Yuri Berest

About

Yuri Berest is a professor in the Department of Mathematics at Cornell University, with an educational background that includes a Ph.D. from Université de Montreal obtained in 1997. His research interests encompass representation theory, algebraic geometry, homological algebra, and mathematical physics, with a particular focus on the interactions between these fields. His recent work involves derived algebraic geometry, algebraic homotopy theory, and their applications in representation theory and low-dimensional topology. Berest has contributed to various areas including representation homology, Lie algebra cohomology, derived Harish-Chandra homomorphism, and the study of double affine Hecke algebras, among others.

Research topics

• Pure mathematics
• Mathematics
• Combinatorics
• Mathematical physics
• Mathematical analysis

Selected publications

• Representation homology, Lie algebra cohomology and the derived Harish-Chandra homomorphism

  Journal of the European Mathematical Society · 2017-08-07 · 20 citations

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  We study the derived representation scheme DRep _n(A) parametrizing the n -dimensional representations of an associative algebra A over a field of characteristic zero. We show that the homology of DRep _n(A) is isomorphic to the Chevalley–Eilenberg homology of the current Lie coalgebra \mathfrak {gl}_n^*(\bar{C}) defined over a Koszul dual coalgebra of A . This gives a conceptual explanation to some of the main results of [BKR] and [BR], relating them (via Koszul duality) to classical theorems o…

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• Affine cubic surfaces and character varieties of knots

  Journal of Algebra · 2017-11-14 · 12 citations

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• Representation Homology of Topological Spaces

  International Mathematics Research Notices · 2020 · 7 citations

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  Abstract In this paper, we introduce and study representation homology of topological spaces, which is a natural homological extension of representation varieties of fundamental groups. We give an elementary construction of representation homology parallel to the Loday–Pirashvili construction of higher Hochschild homology; in fact, we establish a direct geometric relation between the two theories by proving that the representation homology of the suspension of a (pointed connected) space is isom…

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• Deformed Calogero–Moser Operators and Ideals of Rational Cherednik Algebras

  Communications in Mathematical Physics · 2022 · 5 citations

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• Representation homology of spaces and higher Hochschild homology

  arXiv (Cornell University) · 2017-03-10 · 5 citations

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  In this paper, we study representation homology of topological spaces, that is a natural homological extension of representation varieties of fundamental groups. We give an elementary construction of representation homology in terms of classical (abelian) homological algebra. Our construction is parallel to the Loday-Pirashvili construction of higher Hochschild homology; in fact, we establish a direct geometric relation between the two theories by showing that the representation homology of the…

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Recent grants

• Collaborative Research: Representation Varieties, Representation Homology, and Applications in Algebra, Geometry, and Topology

  NSF · $196k · 2017–2020

• Rings of Differential Operators and the Hadamard Problem

  NSF · $130k · 2004–2009

• Rings of Algebraic Differential Operators in Mathematical Physics and Geometry

  NSF · $287k · 2009–2012

Frequent coauthors

• Farkhod Eshmatov

  39 shared

• Alimjon Eshmatov

  University of Toledo

  37 shared

• Ajay C. Ramadoss

  Indiana University Bloomington

  26 shared

• George Wilson

  Beaumont Hospital, Royal Oak

  19 shared

• Pavel Etingof

  15 shared

• Victor Ginzburg

  15 shared

• Peter Samuelson

  9 shared

• Oleg Chalykh

  9 shared

Awards & honors

• 2019 Simons Fellowships

Similar researchers at Cornell University

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