## The synthetic theory of $\infty$-categories vs the synthetic theory of $\infty$-categories

Emily Riehl

Johns Hopkins University

September 12, 2018

Emily Riehl

Johns Hopkins University

September 12, 2018

Alexander Vishik

The University of Nottingham

September 12, 2018

Abstract: It was observed for a while (at least, since the times of E.Witt) that the notion

of anisotropy of an algebraic variety (that is, the absence of points of degree prime to a given p on it) plays an important role (most notably, in the theory of quadratic forms).

of anisotropy of an algebraic variety (that is, the absence of points of degree prime to a given p on it) plays an important role (most notably, in the theory of quadratic forms).

Alexander Merkurjev

University of California, Los Angeles

September 12, 2018

Abstract:

I will discuss main ideas and steps in the

proof of Milnor and Bloch-Kato Conjectures given by Voevodsky .

André Joyal

Université du Québec á Montréal

September 11, 2018

Abstract: The discovery of the "univalence principle" is a mark of Voevodsky's genius.

Its importance for type theory cannot be overestimated: it is like the "induction principle" for arithmetic.

I will recall the homotopy interpretation of type theory and the notion of univalent fibration.

I will describe the connection between univalence and descent in higher toposes.

Its importance for type theory cannot be overestimated: it is like the "induction principle" for arithmetic.

I will recall the homotopy interpretation of type theory and the notion of univalent fibration.

I will describe the connection between univalence and descent in higher toposes.

Dan Grayson

University of Illinois, Urbana-Champaign

September 11, 2018

Abstract: Vladimir Voevodsky was a brilliant mathematician, a Fields Medal

winner, and a faculty member at the Institute for Advanced Study, until his

sudden and unexpected death in 2017 at the age of 51. He had a special flair

for thinking creatively about ways to incorporate topology and homotopy theory

into other fields of mathematics. In this talk for a general audience, I will

sketch his seminal contributions to two broad areas, algebraic geometry and the

winner, and a faculty member at the Institute for Advanced Study, until his

sudden and unexpected death in 2017 at the age of 51. He had a special flair

for thinking creatively about ways to incorporate topology and homotopy theory

into other fields of mathematics. In this talk for a general audience, I will

sketch his seminal contributions to two broad areas, algebraic geometry and the

Pierre Deligne

Professor Emeritus, School of Mathematics

September 11, 2018

Abstract: In the univalent foundation formalism, equality makes sense only between objects of the same type, and is itself a type. We will explain that this is closer to mathematical practice than the Zermelo-Fraenkel notion of equality is.

Robbert Dijkgraaf

IAS

September 11, 2018

Fabien Morel

Mathematisches Instit der Universität München

September 11, 2018

Abstract: This talk will be a survey on the development of $A^1$-homotopy theory, from its genesis, and my meeting with Vladimir, to its first successes, to more recent achievements and to some remaining open problems and potential developments.

Kasso Okoudjou

MIT& University of Maryland

July 12, 2018

Ashia Wilson

University of California, Berkeley

July 12, 2018