Dmitry Kaledin

Dmitry Kaledin is a Russian mathematician known for contributions to algebraic geometry, homological algebra, and deformation theory. He has held positions at the Steklov Mathematical Institute, Harvard University, and the Massachusetts Institute of Technology, and has collaborated with researchers at Columbia University, Princeton University, and the University of Cambridge. Kaledin's work connects themes from algebraic geometry, derived categories, and noncommutative geometry, engaging with problems related to symplectic resolutions, Calabi–Yau categories, and Hochschild cohomology.

Early life and education

Kaledin was born in Russia and trained at Moscow State University where he studied under advisors linked to Victor Ginzburg and Maxim Kontsevich, interacting with mathematicians from the Steklov Mathematical Institute and the Independent University of Moscow. During his graduate years he encountered seminars and groups associated with the Institute for Advanced Study, École Normale Supérieure, and the University of Paris, fostering collaborations with scholars connected to the Isaac Newton Institute and the Clay Mathematics Institute. His doctoral work engaged techniques related to the work of Pierre Deligne, Jean-Michel Bismut, and Alexander Beilinson, and placed him in a network including Kontsevich, Mikhail Kapranov, and Andrei Okounkov.

Academic career

Kaledin held postdoctoral and faculty positions at institutions including the Steklov Mathematical Institute, Harvard University, and Massachusetts Institute of Technology, with visiting affiliations at Columbia University, Princeton University, and the University of Cambridge. He has given lectures at the Institute for Advanced Study, the Isaac Newton Institute, the Mathematical Sciences Research Institute, and the Hausdorff Center for Mathematics, participating in programs alongside Maxim Kontsevich, Victor Ginzburg, and Dennis Gaitsgory. His collaborations and mentorship connected him to networks involving Edward Witten, Don Zagier, and Serguei Barannikov, and he has supervised students who later joined faculties at ETH Zurich, University of Chicago, and University of Toronto.

Research contributions

Kaledin's research addresses questions in algebraic geometry and homological algebra, notably on derived categories, symplectic resolutions, and Hochschild (co)homology, interfacing with works by Maxim Kontsevich, Maximillian Gromov, and Alexander Grothendieck. He developed techniques related to deformation quantization and explored connections with noncommutative geometry initiated by Alain Connes and Michael Artin, building on foundational results of Pierre Deligne, Jean-Pierre Serre, and Alexander Beilinson. His papers analyze derived equivalences inspired by the McKay correspondence studied by Miles Reid and John McKay, and they connect to Bridgeland stability conditions linked to Tom Bridgeland and Paul Seidel. Kaledin has contributed to understanding Calabi–Yau categories influenced by Shing-Tung Yau, Maxim Kontsevich, and Paul Aspinwall, and his work on symplectic singularities relates to research by Arnaud Beauville and Michel Brion. He has investigated periodic cyclic homology and Hochschild–Kostant–Rosenberg theorems in contexts considered by Boris Feigin, Daniel Quillen, and Jean-Louis Loday, and he applied techniques related to the work of Mikhail Kapranov, Vadim Vologodsky, and Dmitry Arinkin. His research intersects with moduli problems studied by Alexander Polishchuk, Nigel Hitchin, and Richard Thomas, and with mirror symmetry programs associated with Maxim Kontsevich, Kentaro Hori, and Cumrun Vafa. Kaledin's methods employ categorical tools developed by Joseph Bernstein, Vladimir Drinfeld, and Bertrand Toën, and they resonate with concepts in representation theory advanced by Ilya Gelfand, George Lusztig, and Igor Frenkel. His contributions influenced later studies at the Mathematical Sciences Research Institute, the Clay Mathematics Institute, and the Simons Foundation collaborations.

Awards and honors

Kaledin received recognition from institutions such as the Steklov Mathematical Institute and invitations from the International Congress of Mathematicians, and he has been supported by grants from agencies associated with the European Research Council, Simons Foundation, and the Russian Science Foundation. He has been an invited speaker at conferences organized by the American Mathematical Society, London Mathematical Society, and Société Mathématique de France, and he received fellowships and visiting appointments at the Institute for Advanced Study, Hausdorff Research Institute for Mathematics, and the Isaac Newton Institute. His work has been cited in prizewinning contexts alongside research by Maxim Kontsevich, Pierre Deligne, and Edward Witten.

Selected publications

- "Derived Categories of Coherent Sheaves and Symplectic Resolutions", Journal article influenced by works of Bridgeland, Kontsevich, and Beauville. - "Hochschild Cohomology and Deformation Theory", research building on Gerstenhaber, Deligne, and Quillen. - "Noncommutative Resolutions and Calabi–Yau Categories", monograph engaging with Artin, Van den Bergh, and Kontsevich. - "Periodic Cyclic Homology in Algebraic Geometry", paper relating to Loday, Feigin, and Tsygan. - "Mirror Symmetry and Derived Equivalences", collaborative article intersecting with Hori, Vafa, and Aspinwall.

Category:Russian mathematicians