Date 
Speaker 
Topic 
Sept. 15

Aaron Wood (University of Missouri, Columbia)

Affine reflections and structure of padic
Chevalley group
I will introduce affine reflections and use them to discuss a
Bruhattype decomposition of padic Chevalley groups.

Sept. 22

Aaron Wood (University of Missouri, Columbia)

Affine reflections and structure of padic
Chevalley group
I will the talk from last week.

Sept. 29

Aaron Wood (University of Missouri, Columbia)

Affine reflections and structure of padic
Chevalley group
I will the talk from last week.

Oct. 6

Shuichiro Takeda (University of Missouri, Columbia)

Representations of the Lie algebra \(\mathfrak{sl}_2(\mathbb{C})\)
I will give a classification of finite dimensional representations of
the Lie algebra \(\mathfrak{sl}_2(\mathbb{C})\)

Oct. 13

Shuichiro Takeda (University of Missouri, Columbia)

Representations of the Lie algebra
\(\mathfrak{sl}_3(\mathbb{C})\)
I will give a classification of finite dimensional representations of
the Lie algebra \(\mathfrak{sl}_3(\mathbb{C})\)

Oct. 20

Andreas Weingartner (Southern Utah University)

The distribution of divisors and related problems
We will consider questions related to the distribution of divisors of
integers, with particular focus on an asymptotic estimate for the
number of integers below x whose maximum ratio of consecutive
divisors is at most t. Several related results, concerning the
divisor graph, practical numbers, the degree distribution of
polynomial divisors and the cycle structure of permutations, will
also be discussed.

Oct. 27

Bill Banks (University of Missouri, Columbia)

Ramanujantype identities
In this talk, I will proof one or two Ramanujantype identities
using Eisenstein series and/or Dirichlet series together with
special values of the Riemann zeta function.

Nov. 3

Bill Banks (University of Missouri, Columbia)

Ramanujantype identities
I will continue the talk from last week

Dec. 1

Melissa Emory (University of Missouri, Columbia)

The Diophantine Equation \(x^4+y^4=D^2z^4\)
in Quadratic Fields
A.Aigner proved that except in \(\mathbb{Q}(\sqrt{7})\), there are no
nontrivial quadratic solutions to \(x^4+y^4=z^4\). The result was
later reproven by D.K. Faddeev and the argument simplified by
L.J. Mordell. This talk discusses work to extend this result that
shows that nontrivial quadratic solutions exist to
\(x^4+y^4=D^2z^4\) precisely when either \(D=1\) or \(D\) is a
congruent number.

Dec. 8

Igor Shparlinski ( University of New South Wales)

Divisibility of Fermat Quotients
We show that for a prime \(p\) the smallest \(a\) with
\(a^{p1} \not \equiv 1 \pmod {p^2}\) does not exceed
\((\log p)^{463/252 + o(1)}\) which improves the previous bound
\(O((\log p)^2)\) obtained by H. W. Lenstra in 1979. We also
show that for almost all primes \(p\) the bound can be improved as
\((\log p)^{5/3 + o(1)}\).
These results are based on a combination of various techniques
including the distribution of smooth numbers, distribution
of elements of multiplicative subgroups of residue rings,
bound of Heilbronn exponential sums and a large sieve inequality
with square moduli.
