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, 3:30pm4:30pm
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 Ralgebras, quadratic spaces equipped with a group action ("Gforms"), and systems of quadratic forms. The results can be regarded as versions of the Grothendieck–Serre conjecture for certain nonreductive 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 interuniversal Teichmuller theory

room MATH 126
Thu 13 Nov 2014, 3:30pm4:30pm
Abstract
Interuniversal 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 padic Teichmuller theory of Mochizuki. In this theory, the ring structure of a number field is subject to nonring 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.
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Thu 20 Nov 2014, 3:30pm
Number Theory Seminar
room MATH 126


room MATH 126
Thu 20 Nov 2014, 3:30pm4:30pm
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, 3:30pm4:30pm
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, 3:30pm4:30pm
Abstract
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