Seminar Calendar
for events the day of Wednesday, February 15, 2012.

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Questions regarding events or the calendar should be directed to Tori Corkery.
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Wednesday, February 15, 2012

Study Seminar in Geometry and Analysis
3:00 pm   in 347 Altgeld Hall,  Wednesday, February 15, 2012
 Del Edit Copy
Submitted by jathreya.
 Organizational MeetingAbstract: We'll be chatting about the papers we're going to discuss this semester. Possibilities include: 1) Witten's Gauge theoretic interpretation of Kovanov homology of knots (these are they same equations he proposed for Geometric Langlands) 2) Extremals of the determinant of the Laplacian and uniformization. In dimension 2 the fundamental paper would be the one by Osgood, Phillips and Sarnak: http://www-ee.stanford.edu/~osgood/papers/extremals1988.pdf 3)Manning's work on the behavior of volume growth entropy along Ricci Flow in the setting of surfaces.

Math 499: Introduction to Graduate Mathematics
4:00 pm   in 245 Altgeld Hall,  Wednesday, February 15, 2012
 Del Edit Copy
Submitted by seminar.
 Peter Loeb (Department of Mathematics, University of Illinois)Infinitesimals in Analysis and Probability TheoryAbstract: The notion of an infinitesimal quantity has been used in mathematics for over 2200 years. It eluded rigorous treatment until the work using model theory of Abraham Robinson in 1960 established a rigorous foundation for the use of infinitesimals in mathematics. Recent extensions and applications of his theory, now called nonstandard analysis, have produced new results in many areas including operator theory, stochastic processes, mathematical economics and mathematical physics. In all of these areas, infinitely small and infinitely large quantities can play an essential role in the creative process. At the level of calculus, the integral can now be correctly defined as the nearest ordinary number to an infinitely large sum of infinitesimal quantities. In Probability theory, Brownian motion can now be rigorously parameterized by a random walk with infinitesimal increments. In economics, an ideal economy can be formed from an infinite number of agents each having an infinitesimal influence on the economy. Spaces formed with nonstandard analysis give the simplest probability spaces for a continuum of independent random variables or traders in an economy. The talk gives an introduction to this fruitful area of mathematics.