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From Teichm├╝ller to Mochizuki: arithmetic-anabelian IUT, its effective version and applications
23.1.2020, 16:15 - 17:15
Speaker:Prof. Ivan Fesenko, Mathematical Sciences, University of Nottingham
Location:Mathematisches Institut, Bunsenstr 3-5SitzungszimmerGras Geo Map
Organizer:Mathematisches Institut
I will talk about a recent work of 5 coauthors: Sh. Mochizuki, A. Minamide, Yu. Hoshi (Kyoto Univ.) and W. Porowski and I (Univ. Nottingham). It is an extension of the inter-universal Teichm├╝ller theory of Sh. Mochizuki; for an updated short description of the study of IUT and links see
This work incorporates the even residue characteristic, which, as usual in number theory, is more difficult than the odd residue characteristic. It then goes through the details of IUT to produce effective estimates of constants and the proof of effective form of one of abc inequalities, and to its further applications to various Diophantine equations. In the particular case of one of such equations, the Fermat equation, this work, entirely independently of modularity and the work of Wiles and Taylor, proves the first case of FLT for all prime exponents and proves the second case of FLT for all prime exponents except those between 2^{31} and 9.6x10^{13}.
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