Workshops & seminars

Visitor Seminar - Dr. Amnon Besser (Ben Gurion University)

DATE & TIME
Friday, December 2, 2022
3:30 p.m. – 4:30 p.m.
SPEAKER(S)

Dr. Amnon Besser (Ben Gurion University)

COST

This event is free

ORGANIZATION

Department of Mathematics and Statistics

WHERE

J.W. McConnell Building
1400 De Maisonneuve Blvd. W.
Room LB 921-04

WHEEL CHAIR ACCESSIBLE

Yes

p-adic methods for solving Diophantine equations

The problem of finding rational or integer solutions to polynomial equations is one of the oldest problems in mathematics and is one of the key driving forces in the development of Number Theory.  In the last 15 years new methods were developed that can sometimes effectively solve this problem. These methods attempt to find the solutions inside the larger set of solutions of the same equation in the field of p-adic numbers as the vanishing set of some computable function. When these methods work they give the rational solutions to arbitrarily large p-adic precision, which usually suffices to rigorously recover the full set of solutions.

I will survey the new methods, originating from the work of Kim and from the more recent work of Lawrence and Venkatesh. I will then explain my work with Muller and Srinivasan that uses a p-adic version of the notion of norms on line bundles and associated heights, as used for example in arithmetic dynamics, to give a new approach to some Kim type results.

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