundations are based on the combination of this view with the discovery that it is possible to directly formalize reasoning about homotopy types using Martin-Lof type theories.

Danielle S. Allen, UPS Foundation Professor, School of Social Science; Angelos Chaniotis, Professor, School of Historical Studies

Institute for Advanced Study

November 12, 2010

Enrico Bombieri

Institute for Advanced Study

October 29, 2010

In this lecture, Enrico Bombieri, IBM von Neumann Professor in the School of

Mathematics, attempts to give an idea of the numerous different notions of truth in mathematics. Using accessible examples, he explains the difference between truth, proof, and verification. Bombieri, one of the world’s leading authorities on number theory and analysis, was awarded the Fields Medal in 1974 for his work on the large sieve and its application to the distribution of prime numbers. Some of his work has potential practical applications to cryptography and security of data transmission and identification.Matias Zaldarriaga, Professor, School of Natural Sciences

Institute for Advanced Study

September 24, 2010

In this talk, Professor Matias Zaldarriaga discusses the development of the modern study of cosmology, beginning with the discovery of the expansion of the Universe by Edwin Hubble, through current efforts to map the cosmic microwave background, test ideas about the initial conditions of the Universe, and explain the accelerated expansion of the Universe.

Didier Fassin, James D. Wolfensohn Professor, School of Social Science

Institute for Advanced Study

September 25, 2010

This lecture was part of the Institute for Advanced Study’s celebration of its eightieth anniversary, and took place during the events related to the Schools and Mathematics and Natural Sciences.

Nima Arkani-Hamed, Professor, School of Natural Sciences

Institute for Advanced Study

September 24, 2010

Jean Bourgain, Professor, School of Mathematics

Institute for Advanced Study

September 24, 2010

Vladimir Voevodsky, Professor, School of Mathematics

Institute for Advanced Study

September 25, 2010

This lecture was part of the Institute for Advanced Study’s celebration of its eightieth anniversary, and took place during the events related to the Schools of Mathematics and Natural Sciences.

Avi Wigderson

Institute for Advanced Study

May 25, 2010

The Stepanov method is an elementary method for proving bounds on the number of roots of polynomials. At its core is the following idea. To upper bound the number of roots of a polynomial f(x) in a field, one sets up an auxiliary polynomial F(x) , of (magically) low degree, which vanishes at the roots of f with high multiplicity. That appropriate F exits is usually proved by a dimension argument.