Why are random matrix eigenvalues cool?

Some fun tidbits

Girko’s Circular Law, n=2000

Wigner’s Semi-Circle

Elements of Wigner’s Proof

Catalan Numbers

Finite Versions

How many eigenvalues of a random matrix are real?

How many eigenvalues of a random matrix are real?

How many eigenvalues of a random matrix are real?

Numerical Analysis:
Condition Numbers

Von Neumann & co.

Von Neumann & co. estimates
 (1947-1951)

Random cond numbers, n®¥

Finite n

Small World Networks:
 & 6 degrees of separation

Small World Networks:
 & 6 degrees of separation

The Riemann Zeta Function

The Riemann Hypothesis

The Riemann Hypothesis

Computation of Zeros

Nearest Neighbor Spacings & Pairwise Correlation Functions

Spacings

Some fun tidbits

Why cool?