Abstract for James Sellers' Talk
Title: Research in Integer Partitions: Alive and Well
Abstract: Since my early
days of graduate school, I have been fascinated by integer partitions.
As with many other areas of mathematics, partition theory provides a
number of easily-phrased questions (that elementary school students can
understand) whose answers are either deep or (currently) non-existent.
In this talk, I will gently introduce you to the basics of the subject
and discuss some of the people who have inspired research in the field
over the last several years. I will also prove some well-known
partition-theoretic results, including Euler's famous result that the
number of partitions of an integer n into odd parts equals the number
of partitions of n into distinct parts. This result is approximately
250 years old, but is by no means "dead". I will demonstrate some
results related to this one which have arisen quite recently (within
the last year). My hope is that all will find this talk
refreshing and that some will be spurred on to future studies in
partitions.