UIUC Dept. of Mathematics Seminar Calendar

     October 2009          November 2009          December 2009    
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Wednesday, February 4, 2009

Math 499: Introduction to Graduate Mathematics
4:00 pm in 245 Altgeld Hall, Wednesday, February 4, 2009

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Florin Boca (Department of Mathematics, University of Illinois)
Fat lattice points and limiting distributions

Wednesday, February 11, 2009

Wednesday, February 25, 2009

Wednesday, March 4, 2009

Wednesday, March 11, 2009

Wednesday, March 18, 2009

Wednesday, April 1, 2009

Wednesday, April 8, 2009

Math 499: Introduction to Graduate Mathematics
4:00 pm in 245 Altgeld Hall, Wednesday, April 8, 2009

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Zoi Rapti (Department of Mathematics, University of Illinois)
DNA Modeling: from probabilities to waves
Abstract: In this talk we will review some of the well known models for the DNA double strand, discuss their behavior, and, when appropriate, make comparisons. Most of the models that are suitable for mathematical analysis are coarse, in the sense that they only take into account the most important factors of DNA stability. We will explain how one can obtain the probabilities for large opening in the double strand, that is, the probabilities for the formation of regions where the hydrogen bonds are partially or totally broken. We will then consider the dynamical behavior of the systems and discuss how waves propagate along the strand and what mechanisms cause the emergence of localized structures. No background in biology in necessary.

Wednesday, April 22, 2009

Math 499: Introduction to Graduate Mathematics
4:00 pm in 245 Altgeld Hall, Wednesday, April 22, 2009

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Zoltan Furedi (Department of Mathematics, University of Illinois)
Tangent unitballs in normed spaces
Abstract: A family of pairwise disjoint, tangent balls of the same radii in the d-dimensional Euclidean space cannot have more than d+1 members. In the maximum norm 2^d is possible (hypercubes with a common vertex). The case of l_1 norm is unsolved (2d is conjectured). Our aim is to show that there is a smooth, centrally symmetric, strictly convex body in dimension d such that one can find 1.03^d (exponentially many!) translated copies pairwise tangent to each other. The proof applies Extremal Hypergraph Theory, some probabilily and of course a little of the geometry of the space.

Wednesday, April 29, 2009

Wednesday, May 6, 2009

Math 499: Introduction to Graduate Mathematics
4:00 pm in 245 Altgeld Hall, Wednesday, May 6, 2009

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Dirk Hundertmark (Department of Mathematics, University of Illinois)
Why are dirty metals bad conductors? A mathematicians point of view
Abstract: It is a fact of life that dirty metals are bad conductors. But why is this so? There are no perfect crystals in real life, one will always have randomly distributed impurities or defects in the crystalic structure. In the 1950s, Phil Anderson, a graduate of the UofI high-school (and Nobel price winner) invented and studied a model for electrons in a disordered crystal, now called the Anderson model. It is the quantum mechanical analogue of a random walk in a random environment. I will discuss some rigorous results, with the emphasis on a simple proof of localization (i.e., trapping of electrons) for large disorder.

Monday, September 21, 2009

Monday, September 28, 2009

Math 499: Introduction to Graduate Mathematics
4:00 pm in 245 Altgeld Hall, Monday, September 28, 2009

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Marius Junge (Department of Mathematics, University of Illinois)
Form operator algebras to quantum information theory
Abstract: A former graduate student of mine, now Professor in Copenhagen, complained to me once: But you see connections everywhere! That being said, I believe that ideas coming form more than one field in mathematics, will play a major role in future research. However, all these interactions often start with one of these small, almost obvious little ideas, and than are boosted to something big. The aim of this talk is to study the common feature between operator algebras and quantum information theory, the notion of a completely positive map. I intend to state one of the biggest events in the last years, the failure of the additivity conjecture for channels by Hastings and what this has to do with entanglement.

Monday, October 19, 2009

Math 499: Introduction to Graduate Mathematics
4:00 pm in 245 Altgeld Hall, Monday, October 19, 2009

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Kenneth Stolarsky (Department of Mathematics, University of Illinois)
Polynomials in Number Theory and Analysis
Abstract: In algebra and analysis one needs eigenvalues of matrices, and in number theory one needs the set of all algebraic numbers, so roots of polynomials, with or without integer coefficients, are of central importance. There is much more to the study of polynomials than the fundamental theorem of algebra. Various easily stated problems (even for polynomials with coefficients not constrained to be integers) remain open. In particular, there are many ways to measure the size of a polynomial, and these lead to interesting results and open problems about the largest or smallest polynomial satisfying a given condition. Polynomials can enter into problems whose formulation does not mention polynomials. One example is finding universally optimal distributions of points on spheres. Another is the open problem of determining the mod 1 distribution of x^n for a given x > 1 (e.g. x = 3/2). This has led to the concept of a PV number.

Monday, October 26, 2009

Math 499: Introduction to Graduate Mathematics
4:00 pm in 245 Altgeld Hall, Monday, October 26, 2009

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George Francis (Department of Mathematics, University of Illinois)
Mathematical Visualization
Abstract: Mathematical Visualization (mathviz for short) is almost a mathematical discipline despite its frivolous name. As old as Euclid's Elements, where figures first appear in a systematic way to illustrate geometrical theorems, it reached an uprecendented level of importance in the late renaissance, when artists discovered the rules of linear perspective, inadvertently laying the foundation of projective geometry, and thus, of non-Euclidean geometry. It rose to another zenith in the late 19th century with algebraic geometers and analysts determined to provide the imagination assistance with plaster and string, as preserved in our Altgeld model cases. Mathviz (barely) survived the iconoclastic age of Bourbaki, to again burst into flower in the information age. My talk concerns this latest chapter, concentrating on areas of mathematics that simply could not be investigated without computer graphics, but also with some practical advice on more mundane aspect of this "new kind of mathematics".

Monday, November 2, 2009

Monday, November 16, 2009

Monday, November 30, 2009