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Seminar
FIELD Mathematics
DATE July 12 (Thu), 2018
TIME 16:00-18:00
PLACE 1424
SPEAKER Lee, Seok Hyeong
HOST Kim, Seungki
INSTITUTE Princeton University
TITLE Geometric perspective for ring parametrizations
ABSTRACT

Since Manjul Bhargava's phenomenal 'Higher Compositions Laws' (HCL) works which gave parametrizations of number fields of degree 2, 3, 4, 5 using certain integral forms, various generalizations and improvements of HCL came out so far. One of them was Melanie Wood's works where she generalized some part of HCL to arbitrary bases (degree 2 algebra over arbitrary schemes, etc.) and added some additional correspondences in the list.
In this explanatory talk, I will go over how Wood's hypercohomology construction provides the alternative scheme-theoretic approach for HCL and gives explicit procedure for computations. I will especially focus on its computational aspects and show explicit calculations of global functions in some cases.

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