# Yuri Berest

439 Malott Hall

Ph.D. (1997) Université de Montreal (Canada)

### Research Area

Representation theory, noncommutative geometry, mathematical physics

My research interests include representation theory, algebraic geometry, homological algebra, and mathematical physics. I am particularly interested in various interactions between these fields and their applications. Some of my recent work is related to derived algebraic geometry, homotopical algebra, quantum topology and integrable systems.

### Selected Publications

*Representation homology of spaces and higher Hochschild homology* (with A. C. Ramadoss and Wai-kit Yeung), https://arxiv.org/abs/1703.03505

*Representation homology, Lie algebra cohomology and the derived Harish-Chandra homomorphism* (with G. Felder, A. Patotski, A. C. Ramadoss and T. Willwacher), J. Eur. Math. Soc. 19 (2017), 2811-2893.

*Stable representation homology and Koszul duality* (with A.C. Ramadoss), J. Reine Angew. Math. 715 (2016), 143–187.

*Double affine Hecke algebras and generalized Jones polynomials* (with P. Samuelson), Compos. Math. 152 (2016), 1333–1384.

*Dixmier groups and Borel subgroups* (with A. Eshmatov and F. Eshmatov), Adv. Math. 286 (2016), 387–429.*Derived representation schemes and cyclic homology* (with G. Khachatryan and A. C. Ramadoss), Adv. Math. 245 (2013), 625–689.*Quasi-invariants of complex reflection groups* (with O. Chalykh), Compos. Math. 147 (2011), 965–1002.*Cherednik algebras and differential operators on quasi-invariants* (with P. Etingof and V. Ginzburg), Duke Math. J. 118 (2003), 279–337.

*Automorphisms and ideals of the Weyl algebra* (with G. Wilson), Math. Ann. 318 (2000), 127–147.

*The problem of lacunas and analysis on root systems*, Trans. Amer. Math. Soc. 352 (2000), 3743–3776.