It is with great regret that the Mathematics Department must note the passing last week, at age 81, of our colleague Professor Emeritus and Distinguished Research Professor Veeravalli Seshadri Varadarajan.

Professor Varadarajan, known to all as Raja, led a research career of lasting international influence.  He was in active service at UCLA  for 49 years until  his  retirement in 2014.  His research activity continued until his death.  At UCLA, with balanced emphasis upon research, exposition, teaching and mentoring he was a superb colleague who inspired respect and devotion among those lucky enough to work with him.  He did sustained and significant work in at least 5 areas over his long career. His international recognitions include an honorary doctorate in physics from the University of Genoa, and the Lars Onsager medal from the Norwegian University of Science and Technology.  For his 60th birthday, and his retirement, conferences were held in his honor. He was  a speaker at the International Congress of Mathematicians in 1974, a high honor for a mathematician at any stage of career.

Born in 1937 in Bangalore, India,  Raja received his PhD in 1960 from  the Indian Statistical  Institute (ISI) at Kolkata, where he studied under  C. R. Rao.  With the others of the “famous four” from ISI  in this period,  the gifted young researchers K.R. Parthasarathy, R. Ranga Rao, and S.R.S. Varadhan, Raja is regarded as someone who played an early important role in the development of probability theory in India.  Raja was a professor at ISI from 1962 to 1965.  In 1968 he published an influential monograph, the first of many, Geometry of Quantum Theory which was based in part on his research to that date.  Its second edition remains in print.

In 1965, at age 28, Raja came to UCLA as Associate Professor.  He had come  from India shortly before with his wife Veda.  She later did graduate study at UCLA, earning a master’s degree in atmospheric sciences in 1976.  At UCLA Raja found Richard Arens, Donald Babbitt, and Robert Blattner to be colleagues with sympathetic interests.  Indeed, by that time  Raja’s primary interest was turning to  the theory of semisimple Lie groups and their representations, and especially the transformative theory of Harish-Chandra who became a friend.  Over the next 25 years, he and his collaborators  T. J. Enright, J.J. Duistermaat, R. Gangolli, J. A. C. Kolk and P. C. Trombi, made diverse important contributions to this developing theory.  Raja also wrote a number of excellent  expository articles on Harish-Chandra’s work.

Continuing his commitment to exposition, Raja wrote several textbooks for graduate students. His 1974 Lie Groups, Lie Algebras, and Representations  was  the first of its kind and remains a standard reference text.  His 1989 An Introduction to Harmonic Analysis on Semisimple Lie Groups is used by many as well. In addition, with R. Gangolli, he published in 1988 a 385 page research/expository monograph  in the famous Ergebnisse series of the Springer press. 

Inspired by problems arising from Harish-Chandra’s  theory,  Raja collaborated with UCLA colleague Don Babbitt, from 1983 until 1991,  in basic research on the theory of  meromorphic differential equations with irregular singular points. They published six articles, and an Asterisque monograph in 1989 on the topic. This work brought him for the first time, as an active user,  into contact with Grothendieck’s theory of schemes and it  had a lasting impact on his perspective.  Around this time, Raja’s concerns returned (they had never really left !)  to quantum theory.  He became interested in the new theory of quantum groups,  in  problems of quantization, and in novel topics such as arithmetic, including non-archimedian,  physics. He published numerous research and expository articles on all these topics, and hit high points with his  2004 exposition Supersymmetry for Mathematicians: an introduction, which became an AMS ‘bestseller’, and his 2006 collaborative paper which defined and developed the  notion of a unitary representation of a Lie supergroup. After retirement, Raja continued  research. With R. Gangolli, he edited important unpublished manuscripts of Harish-Chandra in which theorems announced by Harish-Chandra before his early death are given proof. This volume forms now forms the fifth of Harish-Chandra’s collected papers. The first four volumes were edited by Raja alone.

Throughout his career, Raja had a strong interest in the origins of the ideas of mathematics and physics and he published numerous articles in this area.  In 2006 he published, also with the AMS, the 300 page  Euler Through Time: a new look at old themes. This highly readable book is meant for the contemporary mathematician and shows how Euler’s work connects to important themes of current research. Finally, in 2011 he published the book Reflections on Quanta, Symmetries and Supersymmetries  which was  called “brilliant, stimulating and informative” by a reviewer.  This was the last of his book length publications but there are three volumes of his selected papers which appeared in 1999 (first volume) and in 2013. However, article publication continued and even today there is one in late stage  of review at a journal.

In 1992 Raja had a major heart attack that left him physically weakened for life. It led him to a change of perspective on  research. He felt that he could now explore his research interests more freely than before. His  new perspective brought him, in addition to the great productivity noted above, many graduate students whose PhD’s he supervised. He said he had learned to help a student discover and follow their own path, not impose his own.  Twelve of his seventeen research students began and finished in this period, which ended only with his retirement in 2014. Raja wrote  numerous articles with  students and former students and  was warmly and deeply devoted to them, his friends, and his collaborators. For decades, he and Veda  welcomed all into their home in Pacific Palisades with its beautiful garden and pine trees.    

