The DiPerna Lectures

The DiPerna Lecture was established by friends and colleagues as a memorial to Ronald DiPerna after his untimely death 1989. Each year the Department of Mathematics invites an outstanding applied mathematician to deliver the DiPerna Lecture on recent advances in applied mathematics.

The 2012-2013 DiPerna Lecture will be given by Alan Newell (University of Arizona) on January 24, 2013, 4PM in 60 Evans.

Phyllotaxis as a pattern forming front

Abstract : Science is littered with the debris of unsolved or incompletely solved problems which many modern scientists ignore in their mad marches on to the new frontiers at the outermost reaches of the real and parallel universes and the worlds of fundamental particles and unified field theories. Simple everyday examples are the waves on the surface of the sea, the earth's magnetic field, the flux of turbulent water down a pipe as a function of pressure head and, of prime interest for this lecture, the intriguing and beautiful phyllotactic configurations near the growth shoots of most plants. The fact that in many cases, phylla (flowers, leaves, bracts, florets) lie on intersections of families of spirals enumerated by consecutive numbers from Fibonacci sequences has been known for over four hundred years, since the time of Kepler, but to date there is still no widely accepted theory which can explain all observations. Nevertheless in recent years there has been significant progress, both experimental and theoretical. In this lecture, I will outline what that progress has been and tell you about our (my colleagues in these efforts have been Matt Pennybacker, Patrick Shipman and Zhiying Sun) own idea which is that the phyllotactic configurations and surface deformations on plants are "pushed" pattern forming fronts initiated by instabilities with biochemical and mechanical origins. I will discuss the connections of our results with the cellular automata, optimal packing approaches of Adler, Douady and Couder and Atele, Gole and Hotton and also suggest circumstances in which Fibonacci patterns can be considered universal.

Ronald J. DiPerna, 1947-1989

The following text is from the memorial written for Professor DiPerna shortly after his death.

Ronald J. DiPerna, a professor of mathematics at the University of California at Berkeley, died in Princeton on January 8, 1989. At the time of his death he was a visiting member of the Institute for Advanced Study at Princeton, NJ. His wife, Maria Schonbeck, is a professor of mathematics at the University of California, Santa Cruz. They have one daughter, Lauren.

DiPerna was born in Sommerville, Massachusetts, on February 11, 1947. He received his Ph.D. at the Courant Institute of Mathematical Sciences of New York University in 1972, and held faculty positions at Brown University, the University of Michigan, the University of Wisconsin and Duke University before coming to Berkeley in 1985.

DiPerna was known for his work on nonlinear partial differential equations, especially those that are important in fluid dynamics and the kinetic theory of gases. Probably his best known work is his development and application of the method of compensated compactness. This is a very powerful method for controlling oscillation and thereby proving existence theorems. DiPerna proved existence of weak solutions in the large for the equations of compressible gas dynamics and obtained important results concerning the uniqueness of solutions, their large time behavior, and their local regularity as elements of the appropriate abstract spaces.

His recent work concerned integro-differential equations that arise in the kinetic theory of gases and certain types of singularity that arise in incompressible flow.

DiPerna's work is remarkable for the courage and vision with which he attacked and conquered problems of exceptional difficulty. His papers are masterpieces of hard analysis and a source of wonder and inspiration to all those who read them and learn from them. His dedication to mathematics is legendary, and his scientific vision permeates much of contemporary analysis. His very premature death deprives the mathematics community as a whole, and the mathematics department at Berkeley in particular, of a very important and innovative voice.

DiPerna held Guggenheim and Sloan fellowships; he spoke at the International Congress of Mathematicians, and was a member of the Institute for Advanced Study at Princeton. Had he lived, his work would have earned the highest honors that the mathematical community can bestow. The Mathematics Department at Berkeley keenly feels his loss.

Alexandre J. Chorin
Craig Evans
James Gilman
Andrew Majda

Past DiPerna Lecturers

1991 Peter Lax
1992 Andrew J. Majda
1993 James Glimm
1994 Constantine Dafermos
1995 Luc Tartar
1996 Pierre-Louis Lions
1997 Cathleen Morawetz
1998 Tai-Ping Liu
1999 Heinz-Otto Kreiss
2000 Eitan Tadmor
2001 Ciprian Foias
2002 Andrew Stuart
2003 John Ball
2004 Benoit Perthame
2005 Charles Fefferman
2006 Alberto Bressan
2007 Yuxi Zheng
2008 Gui-Qiang Chen
2009 Andrew J. Majda
2010 Lai-Sang Young
2011 Vladimir Rokhlin

2012 Emmanuel Candes