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Spring 2009 schedule

Date Speaker Title
January 28 Yuliya Gorlina Alexandrov’s theorem
I will give a brief overview of a new proof (by Bobenko and Izmestiev) that any convex Euclidean polyhedral metric on the 2-sphere can be realized as the surface of a convex polytope in R3. The talk will be accessible to all graduate students who are comfortable with gluing triangles or tetrahedra together.
February 4 Matt Thomas A beginner’s guide to geometric quantization
Geometric quantization provides a method of constructing quantum-mechanical analogues of classical mechanical systems. Not only is this interesting in a physical context, it also allows us to connect symplectic geometry (the classical mechanics setting) to Hilbert spaces (the quantum-mechanical setting).
February 11 Geillan Aly Topological quantum field theory in 2 dimensions
Using pretty pictures, algebra, and a hair of category theory, a Topological Quantum Field Theory will be defined. Where is the topology? Everywhere. A toy model will be provided as an example. This talk should be accessible to any grad student who can think in two dimensions (possibly three).
February 18 Joceline Lega GK-12 funding opportunities for 2009-10
The National Science Foundation, through its GK-12 program (Graduate Teaching Fellows in K-12 Education), funds grants to support graduate students interested in spending a year in a K-12 classroom, working in partnership with a K-12 teacher. We are expecting to receive such funding, starting in 2009, at the level of 10 fellowships per year, for 5 years. Last week, an application form for 2009-10 was circulated by email to all graduate students enrolled in the Graduate Program in Mathematics and in the GIDPs in Applied Mathematics and Statistics.

The purpose of the two informational sessions (Graduate Colloquium on 2/18 and Brown Bag Colloquium on 2/20) held this week is to provide a description of this program and to discuss issues such as benefits for participants and responsibilities of GK-12 fellows. Members of the management team will be present to answer questions and former GK-12 fellows will describe their experience with similar programs on campus.

All students who are interested in applying for a GK-12 fellowship, either for 2009-10 or 2010-11, are encouraged to attend.

February 25 Martin Leslie Why you can’t integrate exp(x^2)
You may remember being told in calculus that there are certain functions that don’t have elementary antiderivatives. Many years later you now have the background to understand why. I will introduce basic differential algebra and give the statement and selected applications of Liouville’s theorem on elementary antiderivatives. There will also be some discussion of the Risch algorithm for finding antiderivatives and of differential Galois theory.
March 4 Enrique Acosta Cardinals and ordinals part I
In a (hopefully) very accessible talk, I will introduce ordinal numbers the way Cantor first thought of them, and then explain the definition found in modern set theory. This will lead to a discussion of what a cardinal really is, what set theory is about, what large cardinals are, and why 0=1 is the largest of them all.
March 11 Enrique Acosta Cardinals and ordinals part II
In a (hopefully) very accessible talk, I will introduce ordinal numbers the way Cantor first thought of them, and then explain the definition found in modern set theory. This will lead to a discussion of what a cardinal really is, what set theory is about, what large cardinals are, and why 0=1 is the largest of them all.
March 18 (Spring break)  
March 25 Tom LaGatta Riemannian first-passage percolation
Standard first-passage percolation (FPP) is a random model of discrete geometry, and a generalization of classical percolation. The model is simple: take the lattice Z^2 and associate to each bond (edge) a random number, called the passage time. This induces a metric, where the shortest distance between two points is the minimum of passage times over all paths which connect the two points. Imagine fluid flowing through a grid of pipes of different sizes.

Riemannian FPP is a continuum analogue of this: instead of a random metric on the lattice, consider a random Riemannian metric on the plane. Both models have a global geometric structure; the advantage of the second is that it has a local structure as well. For this talk, I will define the models and present some of the interesting questions one asks. I will also discuss some of the hurdles I’ve had to overcome in this study.

This talk will be accessible to a general mathematical audience, and I will assume no background in probability, mathematical physics nor Riemannian geometry.

April 1 Chol Park Computing the weak Mordell-Weil group
From the descent theorem, we see that given generators for the weak Mordell-Weil group E(K)/mE(K), a finite amount of computation will always yield generators for the Mordell-Weil group E(K). Unfortunately, there is no comparable algorithm currently known which is guaranteed to give generators for E(K)/mE(K) in a finite amount of time. However, if the conjecture that the Shafarevich-Tate group is finite is true, we have an algorithm for computing the generators of E(K)/mE(K).
April 8 Chantel Blackburn Constructing the simple representation modules of finite groups using GAP
In the field of representation theory it is of interest to construct the fundamental building blocks (simple modules) of the representation modules of a group. Representations are difficult to handle in practice because they often must be realized as large matrices. Therefore, a great deal of information about representations of groups has been gleaned instead from simpler functions called characters. This talk will demonstrate (via an introduction to representation theory) how the computer algebra system GAP can be used to construct the simple modules of a group by simply obtaining information about its characters already available in a GAP data library.
April 15 Jeff Taft Scratching the rectifiable current of geometric measure theory
This will be a friendly introduction to the subject of geometric measure theory. I do not intend to be very rigorous, but rather I would like to provide a feel for what the subject is. I will focus on some of the problems it is used to solve, and why the geometric measure theory approach works better than the traditional surface theory approach.
April 22 Alex Petrov Drinfeld à la carte
On the menu for this week:

1) Carlitz exponential
2) Carlitz factorial
3) Carlitz cyclotomic fields
4) Drinfeld modular forms

You also get to choose bagels, cookies and soda on the side.

April 29 Josh Chesler Reflections on an academic job search
If you work really hard for six years in grad school, then, if you’re lucky, you may get a job. Then you’ll have the privilege to work really hard for the next 40 or 50 years in a location not of your choosing. Someday you may even get tenure and by then, when the bitterness and/or enthusiasm have been replaced by a droning complacency, it will just feel right to work really hard all the time in a location not of your choosing. But achieving this satori requires a respect for the path. So far, my path has lead me through a successful academic job search; I’ll tell you about what I did right and wrong along the way and about the entire job search process. And someday you too may have the honor of getting dressed up so you can perform for a bunch of strangers who, by some cosmic mishap, get to decide your fate. This talk will include practical information and bagels for graduate students at all stages.
May 6 Ben Dyhr Free beer
The self-avoiding random walk (SAW) is a deceptively easy-to-describe model of deep interest to chemists and physicists. The macroscopic structure of long SAWs is of fundamental importance for models of linear polymers in chemical physics, which can be composed of thousands of monomers. On the other hand, as a mathematical object, basic questions about SAW illude rigorous probabilistic methods, so much of the literature on SAW relies on numerical and nonrigorous approaches. I will present a palatable talk aimed at a general audience, with lots of pretty pictures, describing current work of Michael Gilbert, Tom Kennedy, Shane Passon and myself on SAW, both rigorous and numerical.

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