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

### NEWS in the Department of Mathematics Graduate Announcements

Ben Cooper - PhD preliminary examination
Date: Thursday, December 12, 2013
Place: Weber, 201
Time: 1:00 p.m.

Title:   Transitive Hyperovals, Abstract Hyperovals and Partial Geometries

Committee:
Dr. Renzo Cavalieri
Dr. Jeanne Duflot
Dr. Anton Bohm

Abstract: A hyperoval is a ($q$+2)- arc of a projective plane $\pi$, of order $q$ with $q$ even. Let $G$ denote the collineation group of $\pi$ containing a hyperoval $\Omega$. We say that $\Omega$ is transitive if for any pair of points $x$, $y$ $\in$ $\Omega$, there exists a $g$ $\in$ $G$ fixing $\Omega$ setwise such that $x^{g}$ $=$ $y$. In 1987, Billotti and Korchmaros proved that if $4||G|$, then either $\Omega$ is the regular hyperoval in PG(2,$q$) for $q$=2 or 4 or $q$ $=$ 16 and $|G||$144. In 2005, Sonnino proved that if $|G|$ $=$ 144, then $\pi$ is desarguesian and $\Omega$ is isomorphic to the Lunelli-Sce hyperoval. Using a computational approach our long term aim is to show that if $G$ is the collineation group of a projective plane containing a transitive hyperoval with 4 $| |G|$, then $|G|$ $\geq$ 144. We also show that there is no hyperoval in a projective plane of order 12 with a group of order divisible by 11 or 13, by showing that there is no partial geometry  $pg(6,10,5)$ admitting a group of order 11 or of order 13, and that there is no hyperoval in a projective plane of order 12 with a dihedral subgroup of order 14, by showing that that there is no partial geometry $pg(7,12,6)$ admitting a dihedral group of order 14. The latter results are achieved by studying abstract hyperovals and their symmetries.

## 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
**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

## AMS - AMERICAN MATHEMATICAL SOCIETY Fan China Exchange Program

Grants to support collaborations between Chinese and U.S./Canadian researchers are made possible
through the generosity of Ky and Yu-Fen Fan.

The Fan China Exchange
Program is intended to send eminent mathematicians from the U.S. and Canada to make a positive
impact on the mathematical research community in China and to bring Chinese scientists in the early
stages of their research to the U.S. and Canada to help further their careers. The program
encourages host institutions to provide some type of additional support for the travel or living
expenses of the visitor and to ensure a suitable length of stay.

Applications received before March 15 will be considered for the following academic year.

For more information on the Fan China Exchange Program and application process see
www.ams.org/employment/chinaexchange.html or contact the AMS Membership and Programs Department by
telephone at 800-321-4267, ext. 4170 (U.S. and Canada), or 401-455-4170 (worldwide), or by email at prof-serv@ams.org.

Mathematical Sciences Research Institute’s (MSRI)