Related papers: The work of Andrei Okounkov
Invited book review, as submitted to the electronic database MathSciNet, of the 2006 Cambridge University Press book, "Geometry of Quantum States," by Ingemar Bengtsson and Karol Zyczkowski
This is a survey article, to appear in the Proceedings of the 2018 International Congress of Mathematicians. (Revised, with added and updated references.)
This paper is a survey on the representation theory of Hecke algebras, Ariki-Koike algebras and connections with quantum group.
We include here some material that did not make its way into the published version (Bull. Symb. Log 18-2, June 2012, pp. 161-229, arXiv:1007.2376), in particular a proof of Theorem K to the effect that there is an initial segment of the…
We reminisce and discuss applications of algorithmic probability to a wide range of problems in artificial intelligence, philosophy and technological society. We propose that Solomonoff has effectively axiomatized the field of artificial…
Provides a counterexample to a long standing conjecture of A. Adem regarding the behaviour of the integral cohomology of a p-group.
This work was partially supported by the Program of Fundamental Research of the Department of Physics and Astronomy of the National Academy of Sciences of Ukraine "Mathematical models of non equilibrium processes in open systems" N…
We develop an analogue of probability theory for probabilities taking values in topological groups. We generalize Kolmogorov's method of axiomatization of probability theory: main distinguishing features of frequency probabilities are taken…
In honor of Minkowski's great contribution to Special Relativity, celebrated at this conference, we first review Wigner's theory of the projective irreducible representations of the inhomogeneous Lorentz group. We also sketch those parts of…
We present a set of principles and methodologies which may serve as foundations of a unifying theory of Mathematics. These principles are based on a new view of Grothendieck toposes as unifying spaces being able to act as `bridges' for…
This is a popular article about the work of Hugo Duminil-Copin, 2022 Fields medalist.
Abhyankar proved that every field of finite transcendence degree over $\mathbb{Q}$ or over a finite field is a homomorphic image of a subring of the ring of polynomials $\mathbb{Z}[T_1, \dots, T_n]$ (for some $n$ depending on the field). We…
This is the text of a series of five lectures given by the author at the "Second Annual Spring Institute on Noncommutative Geometry and Operator Algebras" held at Vanderbilt University in May 2004. It is meant as an overview of recent…
In this paper we give an alternative proof and a refinement of a recent result of S.D.Iliadis concerning isometrically containing mappings. We address also a recent result by A.I.Oblakova.
The results summarized here are intended as rigorous mathematical statements on various physical models coming from condensed matter physics, statistical mechanics (classical and quantum), quantum field theory and cold atoms physics. The…
It is shown that the criticism of Voitkiv [Phys. Rev. A 74, 027403 (2006)] is based on one assumption, which is false for an ionized electron, initially bound by the Coulomb potential, in a strong circularly polarized laser field. A certain…
Gibbs random fields corresponding to systems of real-valued spins (e.g. systems of interacting anharmonic oscillators) indexed by the vertices of unbounded degree graphs with a certain summability property are constructed. It is proven that…
We develop the methods used by Rudnev and Wheeler to prove an incidence theorem between arbitrary sets of M\"{o}bius transformations and point sets in $\mathbb F_p^2$. We also note some asymmetric incidence results, and give applications of…
A field theoretic representation of the classical partition function is derived for a system composed of a mixture of anisotropic and isotropic mobile charges that interact {\sl via} long range Coulomb and short range nematic interactions.…
This is the written version of a talk I gave at the 35th Symposium Ahrenshoop in Berlin, Germany, August 2002. It is an exposition of joint work with S. Doplicher, K. Fredenhagen, and Gh. Piacitelli [1]. The violation of unitarity found in…