Prof. J. Willard Gibbs

Patterns in Eigenvalues: the 70th Josiah Willard Gibbs Lecture

Typical large unitary matrices show remarkable patterns in their eigenvalue distribution. These same patterns appear in telephone encryption, the zeros of Riemann’s zeta function, a variety of physics problems, and in the study of Toeplitz operators. This paper surveys these applications and what is currently known about the patterns.

Josiah Willard Gibbs and the Extension of the Principles of Thermodynamics.

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Willard Thompson

Complexity theory has a profound influence on the field of cryptology. The time complexity of breaking a cipher system must be significant enough to thwart any adversary from succeeding. However, with the emergence of quantum computers an adversary may have no difficulty in breaking known cipher systems. If quantum computers would exist today new mechanisms for security would need to be built. ...

6 . 042 J / 18 . 062 J , Fall ’ 05 : Mathematics for Computer Science October 3 Prof . Albert

A 1994 University of Chicago study entitled The Social Organization of Sexuality found that on average men have 74% more opposite­gender partners than women, confirming a view that men are more promiscuous. But whoever reported this finding was lying or confused! We’ll show you how to use the properties of vertex degrees in a graph to prove this. Let’s recast opposite­gender partnering in graph...