# 1997 Dartmouth Kemeny Lecture Series

will present the following series of lectures

### A Non-Euclidean Big Bang

##### Wednesday, April 30, 7:00 pm, Filene Auditorium

**Abstract. **We will follow an expanding shock wave as it evolves in a particular non-euclidean
space. Besides the fact that the pictures are nice, this particular shock wave has connections
with unsolved problems in number theory. All necessary facts about non-euclidean geometry
will be covered in the talk. This talk will be accessible to an undergraduate audience.

### L-functions and Class Fields

##### Thursday, May 1, 4:00 pm, 102 Bradley Hall

**Abstract.** It has long been recognized that zeta functions and L-functions attached to number
fields carry in their analytic structure an amazing amount of information about those fields. In
the last quarter century, conjectures have evolved showing how values of these functions at
particular points can sometimes be used to determine the fields in question. The numerical
evidence is convincing, but the conjectures remain unproved.

**High Tea.** Will be served at 3:30 pm in the Faculty Lounge on the second floor of Bradley Hall.

### Zeta Functions of Graphs and Quadratic Covers

##### Friday, May 2, 4:00 pm, 102 Bradley Hall

**Abstract**. There are several interrelated ways to define a zeta function of a finite graph which
mimic zeta functions of number fields. The simplest of these are functions of one variable. The
more complicated functions are functions of several variables which reduce to the one variable
function when the variables are specialized. All of these functions behave in a manner similar
to the theory of zeta functions and their factorizations into L-functions in the number field
setting. In this talk we will survey some of these functions and their interrelations.

**High Tea.** Will be served at 3:30 pm in the Faculty Lounge on the second floor of Bradley Hall.
**Hosts. **Tom Shemanske and Dorothy Wallace are the hosts. Anybody who is interested in having
dinner with the speaker during his visit to Dartmouth should contact either Tom at 646-3179
or Dorothy at 646-3610.

*All talks will be self-contained and accessible to graduate students.
*