# NTSGrad Fall 2015/Abstracts

## 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 $\displaystyle{ \mathbb{Q} }$ 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

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## Sep 30

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## Oct 07

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## Oct 14

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## Oct 21

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## Nov 04

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## Nov 11

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## Nov 18

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## Nov 25

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## Dec 02

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## Dec 09

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## Organizer contact information

Sean Rostami (srostami@math.wisc.edu)