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 Events
Uriya First
UBC
Thu 6 Nov 2014, 3:30pm
Number Theory Seminar
room MATH 126
Rational isomorphism of quadratic forms and related objects
room MATH 126
Thu 6 Nov 2014, 3:30pm-4:30pm

Abstract

Let R be a discrete valuation ring with fraction field F. Two algebraic objects (say, quadratic forms) defined over R are said to be rationally isomorphic if they become isomorphic after extending scalars to F. In the case of unimodular quadratic forms, it is a classical result that rational isomorphism is equivalent to isomorphism. This has been recently extended to "almost umimodular" forms by Auel, Parimala and Suresh. I will present further generalizations to related objects: hermitian forms over involutary R-algebras, quadratic spaces equipped with a group action ("G-forms"), and systems of quadratic forms. The results can be regarded as versions of the Grothendieck–Serre conjecture for certain non-reductive groups. (Joint work with Eva Bayer–Fluckiger.)
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Morningside Center of Mathematics and Purdue
Thu 13 Nov 2014, 3:30pm
Number Theory Seminar
room MATH 126
Introduction to Mochizuki's works on inter-universal Teichmuller theory
room MATH 126
Thu 13 Nov 2014, 3:30pm-4:30pm

Abstract

Inter-universal Teichmuller theory, as developed by Mochizuki in the past decade, is an analogue for number fields of the classical Teichmuller theory, and also of the p-adic Teichmuller theory of Mochizuki. In this theory, the ring structure of a number field is subject to non-ring theoretic deformation. Absolute anabelian geometry, a refinement of anabelian geometry, plays a crucial role in inter-universal Teichmuller theory. In this talk, we will try to give an introduction to these ideas.
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TBA
Thu 20 Nov 2014, 3:30pm
Number Theory Seminar
room MATH 126
room MATH 126
Thu 20 Nov 2014, 3:30pm-4:30pm

Abstract

 
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Oxford University
Thu 27 Nov 2014, 3:30pm
Number Theory Seminar
room MATH 126
TBA
room MATH 126
Thu 27 Nov 2014, 3:30pm-4:30pm

Abstract

 
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UCLA
Thu 5 Mar 2015, 3:30pm
Number Theory Seminar
room MATH 126
TBA
room MATH 126
Thu 5 Mar 2015, 3:30pm-4:30pm

Abstract

 
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