The year 2003 marked the tenth anniversary of the death of Wolfgang Wasow. The 8th Memorial Lecture, funded by a generous endowment established by Wolfgang's children, was given on November 12, 2003 by Nancy Kopell onRhythms in the nervous system: From cells to behavior via dynamics.

Nancy Kopell is the William Goodwin Aurelio Professor of Mathematics and Science at Boston University and is one of the leading biomathematicians in the world. She is co-director of the Center for BioDynamics (CBD) at Boston University, a multidisciplinary center which aims to train undergraduates, graduates, and postdoctoral fellows in leading techniques from dynamical systems theory and its applications to biology and engineering. A former MacArthur Foundation Fellow, Professor Kopell was elected to the National Academy of Sciences in 1996.

The abstract of her lecture was:

*The nervous system produces rhythmic electrical activity in many
frequency
ranges, and the rhythms displayed during waking are tightly tied to
cognitive state. This talk describes ongoing work whose ultimate aim is to
understand the uses of these rhythms in sensory processing, cognition and
motor control. The method used is to address the biophysical underpinnings
of the different rhythms and transitions among them, to get clues to how
specific important subsets of the cortex and hippocampus process and
transform spatio-temporal input. We focus on the gamma rhythm (30-80 hz),
which is associated with attention and awareness, and theta (4-12),
associated with active exploration and learning of sequences. Via case
studies, we show that different biophysics corresponds to different
dynamical structure in the rhythms, with implications for function. The
mathematical tools come from dynamical systems, and include the use of
low-dimensional maps, probability and geometric singular perturbations.*

Professor Kopell also gave a more technical lecture Ä neuron as a
chain of oscillators: dynamics of a dopaminergic neuron" in the
Applied Math/PDE seminar on November 13, 2003.

The 8th annual LAA Lecture was given by **Peter Sarnak** of
Princeton University and New York
University on October 17, 2003. The title of his lecture was *Ramanujan
Graphs* and his abstract reads as follows:

*Highly connected but sparse graphs (ëxpanders") have proven to be
fundamental building
blocks in many algorithms in computational complexity theory. We review
the definition(in terms of eigenvalues of the adjacency matrix) and
construction of Ramanujan Graphs, these being optimal in this connection.
We then discuss recent developments related to the eigenvalues and random
graphs and matrices as well as higher dimensional Ramanujan Buildings.*

Peter Sarnak is Eugene Higgins Professor of Mathematics at Princeton University and Professor of Mathematics at the Corant Institute of Mathematical Sciences, NYU. Professor Sarnak has made many major contributions to number theory and to problems in analysis motivated by number theory. He is a 2003 winner of the AMS's Levi L. Conant Prize, a 2001 winner of the Ostrowski Prize, and a 1998 winner of SIAM's Polyá Prize. He was elected to the U.S. National Academy of Sciences and the U.K. Royal Society in 2002. He has supervised the theses of over 30 graduate students.

2004 LAA Lecture Craig Tracy UC-Davis April 26, 2004 |