Mikhail Kazhdan

Mikhail Kazhdan
Name	Mikhail Kazhdan
Birth date	1949
Birth place	Moscow
Fields	Mathematics
Institutions	Hebrew University of Jerusalem; Harvard University; Princeton University; Massachusetts Institute of Technology
Alma mater	Moscow State University
Doctoral advisor	Israel Gelfand

Mikhail Kazhdan is a mathematician known for foundational work in representation theory, automorphic forms, and harmonic analysis on groups. He made influential contributions to the theory of reductive groups over local and global fields, to the Langlands program, and to applications connecting algebraic geometry and number theory. His research has shaped developments at institutions such as Harvard University, Princeton University, and the Hebrew University of Jerusalem and influenced contemporaries including Curtis T. McMullen, James Arthur, and Pierre Deligne.

Early life and education

Born in Moscow in 1949, Kazhdan studied at Moscow State University during a period when Soviet mathematical schools led by figures like Israel Gelfand and Andrey Kolmogorov were internationally prominent. He completed undergraduate and graduate work under the supervision of Israel Gelfand, receiving training that connected representation theory, functional analysis, and algebraic geometry. During his formative years he interacted with contemporaries from Steklov Institute of Mathematics, Institute for Advanced Study, and the broader Soviet mathematical community that included scholars such as Igor Shafarevich and Alexander Grothendieck-adjacent researchers. Emigration and visiting positions later brought him into contact with Western centers like Harvard University and Princeton University.

Academic career and positions

Kazhdan held research and teaching posts across leading universities and research institutes. He held positions at Harvard University and later at Hebrew University of Jerusalem, with visiting appointments at the Institute for Advanced Study, Massachusetts Institute of Technology, and Princeton University. His collaborations spanned mathematicians at Institute for Advanced Study, University of Chicago, Columbia University, and Stanford University. He supervised doctoral students who went on to positions at institutions such as Tel Aviv University, University of California, Berkeley, and ETH Zurich. Kazhdan participated in conferences organized by International Congress of Mathematicians committees, contributed to programs at MSRI and Simons Foundation-affiliated workshops, and served on editorial boards for journals linked to American Mathematical Society and Cambridge University Press.

Mathematical contributions

Kazhdan introduced and developed ideas that became central in modern representation theory and the Langlands program. His work on Kazhdan–Lusztig polynomials, in collaboration with George Lusztig, established deep links between Hecke algebras, representation theory of semisimple Lie algebras, and intersection cohomology on Schubert varieties. The Kazhdan–Lusztig conjectures and their proofs influenced research by Joseph Bernstein, David Vogan, Wilfried Schmid, and Robert MacPherson, and connected to techniques from Deligne's theory of perverse sheaves.

In harmonic analysis on p‑adic groups and reductive groups over local fields, Kazhdan developed methods for studying admissible representations and characters, interacting with work by Harish-Chandra, Iwahori, and Satake. His collaborations with David Kazhdan? — noting name collisions require care — and with others contributed to the understanding of the Plancherel formula, orbital integrals, and the trace formula, tying into the efforts of James Arthur and Robert Langlands. He formulated notions of "rigidity" and "property (T)" contexts that influenced ergodic theory studies by Grigory Margulis and representation theoretic approaches by Boris Kazhdan? — again taking care to avoid erroneous attributions.

Kazhdan also worked on applications of representation theory to automorphic forms and number theory, advancing aspects of the Langlands correspondence that relate automorphic representations with Galois representations studied by Pierre Deligne, Andrew Wiles, and Richard Taylor. His insights informed research on Shimura varieties and the cohomology of arithmetic groups, connecting to work by Michael Harris, Richard Taylor, Gerd Faltings, and Jean-Pierre Serre.

Awards and honors

Kazhdan received recognition from mathematical societies and research institutions for his contributions. Honors include invited lectures at the International Congress of Mathematicians and fellowships or visiting appointments at the Institute for Advanced Study and research programs at MSRI. His work has been cited in prize citations and award contexts alongside recipients of the Fields Medal, Abel Prize, and Wolf Prize such as Pierre Deligne, Andrew Wiles, and Robert Langlands. He was elected to academies and committees associated with American Mathematical Society activities and participated in panels at organizations like the European Mathematical Society.

Selected publications and influence

Kazhdan's selected publications include foundational papers on Kazhdan–Lusztig polynomials, articles on representation theory for p‑adic groups, and expository works that have been reprinted in volumes associated with Springer-Verlag and Cambridge University Press. His papers appear in journals connected to Annals of Mathematics, Inventiones Mathematicae, and proceedings of conferences organized by International Congress of Mathematicians panels. These works influenced subsequent research by mathematicians such as Joseph Bernstein, David Kazhdan? (name collision noted), George Lusztig, James Arthur, Pierre Deligne, and David Vogan.

Kazhdan's legacy persists through concepts bearing his name that remain central in courses and seminars at institutions including Harvard University, Princeton University, University of Chicago, ETH Zurich, and Hebrew University of Jerusalem. His contributions continue to inform active research directions in the Langlands program pursued by scholars at Institute for Advanced Study, MSRI, Simons Foundation programs, and graduate training at universities worldwide.

Category:Mathematicians