Professor of Mathematics
Equidistribution, groups and primes
The question of the size of
eigenfunctions on locally symmetric spaces is a natural unified
generalization of the classical Ramanujan Conjecture as well as of the
classical Lindelof Hypothesis. We will formulate some general conjectures
about these and describe some techniques and bounds that have been developed
to obtain approximations towards them.
In the second lecture we will discuss the use of this spectral theory as
well as ergodic theoretic methods to establish some strong equidistribution
of integral points as well as of measures associated with such points, in
locally symmetric spaces.
In the third lecture we will
discuss how to implement a Brun type combinatorial sieve on the orbit of a
The influence of some Tom
Wolff's work on various aspects of these topics will be highlighted.
The talks will be arranged as
Lecture 1 (April 4):
L-p norms of eigenfunctions on locally symmetric spaces
Lecture 2 (April 5):
Counting and equidistribution of integers and of measures on
locally symmetric spaces
Lecture 3 (April 7):
The Brun Sieve on an orbit
You are invited to attend a dinner following theThomas Wolff Memorial Lectures in Mathematics The Athenaeum on Tuesday, April 4, 2006
Host bar 5:45 p.m.
Dinner 6:30 p.m.
Citrus Avocado Salad
Grilled Rosemary Marinated Free Range Chicken
White Chocolate Cheesecake
Please indicate if you require a vegetarian or kosher meal
For reservations, please contact Stacey V. Croomes at 626-395-4336 or send payment by March 29, 2006 made out to Caltech for $35.00 per person to:
Stacey V. Croomes
Pasadena, CA 91125
Peter Sarnak is a world leader in the field lying on the interface between analysis and number theory, which is seeing vibrant resurgence of late. He is well known for his pioneering work on quantum unique ergodicity, his book with N. Katz, Random Matrices, Frobenius Eigenvalues and Monodromy, his paper with Iwaniec on Landau-Siegel zeros, and his recent work with J. Cogdell and I. Piatetski-Shapiro resulting in the complete resolution of the eleventh problem of Hilbert on the representability of integers in a number field by integral quadratic forms. Sarnak is a member of the National Academy of Sciences and the Royal Society. He has won many accolades including the Polya prize in 1998, the Ostrowski Prize in 2001, and the Cole Prize in Number Theory in 2005.
The Thomas Wolff
Thomas Wolff lectures, sponsored by donations from his widow and his parents, memorialize
Caltechs great analyst who was tragically killed at age 46 in an automobile accident
in July 2000. Wolff was a specialist in
analysis, particularly harmonic analysis. Professor Wolff made numerous highly original
contributions to the mathematical fields of Fourier analysis, partial differential
equations, and complex analysis. A recurrent theme of his work was the application of
finite combinatorial ideas to infinite, continuous problems.
early work on the Corona theorem, done as a Berkeley graduate student, stunned the
mathematical community with its simplicity. Tom
never wrote it up himself since several book writers asked for permission to include the
proof in their books where it appeared not long after he discovered it. After producing a number of very significant
papers between 1980 and 1995, he turned to the Kakeya problem and its significance in
harmonic analysis, works whose impact is still being explored.
Peter Jones, professor of mathematics at Yale, described Toms contributions as
follows: “The hallmark of his approach
to research was to select a problem where the present tools of harmonic analysis were
wholly inadequate for the task. After a period of extreme concentration, he would come up
with a new technique, usually of astonishing originality. With this new technique and his
well-known ability to handle great technical complications, the problem would be solved.
After a few more problems in the area were resolved, the field would be changed forever.
Tom would move on to an entirely new domain of research, and the rest of the analysis
community would spend years trying to catch up. In the mathematical community, the common
and rapid response to these breakthroughs was that they were seen not just as watershed
events, but as lightning strikes that permanently altered the landscape.”
Wolff was noted for his analytic prowess, the depth of his insights, and the passion with which
he nurtured the talents of young mathematicians. We