With the help of the UGA Math
Club, I have organized the following activities in recent years. Suggestions
for future speakers are welcome.
2011-2012
Math Club Talk: Professor Kang Li, UGA
Computer Science Department
Internet security
2010-2011
Math Club Talk: Professor
Walter Robinson, NC State
Wed, April 20, 5pm – 6pm
Boyd Graduate Studies Bldg., Room 328.
Commitment, Chaos, and Noise: Insights
into Global Warming from the World’s Simplest Climate Models
Abstract:
“If global warming is real, why isn’t each year warmer than the one
before?” “Why can’t we stop global warming right now?”
“Why do we need big expensive climate models to make predictions?”
These are the sorts of questions intelligent people ask about global warming.
We can begin to understand the answers using two very simple mathematical
models of the climate system. One is a stochastic linear model; the other is a
nonlinear model, due to the late Edward Lorenz. In this talk we explore the
dynamics of these models, their relevance to the real world, and their
implications. The models are run “live”, so audience members can
request model experiments.
Pizza and refreshments after the talk
in the Matrix (308 Boyd).
Thursday March 3rd, 5pm – 6pm
Boyd Graduate Studies Bldg., Room 304
Sums of harmonic
integers
Abstract: Let
us say that an integer is harmonic if its absolute value is a power of 2
times a power of 3. Can 4985 be written as the sum of three harmonic integers?
The question would be much easier to answer if we didn't allow negative
summands! We will explain the significance of this problem, trace its origin
back to the 14th century, and give a simple solution. I'll also describe some
other recent results about sums of harmonic integers.
Dr. Howe is a research mathematician working at a federally funded think tank
for mathematical research, including research in cryptography. He will be glad
to discuss with interested audience members on how to best prepare for such a
career.
2009-2010
September 10, 5:00-6:00 pm,
Room 304 in Boyd Graduate Studies Building
Charles Perry, Career Consultant at UGA in charge of math majors
will
give a general presentation on preparing for a job search or grad school with
some tips about resumes, cover letters and interviews.
2008-2009
Wednesday February 4th, 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. Two short presentations by faculty, three short presentations by current math majors. Pizza and refreshments served.
April
15, 2009, 3:30pm, Miller Learning Center, Room 102,
First
Cantrell Lecture, Fields medalist David Mumford (Brown),
Mathematics
and the Diversity of Cultures
Mathematics has played a vital role in
every culture. Looking at the three cultures -- China, India and the West --
one can, to some extent "replay" the history of math from three
different starting points. Sometimes one finds that it developed with strong
parallels but sometimes with deep differences. I will use the development of
five mathematical ideas in these different cultures to illustrate this. Does
this complex history support or refute the Platonic idea that mathematics has a
universal existence, independent of its discovery by humanity?
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)
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).