Casey Warmbrand
Graduate Teaching Assistant
Department of Mathematics
The University of Arizona
Tucson, AZ 85721

Office: Math Bldg, Room 217
Phone: (520) 626-4996
Email: caseyw@math.arizona.edu

I am currently a TA for Math254-Differential Equations.

My Office Hours will be held on Thursdays from 11am-Noon in Math102 and on Fridays from 11am-Noon in Math217. I will also be available at most any other time by appointment. Please email me to schedule an appointment, please include a few possible meeting times for me to choose from.

Some websites of importance for your course are:

Prof. Bayly's Website

D2L

Webassign

Some of my research interests include Random Matrix Theory, Combinatorics, Tilings, Non-Intersecting Paths, Orthogonal Polynomials, Random Walks, Game Theory, Poker Modeling, and Network Theory.

My main focus recently has been on domino tilings of the Aztec Diamond. Specifically working on deformed the Aztec Diamond in hopes of producing an inscribed cardioid as the asymptotic boundary curve of the new shape that is being tiled.

The picture below on the left is a random tiling of an order 50 Aztec Diamond using 2-by-1 dominos. The one on the right is a order 20 regular hexagon tiled by lozenges, three different types of unit area rhombi shown below in green, blue, and red.
Of particular interest is the inscribed "circle" that is appearing as the number of tiles increases.

Aztec Hexagon

Props to Jim Propp (pun intended) and others for the creation of these tilings.

Over the first few weeks of the Fall semester of 2007 I gave a series of talks summarizing the work of Kurt Johansson and his application of technique developed by Lindström, Gessel and Viennot to compute asymptotic probabilities of objects related to the Aztec diamond.

Here are the slides from the first 3 weeks:
Talk #1 - Aztec Diamonds.
Talk #2 - Determinants and Non-Intersecting Paths.
Talk #3 - The Lindström-Gessel-Viennot Method.

Here is a paper I co-authored a while back (pdf):
On Network Theory - Published: PNAS | May 17, 2005 | vol. 102 | no. 20

Here is a paper I wrote recently on Poker Models - Under Revisions

Here is a copy of my Master's Thesis, a large N asymptotic analysis of partitions of N, based on the work of A. Vershik and S. Kerov. The partitions are obtained using the Robinson-Schensted algorithm on a uniformly distributed permutation of N objects. The measure on partitions, induced from the uniform measure on permutations by the Robinson-Schensted bijection, is called the Plancherel measure. In order to visualize the partitions and eventually describe them with a function, it is useful to use Young diagrams and Young Tableaux. A limiting shape for partitions is found through rescaling the boundary function as we take the limit N to infinity.

Some other papers I've written for various classes:
Self-Testing and Self-Correcting Algorithms
Ideals defining curves with generic zero

Here is a more recent copy of my Curriculum Vitae (mosly up to date).

I am an avid sports fan; I am always willing to debate why I feel baseball is the greatest sport ever! If a major sport has a team with a 4 letter name ending in "ets", you can bet I am rooting for them.

Barry Bonds may have passed Hank Aaron for the all-time MLB record for career HRs, but Barry still doesn't have a well-defined Erdös-Bacon number!