Mark Kisin

Mark Kisin
Name	Mark Kisin
Birth date	1965
Birth place	London, England
Nationality	British
Fields	Number theory, algebraic geometry, arithmetic geometry
Workplaces	University of Cambridge, Harvard University, Imperial College London
Alma mater	Trinity College, Cambridge, University of Oxford
Doctoral advisor	John H. Coates

Mark Kisin is a British mathematician known for fundamental contributions to number theory and arithmetic geometry, particularly in the theory of p-adic Galois representations, modular forms, and applications to the Langlands program. He has held research and teaching posts at prominent institutions and has developed tools and theorems that influenced work on Fermat's Last Theorem generalizations, Shimura varieties, and modularity lifting theorems. His work connects foundational concepts across algebraic geometry, representation theory, and algebraic number theory.

Early life and education

Kisin was born in London and educated at schools in England before reading mathematics at Trinity College, Cambridge and completing graduate studies at the University of Oxford under the supervision of John H. Coates. During his doctoral work he engaged with problems related to Iwasawa theory, Galois cohomology, and the arithmetic of elliptic curves, interacting with researchers from institutions such as University of Cambridge, Harvard University, and Princeton University.

Academic career and positions

Kisin held postdoctoral and faculty positions at institutions including Harvard University, Imperial College London, and the University of Cambridge, where he served as Professor of Mathematics and a fellow of Trinity College, Cambridge. He has given invited lectures at venues such as the International Congress of Mathematicians, the European Congress of Mathematics, and workshops at MSRI and the Mathematical Institute, Oxford. His collaborations span researchers affiliated with ETH Zurich, Institut des Hautes Études Scientifiques, Columbia University, and the Institute for Advanced Study.

Research and contributions

Kisin developed influential techniques in the study of p-adic Hodge theory, including work on crystalline representations, Barsotti–Tate groups, and integral models of Shimura varieties. He proved modularity lifting theorems that extended methods pioneered by Andrew Wiles and Richard Taylor and contributed to the understanding of Galois representations attached to automorphic forms on GL(n). His results on the existence and properties of crystalline lifts and on the classification of finite flat group schemes had impact on problems related to the Fontaine–Mazur conjecture, the Breuil–Mézard conjecture, and aspects of the local Langlands correspondence.

Kisin's work on integral models of Shimura varieties clarified the structure of these varieties at bad reduction primes and influenced advances in the theory of Rapoport–Zink spaces and the construction of local models used by researchers at Université Paris-Saclay and Princeton University. His methods combined techniques from scheme theory in algebraic geometry with deep input from representation theory, p-adic analytic geometry, and ideas originating in the work of Jean-Marc Fontaine, Gerd Faltings, and Pierre Colmez.

Through substantial collaborations and mentorship, Kisin has shaped research directions at institutions including King's College London, University of California, Berkeley, and Yale University. His lectures and expository notes influenced graduate training in arithmetic geometry and provided tools used in further developments by mathematicians at Stanford University, MIT, University of Chicago, and Brown University.

Honors and awards

Kisin's contributions have been recognized by invitations to give plenary and invited talks at the International Congress of Mathematicians and by election to learned societies. He has received prizes and fellowships from organizations including the Royal Society, the London Mathematical Society, and the European Research Council. His work earned commendations in citation prizes and research awards often conferred by institutions such as Trinity College, Cambridge and national funding bodies in the United Kingdom.

Selected publications

- Kisin, M., "Modularity of 2-adic Barsotti–Tate representations", Annals of Mathematics (work on modularity lifting related to Andrew Wiles and Richard Taylor). - Kisin, M., "Crystalline representations and F-crystals", Publications Mathématiques de l'IHÉS (results on p-adic Hodge theory and crystalline representations). - Kisin, M., "Integral models for Shimura varieties of abelian type", Journal of the American Mathematical Society (work on Shimura varieties and integral models). - Kisin, M., "Moduli of finite flat group schemes, and modularity", Compositio Mathematica (classification results with implications for the Fontaine–Mazur conjecture). - Kisin, M., "Overconvergent modular forms and the Breuil–Mézard conjecture" (papers and lecture notes influencing research on modularity and Breuil–Mézard conjecture).

Category:British mathematicians Category:Number theorists Category:Algebraic geometers