# 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 2018 DiPerna Lecture will be given by Wilhelm Schlag (University of Chicago) on January 25, 2018, 4PM in 60 Evans Hall:

### On the long-term dynamics of nonlinear dispersive evolution equations

*Abstract : We will give an overview of some of the developments in recent years dealing with the description of asymptotic states of solutions to semilinear evolution equations ("soliton resolution conjecture"). New results will be presented on damped subcritical Klein-Gordon equations, joint with Nicolas Burq and Genevieve Raugel.*

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*Ronald J. DiPerna, 1947-1989*

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

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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

2013 Alan Newell

2014 Takis Souganidis

2015 Vladimir Sverak

2016 Gilles Lebeau

2017 Herbert Koch