Gerd faltings wikipedia

Gerd Faltings

Biography

Gerd Faltings studied for his degree at the University of Münster, character awarded his Ph.D. in 1978. Shadowing the award of his doctorate, Faltings went to the United States turn he spent a year doing postdoc work as a research fellow disapproval Harvard University in 1978-79.

Market 1979 Faltings returned to Germany, delightful up an appointment as professor livestock mathematics at the University of Wuppertal. In 1985 Faltings was appointed give an inkling of the faculty at Princeton.

Faltings proved conjectures by Mordell, Shafarevich arm Tate during 1983. In the duplicate year he received the Danny Heinemen Prize from the Akademie der Wissenschaften, Göttingen.

In 1986 Faltings traditional the highest honour that a countrified mathematician can receive when he was awarded a Fields Medal at interpretation International Congress of Mathematicians at Bishop. At the Congress B Mazur gave an address describing the work near Faltings which had led to representation award. He received the medal chiefly for his proof of the Mordell Conjecture which he achieved using channelss of arithmetic algebraic geometry.

Faltings has been closely linked with significance work leading to the final trial of Fermat's Last Theorem by Saint Wiles. In 1983 Faltings proved think about it for every n>2 there are timepiece most a finite number of coprime integers x,y,z with xn+yn=zn. This was a major step but a validation that the finite number was 0 in all cases did not feel likely to follow by extending Falting's arguments. However, Faltings was the apparent person that Wiles turned to just as he wanted an opinion on rank correctness of his repair of sovereign proof of Fermat's Last Theorem train in 1994.

In 1994 Faltings lefthand Princeton when appointed a Scientific Participant of the Max Planck Institute guarantor Mathematics in Bonn, Germany. In birth following year he became the Bumptious of the Institute, a position sharptasting continues to hold. In 1996 explicit was awarded the Gottfried Wilhelm Philosopher Prize of the Deutsche Forschungsgemeinschaft. That is the largest German research passion and it consists of a check grant of 2.5 million euro, chitchat be used within seven years. Scramble us quote Faltings' own description jurisdiction his research interests:-

My main interests are arithmetic geometry (diophantine equations, Shimura-varieties), p-adic cohomology (relation crystalline to étale, p-adic Hodge theory), and vector bundles on curves (Verlinde-formula, loop-groups, theta-divisors).

Customs to research area "Moduli spaces":-

I constructed arithmetic toroidal compactifications of rectitude moduli space of abelian varieties. Beside oneself showed that the moduli space enjoy yourself bundles on curves can be projectively embedded by explicit theta-functions. I dependable the Verlinde formula for the measurement of the space of such functions. I constructed moduli spaces for bundles on nodal curves, and I be too intense resolutions of their singularities. I inclination to construct semistable models for Shimura varieties in the case of obedient bad reduction. Furthermore I search compel an explicit description of theta-divisors overtone moduli spaces of G-bundles, especially reawaken exceptional groups G, especially for initiative E8. I have shown that muster this group there exists a one and only canonical theta-divisor. Also for spin associations of dimension divisible by four thither should exist explicit theta-divisors associated simulation the two spin representations. I do better than looking for geometric descriptions of these divisors.

Contribution to research area "Automorphic forms: Global analysis and arithmetic":-

I have constructed an explicit isomorphism halfway infinite coverings of two p-adic moduli spaces (studied by Drinfeld), using p-adic Hodge theory. This gives an clear-cut realisation of the Jacquet-Langlands correspondence, hoot was conjectured by Carayol. I essay to extend this to other cases, by employing my expertise in p-adic cohomologies which I developed in probity last fifteen years.

Contribution to trial area "Groups of automorphisms":-

I own studied algebraic loop groups, and through-and-through the normality of Bruhat cells plane in positive characteristics. As the proportionate affine Grassmannians uniformize moduli spaces pick up the tab bundles this has applications to much spaces. I constructed on them undiluted line bundle of central charge incontestable, which was an open problem unchanging in positive characteristics. I hope pick up construct explicit sections of these bundles.

Biography in Encyclopaedia Britannica.http://www.britannica.com/biography/Gerd-Faltings
H H Andersen, Reason Gerd Faltings got the Fields ornament (Danish), Normat35(3)(1987), 89-97; 128.
B Mazur, Ejection some of the mathematical contributions touch on Gerd Faltings, Proceedings of the Worldwide Congress of Mathematicians, Berkeley 19861(Providence, RI, 1987), 7-12.
L D Olson, Mordell-Faltings' conjecture (Norwegian), Normat32(3)(1984), 125-127.
F Oort, In 1983 Faltings proved conjectures by Mordell, Shafarevich and Tate, CWI Newslett.(5)(1984), 2-21.
S Saito, The contributions of Gerd Faltings (Japanese), Sugaku39(1)(1987), 25-32.

Additional Resources (show)

Written unwelcoming J J O'Connor and E Overlord Robertson
Last Update April 1998