NTSGrad Fall 2015/Abstracts
Contents
Sep 02
Lalit Jain |
Monodromy computations in topology and number theory |
The monodromy of a family of varieties is a measure of how homology classes vary. Surprisingly, many familiar ideas in number theory, such as Galois representations and Cohen-Lenstra heuristics, are closely linked to monodromy of specific families. In this talk I will define monodromy, explain some number theoretic applications, and describe original work of computing monodromy for moduli spaces of covers of the projective line (Hurwitz spaces). This work generalizes previous results of Achter-Pries, Yu and Hall on hyperelliptic families. Only basic knowledge of algebraic topology and number theory is required. |
Sep 09
Megan Maguire |
Infintely many supersingular primes for every elliptic curve over the rationals. |
In his 1987 Inventiones paper, Dr. Noam Elkies proved that every elliptic curve over [math]\mathbb{Q}[/math] has infinitely many supersingular primes. We shall discuss some of the mathematics needed to prove this result and give a proof. |
Sep 16
Silas Johnson |
Alternate Discriminants and Mass Formulas for Number Fields |
Kedlaya and Wood have explored alternate invariants for number fields, with the idea of replacing the discriminant in standard field-counting questions with one of these alternate invariants. We further explore the space of “reasonable” invariants, expanding on Kedlaya and Wood’s definition. We also discuss a theorem on mass formulas for these invariants. |
Sep 23
Daniel Hast |
Moments of prime polynomials in short intervals. |
How many prime numbers occur in a typical "short interval" of fixed width, and how are primes distributed among such intervals? We examine the analogue of this problem for polynomials over a finite field. Our approach is geometric: we interpret each moment of the distribution in terms of counting certain points on an algebraic variety, and we use an algebraic analogue of the Lefschetz fixed-point theorem to compute the leading terms of this "twisted" point-count. As a motivating example, we realize the "prime polynomial theorem" as a geometric statement. |
Sep 30
SPEAKER |
TITLE |
ABSTRACT |
Oct 07
SPEAKER |
TITLE |
ABSTRACT |
Oct 14
SPEAKER |
TITLE |
ABSTRACT |
Oct 21
SPEAKER |
TITLE |
ABSTRACT |
Oct 28
SPEAKER |
TITLE |
ABSTRACT |
Nov 04
SPEAKER |
TITLE |
ABSTRACT |
Nov 11
SPEAKER |
TITLE |
ABSTRACT |
Nov 18
SPEAKER |
TITLE |
ABSTRACT |
Nov 25
SPEAKER |
TITLE |
ABSTRACT |
Dec 02
SPEAKER |
TITLE |
ABSTRACT |
Dec 09
SPEAKER |
TITLE |
ABSTRACT |
Organizer contact information
Sean Rostami (srostami@math.wisc.edu)
Return to the Number Theory Graduate Student Seminar Page
Return to the Number Theory Seminar Page
Return to the Algebra Group Page