# Difference between revisions of "NTSGrad/Abstracts"

## Sep 06

 Brandon Alberts Introduction to the Cohen-Lenstra Measure The Cohen-Lenstra heuristics describe a conjectured probability distribution for the class group of quadratic fields. In this talk, I will give a brief introduction to the heuristic and how it is related to random groups. The remainder of the talk will focus on the Cohen-Lenstra probability measure for choosing a random p-group. This talk is based on a similar talk given by Bjorn Poonen.

## Sep 13

 Vlad Matei Overview of the Discrete Log Problem The discrete logarithm problem (DLP) was first proposed as a hard problem in cryptography in the seminal article of Diffie and Hellman. Since then, together with factorization, it has become one of the two major pillars of public key cryptography. In its simplest version for $\mathbb{Z}/p\mathbb{Z}$, the problem is given $b\hspace{2mm} ( \text{mod}\hspace{2mm} p)$ and $b^n \hspace{2mm}(\text{mod} \hspace{2mm} p)$ to find $n$. As far as we know, this problem is VERY HARD to solve quickly. Nobody has admitted publicly to having proved that the discrete log can't be solved quickly, but many very smart people have tried hard and not succeeded. This is a prep talk for the Thursday seminar 9/15/2016

## Sep 20

 Wanlin Li Gauss's Genus Theory and 2-Selmer Groups of Elliptic Curves I'm going to talk about how Gauss's genus theory characterized 2 torsion elements of the class group for imaginary quadratic fields and how to use 2 decent to compute the 2-Selmer group for an elliptic curve.

## Sep 27

 Ewan Dalby Modular forms of half integral weight Usually when we think of modular forms we think of functions that gain an integral power of the automorphic factor under a group action. However we can generalize this notion to allow half integral weights. I will describe how this generalization works and it's connections to the theory of integral weight modular forms.

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## Organizer contact information

Brandon Alberts (blalberts@math.wisc.edu)

Megan Maguire (mmaguire2@math.wisc.edu)