The Arithmetics Statistic graduate seminar, organized by Gagan Sekhon and Jamie Weigandt , meets Mondays from 2 to 2:50 p.m.
The current tentative schedule is below.
Date |
Speaker |
Title |
February 7th |
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February 14th |
Daniel Kane |
A problem related to the ABC conjecture |
February 21st |
NO MEETING |
Washington's Birthday |
February 28th |
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March 7th |
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March 14th |
Kevin Wilson |
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March 21st |
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March 28th |
Gagan Sekhon |
Galois properties of points of finite order of an elliptic curve |
April 4th |
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April 11th |
NO MEETING |
Workshop |
April 18th |
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April 25th |
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May 2nd |
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May 9th |
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May 16th |
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Abstracts
- Februay 14th, Daniel Kane: "A problem related to the ABC conjecture "
- Abstract: The ABC conjecture says roughly that the equation A+B=C has no solutions among highly divisible relatively prime positive integers A,B,C. If we weaken what is meant by "highly divisible", there are solutions and we instead find conjectures on the asymptotic number of such solutions. In this talk we discuss techniques for extending the range in which these conjectures are known to be true.
- March 28th, Gagan Sekhon: "Galois properties of points of finite order of an elliptic curve"
- Abstract: I will be presenting a paper by Serre, which proves that the
Galois group associated to points of finite order of an elliptic curve are "as big as possible". More concretely, given an elliptic curve E/K without complex multiplication, where K is a number field, the Galois representation associated to the action on p-torsion points of E is surjective for almost all but finitely many primes p.