Homotopy type theory provides a “synthetic” framework that is
suitable for developing the theory of mathematical objects with
natively homotopical content. A famous example is given by
(∞,1)-categories — aka “∞-categories” — which are categories...
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...
Abstract: The talk will start with discussing the common
features of the three mathematicians from the title: their
non-standard education and specific relations with the community,
outstanding imagination, productivity and contribution to
the...
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...
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.
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.
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...
