Mark Kisin

Mark Kisin (born August 10, 1971 in Vilnius ) is an Australian mathematician who studies arithmetic geometry and algebraic number theory.

Mark Kisin, Oberwolfach 2007

Life

Kisin was born in Lithuania and grew up in Melbourne from the age of five . He studied at Monash University with a bachelor's degree in 1991 and at Princeton University with a master's degree in 1995 and his doctorate in 1998 with Nicholas Katz ( Local constancy in p-adic families of Galois representations ). He was then a Research Fellow at the University of Sydney and until 2003 at the University of Münster . Kisin was Assistant Professor from 2003 and Professor at the University of Chicago from 2005before becoming a professor at Harvard University in 2009 .

He dealt with p-adic Galois representations in number theory with important contributions to the proof of the Serre conjecture by Chandrasekhar Khare and Jean-Pierre Wintenberger (from which the modularity theorem important for the proof of the Fermat conjecture can be derived). In 2009 he obtained partial results to confirm a conjecture by Jean-Marc Fontaine and Barry Mazur , which specifies criteria for when global p-adic Galois representations have "geometric origin" . In the Langlands program , he proved a special case of the Langlands-Rapoport conjecture about the shape of the p-adic points of Shimura varieties.

In 2008 he became a Fellow of the Royal Society and 2012 a Fellow of the American Mathematical Society . In 2010 he was invited speaker at the International Congress of Mathematicians in Hyderabad (India) (The structure of potentially semi-stable deformation rings). From 2004 to 2007 he was a Sloan Research Fellow.

Moduli of finite flat group schemes, and modularity. In: Annals of Mathematics. Volume 170, 2009, pp. 1085-1180
The Fontaine-Mazur conjecture for GL (2). In: J. American Mathematical Society. Volume 22, 2009, pp. 641-690
Potentially semi-stable deformation rings. In: J. AMS. Volume 21, 2008, pp. 513-546
Integral models for Shimura varieties of abelian type. In: J. AMS. Volume 23, 2010, pp. 967-1012
Geometric deformations of modular Galois representations. In: Inventiones Mathematicae. Volume 157, 2004, pp. 275-328
Overconvergent modular forms and Fontaine-Mazur conjecture. In: Inventiones Mathematicae. Volume 153, 2003, pp. 373-454
with Matthew Emerton : A Riemann-Hilbert correspondence for unit F-crystals. Part 1,2, In: Astérisque. Volume 293, 2004
with Matthew Emerton: An introduction to Riemann-Hilbert correspondence for unit F-crystals. In: Alain Adolphson, Francesco Baldassari, Pierre Berthelot, Nicholas Katz, Francois Loeser: Geometric Aspects of Dwork theory. Volume 2, De Gruyter, 2004, pp. 677-700
with Matthew Emerton: Unit L-functions and a conjecture of Katz. In: Annals of Mathematics. Volume 153, 2001, pp. 329-354
Prime to p fundamental groups and tame Galois actions. In: Ann. Inst. Fourier. Volume 50, 2000, pp. 1099-1126
Local constancy in p-adic families of Galois representations. In: Mathematical Journal. Volume 230, 1999, pp. 569-593 (dissertation)
What is a Galois representation? In: Notices AMS. June / July 2007, online

Christophe Breuil : Correspondance de Langlands p-adique, compatibilité local-global et applications, d'après Colmez, Emerton, Kisin ..., Séminaire Bourbaki 1031, 2011