Introduction to Mochizuki's works on Interuniversal Teichmuller theory
Chung Pang Mok (Purdue)
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When 
Jun 25, 2015 from 03:30 pm to 04:30 pm 
Where  Mainz, 05432 (Hilbertraum) 
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Abstract. Interuniversal Teichmuller theory, as developed by Shinichi Mochizuki in the past decade, is an analogue for number fields of the classical Teichmuller theory, and also of the padic Teichmuller theory of Mochizuki. In this theory, the ring structure of a number field is subject to nonscheme theoretic deformation. Absolute anabelian geometry, a refinement of anabelian geometry, plays a crucial role in interuniversal Teichmuller theory. In this talk, we will try to give an introduction to these ideas, using analogy from the theory of hyperbolic manifolds. Although F_1geometry is not used in Mochizuki's works, some of the ideas involved could be regarded as a manifestation of some kind of F_1geometry, for example the crucial use of monoid structures.