Perverse schobers and semi-orthogonal decompositions
Mikhail Kapranov
Institute for Advanced Study
September 14, 2018
Vladimir Voevodsky
On the proof of the conservativity conjecture
Joseph Ayoub
University of Zurich
September 14, 2018
Abstract: I will review the strategy of the proof of the conservativity conjecture for the classical realisations of Voevodsky motives over a characteristic zero fields. I will also mention some other consequences of this proof such as the nilpotence of endomorphisms acting by zero on cohomology.
Algebraic K-theory, combinatorial K-theory and geometry
Inna Zakharevich
Cornell University
September 14, 2018
Univalence from a computer science point-of-view
Dan Licata
Wesleyan University
September 14, 2018
Abstract: One formal system for Voevodsky's univalent foundations is Martin-Löf's type theory. This type theory is the basis of proof assistants, such as Agda, Coq, and NuPRL, that are used not only for the formalization of mathematics, but in computer science for verification of programs, systems, and programming language designs and implementations. These applications rely on the fact that constructions in type theory can be interpreted constructively as programs.
A search for an algebraic equivalence analogue of motivic theories
Eric Friedlander
University of Southern California
September 13, 2018
Abstract: We reflect on mathematical efforts made years ago, initiated by Blaine Lawson and much influenced by Vladimir Voevodsky's work. In work with Lawson, Mazur, Walker, Suslin, and Haesemyer, a "semi-topological theory" for cohomology and K-theory of complex (or real) varieties has evolved which has led to a few computations and many conjectures.
Universal Chow group of 0-cycle and nilpotence
Claire Voisin
Collége de France
September 13, 2018
Even spaces and motivic resolutions
Michael Hopkins
Harvard University
September 13, 2018
Abstract: In 1973 Steve Wilson proved the remarkable theorem that the even spaces in the loop spectrum for complex cobordism have cell decompositions with only even dimensional cells. The (conjectural) analogue of this in motivic homotopy theory leads to a surprising resolution of cellular varieties into motivic complexes. In this talk I will survey this situation and describe joint with with Mike Hill and with Jean Fasel and Aravind Asok progress and on potential applications.
Towards elementary infinity-toposes
Michael Shulman
University of San Diego
September 13, 2018
Abstract: Toposes were invented by Grothendieck to abstract properties of categories of sheaves, but soon Lawvere and Tierney realized that the elementary (i.e. "finitary" or first-order) properties satisfied by Grothendieck's toposes were precisely those characterizing a "generalized category of sets". An elementary topos shares most of the properties of Grothendieck's, as well as supporting an "internal language" that enables it to be used as a basis for mathematics.
Voevodsky proof of Milnor and Bloch-Kato conjectures
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 .
Isotropic motivic category
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).