Department of Mathematics     Indiana University     Rawles Hall     831 East 3rd St     Bloomington, IN 47405     Phone: (812) 855-3171     FAX: (812) 855-0046

Abstracts

September 23rd, 2009 - Finite Projective Planes by Professor Michael Larsen September 16th, 2009 - Algebra helps keep you from getting out of joint by Professor Nets Katz We say that a point P is a joint for a set of lines in three dimensional space provided that at least three of the lines meet at P in a noncoplanar fashion. We show that N lines in space have at most O(N^{3/2}) joints. The key ingredient in the proof is Bezout's lemma, a classical result in algebra. April 22nd, 2009 - A friendly introduction to harmonic analysis by Professor Nets Katz I'll give a brief description of the field of harmonic analysis, its subject matter, its methods, and its successes. April 15th, 2009 - Vortices - How They Whirl and Twirl by Professor John Challifour Vortex motion is a frequent occurrence in Nature from the bathtub to storms to superconductors and superfluids and perhaps in QCD. How are they to be described mathematically? March 25th, 2009 - Mathematics, Genomics and Cancer by Professor Esfandiar Haghverdi Recent technological advances in biology and computational power has made it possible to measure, store, and process massive amounts of biological data (e.g., gene expression, copy number, etc.) We now face the challenge of transforming this wealth of data into useful information for our understanding of the machinery involved in biological processes as diverse as tissue regeneration and cancer. In particular, the study of cancer genomics has brought forward many promising and challenging venues for biologists as well as mathematicians. These have crucial applications from cancer therapeutics to ecotoxicogenomics. The high dimensionality of data in such applications, especially when contrasted with the small number of samples, poses new and unprecedented challenges to statistical methods. Thus dimensionality reduction techniques leading to a subset of features, also known as signatures, are among the most common approaches in dealing with massive data-sets. On the other hand, it has become evident that mathematical/statistical methods alone will not provide us with biological meaning, quite often the best method to use is not determined solely by mathematical measures; the nature of the biological problem under study plays an equally critical role. In this talk, I will review some recent work (last 10 years) in cancer genomics with an eye towards venues where mathematicians can make substantial contributions. November 5th, 2008 - Evils of Quaternionic Analysis by Professor Matvei Libine First I will define quaternions. Then I will describe different ways of defining complex holomorphic functions and explain what happens when you extend these definitions to quaternions. Finally, I will state a quaternionic analogue of the Cauchy formula which tells you how to recover a function inside a ball if you know its values on the boundary sphere. "Quaternions came from Hamilton after his really good work had been done; and, though beautifully ingenious, have been an unmixed evil to those who have touched them in any way, including Clerk Maxwell." -- Lord Kelvin, 1892. October 15th, 2008 - Aristotle in the Land of Quantum States: a taste of logic old and new by Professor Larry Moss This talk will introduce math students to logic by motivating and proving a "completeness theorem" for a logical system inspired by Aristotle's syllogisms. The mathematical tool used in the proof is a representation theorem for "orthoposets", a topic originating in the study of quantum logic. This talk will be completely elementary. October 8th, 2008 - Riddle Me This by Professor Chris Connell Do you think you have a riddle that will stump a room full of math lovers and professors alike? Are you ready to have your mind exercised with riddles that will make you think 'outside the box'? Come to math club tomorrow and discuss your favorite riddles over pizza in a discussion led by riddle enthusiast, Professor Chris Connell. October 1st, 2008 - N-tuplewise Independence and the Central Limit Theorem by Professor Richard Bradley Perhaps the most important classical ``law of averages'' in probability theory is the Central Limit Theorem (CLT), for sequences of independent, identically distributed random variables. For a given positive integer N, if the assumption of independence is replaced by the (weaker) assumption of ``N-tuplewise independence'' (any N of the random variables are independent), the CLT can fail to hold. This talk will give an elementary exposition of this topic. September 24th, 2008 - A Lie Group is Your Friend by Professor Jiri Dadok Theorem 1.1: There are strong connections between branches of mathematics. Proof: Consider Lie groups. Originally invented to solve differential equations they now play a role in topology, harmonic analysis, probability/statistics, geometry, complex analysis, mathematical physics, and of course algebra. Come and meet friends you may not have realized you had. September 17th, 2008 - Multilinearity by Professor Ciprian Demeter I will describe multilinearity in Ergodic theory and Harmonic analysis, with particular focus on things like Furstenberg's averages, bilinear Hilbert transform and existence of arithmetic progressions. September 10th, 2008 - Minimal Surfaces Old And New by Professor Matthias Weber Professor Weber will explain what minimal surfaces are, why they are interesting, and what the current research is about. Please bring scissors and glue for a fun project. For more information about minimal surfaces be sure to visit Weber's website, and view the gallery of images he has created.