Chandrashekhar Khare

Chandrashekhar Khare (* 1967 in Mumbai ) is an American mathematician of Indian origin who deals with arithmetic, algebraic geometry and number theory.

Life

Khare studied at the University of Cambridge (Bachelor in 1989, master's degree in 1996) and received his doctorate in 1995 at Haruzo Hida at California Institute of Technology on modular forms ( congruence between peak shapes , Congruences between cusp forms ), where he solved a long open problem. He then spent nine years at the Tata Institute of Fundamental Research , where he became a Fellow in 1996 and an Associate Professor in 2001. At the same time, he was Associate Professor at the University of Utah from 2001 , where he switched entirely in 2004. From 2007 he was a professor at the University of California, Los Angeles (UCLA)

From 2005 he announced the proof of Serre's conjectures in number theory in preprints , initially for a special case (“level 1”). With the French mathematician Jean-Pierre Wintenberger (University of Strasbourg) he had previously worked out his general strategy for proving the conjectures and had proven other special cases.

The conjectures made by Jean-Pierre Serre in 1972, which connect two-dimensional representations of the absolute Galois group of number fields with modular functions, play an important role in number theory and especially in the Langlands program and have, among other things, (as Serre recognized) about Andrew Wiles and Richard Taylor and others proved the Fermat conjecture to result in modularity . The proof of the conjecture, which also builds on the methods of Wiles and Taylor, came as a surprise, since the conjecture was considered by most mathematicians to be beyond the reach of current methods.

In 1999 he was named Scientist of the Year at the Indian Science Academy. In 2007 he received the Fermat Prize and in 2011 with Wintenberger the Cole Prize in number theory. In 2008 he was a Guggenheim Fellow. In 2010 he was invited speaker with Jean-Pierre Wintenberger at the International Congress of Mathematicians in Hyderabad ( Serre's Modularity Conjecture ). He is a fellow of the American Mathematical Society .

Khare has been a US citizen since 2007.

Fonts

• Khare Serre's modularity conjecture: the level 1 case , Duke Math. Journal, Vol. 134, 2006, pp. 557-589
• Khare, Wintenberger: Serre's modularity conjecture , part 1, 2, Inventiones Mathematicae, Volume 178, 2009, pp. 485-504, 505-586
• Khare, Wintenberger: On Serre's conjecture for 2-dimensional mod p representations of ${\displaystyle Gal({\bar {\mathbb {Q} }}/\mathbb {Q} )}$ , Annals of Mathematics, Volume 169, 2009, pp. 229-253, Preprint, pdf

Web links

• Homepage at UCLA
• The Hindu, April 25, 2005
• Homepage in Utah
• To prove the Serre conjecture in plus math 2005
• Acknowledgment on the occasion of the Guggenheim Fellowship

Individual evidence

1. ↑ Acknowledgment of the Cole Prize Winners in Notices AMS, April 2011
2. ↑ Chandrashekhar Khare in the Mathematics Genealogy Project (English)
3. ↑ A special case of the Serre conjecture, from which the Fermat conjecture follows, was also proven independently of Khare and Wintenberger in 2004 by the Spanish mathematician Luis Dieulefait