Education is not the filling of a pail, it is the lighting of a fire. - W. B. Yeats

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### NEWS in the Department of Mathematics

Graduate Announcements

### Anne Ho - PhD preliminary examination

Date: Wednesday, July 30, 2014

Place: Weber, 201

Time: 10:00 a.m.

Title: Counting Artin-Schreier Curves Over Finite Fields

### Advisor: Dr. Rachel Pries

Committee:

Dr. Tim Penttila

Dr. Jeff Achter

Dr. Myung Hee Lee

### ** ** Abstract:
A number of authors have considered the weighted sum of various sets of curves over finite fields $k := F_q$. We denote this $\sum_{[C]} 1/|Aut_k(C)|$ where $[C]$ is the $k$-isomorphism classes of the curves, and $Aut_k(C)$ is the automorphism group of $C$ over $k$. These types of curves include elliptic curves over fields of any characteristic $p$ (Howe), hyperelliptic curves over fields of characteristic two (Van der Geer, Van der Vlugt), as well as Artin-Schreier curves of genus two and three over fields of characteristic two (Nart et al.). We extend the work of these authors by considering Artin-Schreier curves with a more general genus $g$ over fields of any characteristic $p$. We will discuss our results and methods of counting, which include looking at ramification divisors, finding associated rational models $y^p – y = u(x)$, and examining the actions of $PGL_2(k)$ on the models. We will end by discussing open cases and a conjecture.

## The AMS announces MATHEMATICS RESEARCH COMMUNITIES

Snowbird Resort, Utah

The AMS invites mathematicians just beginning their research careers to become part of Mathematics Research Communiities, a program to develop and sustain long-lasting cohorts for collaborative research projects in many areas of mathematics. Women and underrepresented minorities are especially encouraged to participate. The AMS will provide a structured program to engage and guide all participants as they start their careers. The program will include:

**One-week summer conference for each topic

**Special Session at the national meeting

**Discussion networks by research topic

**Funding for additional collaborations

**Longitudinal study of early-career mathematicians

June 8-14, 2014

Cluster Algebras

June 15-21, 2014

Algebraic and Geometric Methods in Applied Discrete Mathematics

June 24-30, 2014

Mathematics of Quantum Phases of Matter and Quantum Information

June 24-30, 2014

Network Science

For details, go to: http://www.ams.org/programs/research-communities/mrc

**2014 MSRI SUMMER GRADUATE SCHOOLS**

This coming summer MSRI is hosting three summer graduate schools in Berkeley, CA and co-sponsoring two* additional schools at off-site locations:

**Dispersive Partial Differential Equations ***June 16 – 27, 2014 at MSRI*

**Séminaire de Mathématiques Supérieures 2014: Counting Arithmetic Objects **June 23 – July 4, 2014 in Montréal, Canada

**IAS/PCMI 2014: Geometry and Materials **June 29 – July 19, 2014 in Park City, Utah

**Stochastic Partial Differential Equations **July 7 – 18, 2014 at MSRI

**Geometry and Analysis **July 28 – August 8, 2014 at MSRI