## Isotropic motivic category

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 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).

Emily Riehl

Johns Hopkins University

September 12, 2018

Benedikt Ahrens

University of Birmingham

September 12, 2018

Abstract: The "equivalence principle" says that meaningful statements in mathematics should be invariant under the appropriate notion of equivalence of the objects under consideration. In set-theoretic foundations, the EP is not enforced; e.g., the statement "1 ϵ Nat" is not invariant under isomorphism of sets. In univalent foundations, on the other hand, the equivalence principle has been proved for many mathematical structures. In this introductory talk, I give an overview of univalent foundations and the equivalence principle therein.

George Shabat

Russian State University for the Humanities

September 12, 2018

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.

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.

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.

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

Juan Maldacena and Douglas Stanford

May 4, 2018

Freeman Dyson

April 13, 2018