Policy handout, in pdf format.
| Date | Speaker | Approximate Subject |
|---|---|---|
| Jan 12 | Allan Donsig | Introduction |
| Jan 19 | Martin Luther King, Jr. Holiday | |
| Jan 26 | Department Colloquium | |
| Feb 2 | Al Peterson | Time Scales |
| Feb 9 | Jamie Radcliffe | Entropy methods in discrete mathematics |
| Feb 16 | Glenn Ledder | Mathematical Modeling in Biology |
| Feb 23 | Mark Walker | K-Theory/Algebraic Geometry |
| Mar 2 | John Orr | Operator Algebras |
| Mar 9 | Tom Marley | Commutative Algebra |
| Mar 16 | Spring Break | |
| Mar 23 | Bo Deng | Mathematical Biology |
| Mar 30 | George Avalos | Numerical Computation of Minimal Norm Control Asymptotics Relative to the Null Controllability of Non-Standard Parabolic-Like Dynamics |
| Apr 6 | Susan Hermiller | Geometric Group Theory |
| Apr 13 | Graduate Student Panel on Finding a Thesis Advisor | |
| Apr 20 | Christine Kelley | Coding Theory |
| Apr 27 | End of Course Wrap Up | |
| Speaker | Abstract |
|---|---|
| Allan Peterson | A time scale T is just a closed nonempty subset of the real numbers. Time scales include the real numbers, the integers, and the Cantor set. Given a smooth function p(t) defined on a time scale and a point s in the time scale we will define a generalized exponential function ep(t,s) which generalizes the exponetial function ept studied in calculus. Many beautiful properties of this generalized exponential function will be examined. |
| Jamie Radcliffe | The physical notion of entropy has spawned a variety of mathematical analogues, one of which is the notion of the entropy of a random variable. Recently there have been a variety of results in combinatorics proved by estimating the entropy of random variables naturally associated with a combinatorial problem. I will discuss the definition and meaning of entropy, and also some of the results that have been proved using this technique. |
| Glenn Ledder | In the multidimensional space of academia, the mathematical modeling region intersects both the mathematics region and the science region, which do not directly intersect each other. Or, to borrow a metaphor from biology, mathematical modeling is the tendon that connects the muscle of mathematics to the skeleton of science. Mathematical modelers employ mathematical methods in the study of science problems, but they do much more than that. They provide a critical analysis of the conceptual models that underlie scientific theories. |
| Mark Walker | Algebraic geometry
is one of the largest and oldest branches of mathematics. What's more, the subject has undergone at least two
"revolutions" since its inception. The first, due to Oscar Zariski
and others, linked algebraic geometry with commutative algebra, and
the two fields have been intertwined ever since. The second was due to
Alexander Grothendieck and his followers, and it resulted in a
tremendous abstraction of the subject. For these reasons, summarizing
what the entire field of algebraic geometry is all about is a rather
daunting task.
K-theory is also a rather vast subject area, having connections with algebraic geometry, commutative algebra, algebraic topology, number theory, and even operator algebra. The flavor of K-theory that I am most mostly interested in concerns its applications to algebraic geometry. In my talk, I will attempt to give a flavor of these subjects by talking about some things of current interest to me. |
| George Avalos | Semidiscrete finte difference and finite element method numerical approximation schemes are presented for the null controllability of two non-standard parabolic PDE control systems. The key feature here is that the null controllers being approximated exhibit the asymptotics of the associated minimal energy function. This is joint work with Michael Gunderson and Scott Hottovy. | Susan Hermiller |
Group theory originated in chemistry, in the study
of symmetries of crystal lattices. Current avenues
of research still include studying a group by studying
a space for which it is a group of symmetries. In my
talk I'll describe some examples of reflection groups.
If someone wants to read a bit more after the talk, it might be best if they come and chat with Professor Hermiller, who could tailor suggested references to their interests. One nice exposition is a paper by Martin Bridson: The Geometry of the Word Problem. |
Christine Kelley | Coding theory is the study of how to reliably and efficiently transmit information from one point in space (or time) to another. The origins of coding theory are attributed to Shannon in 1948 who proved the existence of good codes, and Hamming in 1949 who gave the first explicit code construction. Coding theory lies in the intersection of mathematics, electrical engineering, and computer science, and relies on tools from a broad range of mathematics. In this talk, we will look at some basic families of codes and communication channels, and discuss some of the current directions in this area. |