RFG – The geometry and combinatorics of branched
covers
2009-2010

RFG leader: Brian Osserman

Additional faculty: Michael Kapovich, Fu Liu, Motohico Mulase,
Jennifer Schultens.

Hurwitz theory – the study of branched covers of the Riemann sphere
– has
a long history, and a very interdisciplinary nature. Basic questions can
be stated equivalently in topology, elementary combinatorial group theory,
complex geometry, and algebraic geometry, so they can be understood and
studied even at the undergraduate level. Moreover, applications range from
these areas to string theory and number theory. The purpose of this
Research Focus Group is to introduce undergraduate and graduate students to
the field, and to provide a range of research problems suitable for
participants at all levels.

In addition to the organized activities listed below, participants will
meet regularly with faculty to receive guidance on research. Anyone
interested in participating in or in finding out more about the RFG is
encouraged to email Brian Osserman at
.

Activities

Courses and organized seminars are listed below. In addition, anyone
interested in pursuing research during the year is encouraged to
contact us as early as possible to discuss possible projects, some
of which could be started with essentially no prerequisites.
Math 248AB is in fact independent of the RFG, but RFG participants may
find it helpful to attend the course.

Taught by Motohico Mulase. Without assuming backgrounds in algebraic
geometry or moduli theory, will offer a survey of current areas of
excitement in Hurwitz theory. Topics include:

Taught by Jennifer Schultens. Without prerequisites in topology or algebra,
this elementary introduction to surfaces and coverings of surfaces will
treat the following topics:

Organized by Michael Kapovich, Fu Liu and Brian Osserman. Students
and faculty will give presentations concentrating on background material
in various subareas of Hurwitz theory. Occasional outside speakers will
lecture on their work in the subject.

Organized by Michael Kapovich, Fu Liu and Brian Osserman. Students
and faculty will give presentations on recent and current research, both
their own and that of other researchers in the field. Occasional outside
speakers will lecture on their work in the subject.