Department of

# Mathematics

Seminar Calendar
for events the day of Wednesday, April 19, 2006.

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
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Wednesday, April 19, 2006

3:00 pm in 343 Altgeld Hall,Wednesday, April 19, 2006

#### Coherent sheaves on Calabi-Yau threefolds and D-branes in type IIB string theory

###### Sheldon Katz   [email] (UIUC Math and Physics)

Abstract: I will begin by completing last week's discussion about N=2 supersymmetry in Type II closed string theory and some general comments about N=1 supersymmetry. After that, I'll introduce the notion of coherent sheaves from algebraic geometry and relate to D-branes.

4:00 pm in 245 Altgeld Hall,Wednesday, April 19, 2006

#### The Correct Use of Infinitesimals in Mathematics

###### Peter Loeb (Department of Mathematics, UIUC)

Abstract: The notion of an infinitesimal quantity has been used in mathematics for over 2200 years. It eluded rigorous treatment until the work of Abraham Robinson in 1960 established a rigorous foundation for the use of infinitesimals in mathematics. Recent extensions and applications of his theory, 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 a 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. The talk will give an overview of the basis for this very old, yet relatively new, area of mathematics.