With the help of the UGA Math Club, I have
organized the following activities in recent years. Suggestions for future
speakers are welcome.
2007-2008
September 19, 2007, 5:00-6:30, Conner Hall 104 (Blue Card
event)
A
double-feature talk by James Lauderdale
(Cellular Biology) and Andrew
Sornborger (Mathematics/Engineering),
Visualizing Thought -or- What Can Neuroscientists Learn From the CIA?
If the brain were a computer chip, we could simply map out all of
the circuits that caused it to function and figure out how they
relate to thought and behavior. In real life, however, figuring
out how brains work is much more complicated.
Our talk will describe the kind of things that we do in order
to understand real brains in real animals. Our labs work together
to visualize brain activity in a small tropical fish called a zebrafish.
In order to see a brain at work, we use zebrafish whose neurons glow
with a fluorescent jellyfish protein, high-tech laser microscopy and
mathematics. Using a tag-team format, we will show how mathematics,
such as methods originally developed to eavesdrop on the Russians,
and biology can combine to give new insights into how brains work.
November 14, Math Club Talk, 5:00-6:00, Boyd 304, (Blue Card event)
Janice Wethington (National Security Agency), Factoring Polynomials Over Finite Fields.
The topic of polynomials over finite fields is basic to the
study of cryptography. Certainly, we would want to know when one is irreducible
or how it might factor into irreducibles over the field of interest. This talk
starts with a short review of finite fields and a look at Stickelberger's
Theorem. Then I will give recent results by NSA mathematicians on factoring
polynomials over finite fields. This talk is designed to be accessible by
undergraduate math majors.
Wednesday February 13th, 4:30-6:30, Boyd 328, Math Major Fair , (Blue Card event)
Come mingle with faculty and current/prospective math majors, and learn about some exciting
mathematics happening in the department. Three short presentations by faculty. Pizza and refreshments served.
February 27, Math Club Talk, 5:30-6:30, Boyd 304, (Blue Card event)
Carl Pomerance (Dartmouth), The covering congruences of Paul Erdos.
Note that every integer is either even or odd. That is, the residue classes 0 mod 2
(the even numbers) and 1 mod 2 (the odd numbers) cover all of the integers.
Can this be done where the moduli are all different and larger than 1? Sure, but it's harder: try 0 mod 2, 0 mod 3, 1 mod 4, 1 mod 6, and 11
mod 12. Over 50 years ago, Paul Erdos asked if one can cover with a finite collection of residue
classes with distinct moduli, where the least modulus is arbitrarily large. He later wrote that this was perhaps his favorite problem.
It's not so difficult to find examples with least modulus 3 or 4 or so, but no one knows any examples with least modulus greater than 36.
Can you find one? This talk will give an introduction to this thorny, yet accessible research problem, discussing its origins in antiquity,
some new results, and some related problems.
March 26, 2008, 4:00-5:00, Physics Bldg., Room 202,
First Cantrell Lecture: Bjorn Poonen (Berkeley), Solved and unsolved problems in number
theory.
I
will survey a few of my favorite problems in number theory, such as Fermat's
last theorem (solved)
and the rectangular box problem (unsolved).