2016-2017 Milliman Lectures

Department of Mathematics

University of Washington

After completing her PhD at the University of Pennsylvania in 1974, Fan Chung Graham joined the technical staff of AT&T Bell Laboratories. From 1983 to 1991, she headed the Mathematics, Information Sciences and Operations Research Division at Bellcore, becoming a Bellcore Fellow in 1991. In 1993, she became the Class of 1965 Professor of Mathematics at the University of Pennsylvania. Since 1998, she has been a Professor of Mathematics and Professor of Computer Science and Engineering at the University of California, San Diego and holds the Akamai Chair in Internet Mathematics. Her research interests are primarily in graph theory, combinatorics and algorithm design, in particular in spectral graph theory, extremal graph theory, graph labeling, graph decompositions, random graphs, graph algorithms, parallel structures and various applications of graph theory in Internet computing, communication networks, software reliability, chemistry, engineering and various areas of mathematics.

**
**

__Tuesday, October 25th - Gowen Hall 301, 4-5pm__

Lecture I: Can you hear the shape of a network? --- New directions in spectral graph theory

We will discuss some recent developments in several new directions of spectral graph theory, including random walks for directed graphs, ranking algorithms, network games, graph limits and graphlets, for example.

__Wednesday, October 26th - Smith Hall 205, 4-5pm__

Lecture II: Sequences: random, structured or something in between?

There are many fundamental problems concerning sequences that arise in many areas of mathematics and computation. Typical problems include finding or avoiding patterns;
testing or validating various 'random-like' behavior; analyzing or comparing different statistics, etc. In this talk, we will examine various notions of regularity or irregularity for sequences and mention numerous open problems.

__Thursday, 27th - Smith Hall 205, 4-5pm__

Lecture III: Semigroup spectral theory and graph coloring games

We consider a coloring game on graphs as an example to illustrate the effectiveness of
the semigroup spectral method for determining the spectrum of the directed graphs which arise as the state graphs associated with the game. Originating from the study of the so-called Tsetlin library random walks and the like, this method can be used to analyze dynamic processes such as voting and ranking, provided the random processes satisfy certain "memoryless" conditions (corresponding to left-regular-band semigroups).

Milliman Lectures Homepage