Thursday, August 21N/A, N/A
Thursday, September 4George Andrews, Penn State University
1:15pmRamanujan, Fibonacci numbers, and Continued Fractions or Why I Took Zeckendorf's Theorem Along On My Last Trip To Canada
ABSTRACTThis talk focuses on the famous Indian genius, Ramanujan. One object will be to give some account of his meteoric rise and early death. We shall try to lead from some simple problems involving Fibonacci numbers to a discussion of some of Ramanujan's achievements including some things from his celebrated Lost Notebook.
Thursday, September 11Yuri Suhov, Penn State / University of Cambridge, UK
1:15pmIntroduction to Entropy
ABSTRACTThe entropy is a famous quantity which is used widely in Math, Physics, Biology, Economics, let alone Information Theory. The concept of entropy is also popular in culture: it inspired (and continues
to inspire) poets, artists and musicians. I will introduce and discuss basic properties of entropy which are of interest in many applications. Some of them will be quite surprising. I will also tell some elegant stories involving entropy. No preliminary knowledge of probability theory is required, apart from common sense and first principles.
Thursday, September 18John Roe, Penn State University
1:15pmCommutative implies associative?
ABSTRACTBy introducing the symbol i, with i<sup>2</sup>=-1, one can pass from the field of real numbers to the larger field of complex numbers. In the 19th century various attempts were made to define still larger "generalized number" fields, such as the quaternions and octonions, but all of these sacrifice some of the familiar "laws" of arithmetic: the quaternions are no longer commutative, the octonions not even associative. Notice that the commutative law apparently "dies" first. Around 1940, Heinz Hopf made an investigation of generalized number systems that were commutative but not necessarily associative, and he found that the reals and the complexes are the only examples. In other words, the commutative law implies the associative law (in the context in which he was working). Hopfs methods are topological, and are closely related to developments in topology in the latter half of the 20th century.
<b>Note: The talk starts at 1:25 p.m. </b>
Thursday, September 25Vishal Vasan, Penn State University
1:15pmThe William Pritchard Fluid Mechanics Laboratory
Thursday, October 2Carina Curto, Penn State University
Thursday, October 23Simon Tavener, Colorado State University
Thursday, October 30Greg Lawler, University of Chicago
Thursday, November 6Thomas Tucker, University of Rochester
Thursday, November 13Richard Schwartz, Brown University
Thursday, November 20N/A, N/A