相关论文: A survey of Gersten's conjecture

We revamp the existing theory of Euler class groups and present them in as much generality as possible. We remark on two results of Asok-Fasel and indicate some improvements.

This is a summary of the recent PHYSTAT-$\nu$ Workshops in Japan and at Fermilab, on `Statistical Issues in Experimental Neutrino Physics'.

The purpose of this note is to give an affirmative answer to a conjecture appearing in [Integral Transforms Spec. Funct. 26 (2015) 90-95].

We survey results in the literature that establish the \v{C}ern\'y conjecture for various classes of finite automata. We also list classes for which the conjecture remains open, but a quadratic (in the number of states) upper bound on the…

Some thoughts are presented on the inter-relation between beauty and truth in science in general and theoretical physics in particular. Some conjectural procedures that can be used to create new ideas, concepts and results are illustrated…

This is lecture notes of a talk I gave at the Morningside Center of Mathematics on June 20, 2006. In this talk, I survey on Poincare and geometrization conjecture.

This is an expanded lecture note for "Masterclass on sofic groups and applications to operator algebras" (University of Copenhagen, 5-9 November 2012). It is about algebraic aspects of the Connes Embedding Conjecture. It contains new proofs…

This is the text of my Bourbaki seminar on the proof of the surface subgroup conjecture by Jeremy Kahn and Vladimir Markovic.

This short note shows how the Novikov conjecture for mapping class groups follows from a theorem of Kato and a result theorem of Hamenstadt.

New cases of the multiplicity conjecture are considered.

We formulate a number of related generalisations of the weight part of Serre's conjecture to the case of GL(n) over an arbitrary number field, motivated by the formalism of the Breuil-M\'ezard conjecture. We give evidence for these…

I review recent developments of "non-semisimple" modular tensor categories in the sense of Lyubashenko and the categorical Verlinde formula for such categories (this is a proceedings article for Meeting for Study of Number theory, Hopf…

This article accompanies my ICM talk in August 2002. Three conjectural directions in Gromov-Witten theory are discussed: Gorenstein properties, BPS states, and Virasoro constraints. Each points to basic structures in the subject which are…

Beginning with the conjecture of Artin and Tate in 1966, there has been a series of successively more general conjectures expressing the special values of the zeta function of an algebraic variety over a finite field in terms of other…

The investigation of the ideal class group $Cl_K$ of an algebraic number field $K$ is one of the key subjects of inquiry in algebraic number theory since it encodes a lot of arithmetic information about K. There is a considerable amount of…

A family of congruences interpolating between those of Wilson and Giuga is constructed. Several elementary results are established, in order to present a possible approach to establishing Giuga's conjecture.

The `Congruence Conjecture' was developed by the second author in a previous paper. It provides a conjectural explicit reciprocity law for a certain element associated to an abelian extension of a totally real number field whose existence…

Developing a better understanding of surprising or counterintuitive phenomena has constituted a significant portion of deep learning research in recent years. These include double descent, grokking, and the lottery ticket hypothesis --…

In this expository paper, we present a survey about the history of the geometrization conjecture and the background material on the classification of Thurston's eight geometries. We also discuss recent techniques for immersive visualization…

We explore the recent results announced in "Robust machine learning by median-of-means: theory and practice" by G. Lecu\'e and M. Lerasle. We show that these results are, in fact, almost obvious outcomes of the machinery developed in [4]…