Raja was  Managing Editor of the Pacific Journal of Mathematics for 3 decades. He was an excellent captain  of this well-known  journal. It will devote an issue to articles dedicated to his memory. He also was the first one to manage the Distinguished Lecture Series. Raja was perfect for this task: he knew well a great many transformative researchers and the list of his speakers is a Who’s Who. The Department gave him an award for this contribution.

With Veda, Raja made in March 2019 a 1 million dollar gift to UCLA for creation of a durable visiting Ramanujan Professorship in the Mathematics Department.  It is  in honor of the great Indian mathematician Srinivasa Ramanujan.

Outside of mathematics, Raja loved classical Western and Indian music. Mozart was his particular favorite. He was very fond of mystery novels, especially of the English genre, and also of television shows with such plots. Raja also loved sports. Although cricket had been his first passion, in Los Angeles he became a serious Lakers fan.  Perhaps above all other recreations, he loved good conversation with friends. He had a prodigious memory and could move effortlessly in conversation between his favorite themes.

It has been one  of this writer’s greatest rewards to have had the friendship of Raja Varadarajan. I will cherish the memory of Raja’s  grace,  humor, intelligence, and  fine guidance for the rest of my life.  He is deeply missed by me and many others.

Written, with assistance of colleagues, by UCLA Mathematics Professor Don Blasius

Former IPAM Director and UCLA Professor of Mathematics Russel (Russ) Caflisch is one of 100 new members to be elected into the National Academy of Sciences in 2019.  Russ had a lengthy career at UCLA; he joined the Mathematics Department in 1989 (with a joint appointment in Materials Science and Engineering) and became Director of IPAM in 2008. Russ left UCLA in 2017, and is currently the Director of the Courant Institute of Mathematical Sciences at New York University.

“The National Academy of Sciences (NAS) is a private, non-profit society of distinguished scholars. Established by an Act of Congress, signed by President Abraham Lincoln in 1863, the NAS is charged with providing independent, objective advice to the nation on matters related to science and technology. Scientists are elected by their peers to membership in the NAS for outstanding contributions to research.”

Read the full NAS press release.

Dr. Charles (Chuck) J. Stone passed away on April 16, 2019. Chuck received his Ph.D. at Stanford University in 1961 under the direction of Samuel Karlin, and he joined the UCLA Department of Mathematics faculty in 1964. The early part of his career was devoted to probability theory, working closely with Sidney Port. During the 1970s, Chuck’s interests moved toward statistics. His 1977 paper “Consistent nonparametric regression” contributed to important developments in statistical thinking. After 17 years, Chuck left UCLA for a position in UC Berkeley’s Statistics Department.

Chuck received many honors during his career, including a Guggenheim fellowship in 1980. He was a fellow of the AMS and the IMS, and gave the 1994 IMS Wald Lectures. He was elected to the National Academy of Sciences in 1993.

Recent UCLA math graduate Danh (Danny) Nguyen Luu has been named the sole winner of the 2018 Sacks Prize by the International Association for Symbolic Logic (ASL). The Sacks Prize is awarded for the best dissertation of the year in logic. Previous winners include Gregory Hjorth (former UCLA faculty), Itay NeemanMatthias Aschenbrenner and Artem Chernikov (current faculty).

Danny received his Ph.D. in Spring 2018, under the direction of Igor Pak. According to ASL, Danny’s thesis, The Computational Complexity of Presburger Arithmetic, “contains stunning results on the complexity of the decision problem for the linear theory of the integers. For example, whereas it has been known since the 70’s that the full decision procedure has doubly-exponential lower bounds, Nguyen’s thesis shows that even very restricted fragments have high complexity. Other results deal with VC-dimension of PA formulas and the complexity of the counting problem for various PA-definable sets. The dissertation is a tour de force, combining methods from number theory, discrete geometry, model theory, and computational complexity.”

The Association for Symbolic Logic is an international organization supporting research and critical studies in logic. Its primary function is to provide an effective forum for the presentation, publication, and critical discussion of scholarly work in this area of inquiry.

Photo caption: Researchers Abolfazl Sadeghpour, the study’s co-lead author, Hangjie Ji and Navid Dehdari Ebrahimi with their experimental water capture setup.

Photo credit: Oszie Tarula/UCLA

A key element in the UCLA team’s system is its ability to consistently generate water droplets of the same size and constant flowing speed. These water beads enable the system to effectively capture water vapor, without causing significant pressure drop, and hence fan power consumption. 

“The liquid beads form highly curved surfaces that enhance the rate at which water vapor diffuses through the air,” said Abolfazl Sadeghpour, a UCLA mechanical engineering graduate student and a co-lead author of the study. “Simply said, this is analogous to a snowball rolling downhill. The beads are picking up water vapor as they travel down. And while a drop may seem small, think of an entire array of threads working constantly. The water vapor harvested could add up to quite a bit.”

The study’s other co-lead author is recent mechanical engineering doctoral graduate Zezhi Zeng. Other authors are postdoctoral scholar Hangjie Ji of mathematics, UCLA graduate student Navid Dehdari Ebrahimi of mechanical and aerospace engineering, and Andrea Bertozzi, a distinguished professor of mathematics and mechanical and aerospace engineering and UCLA’s Besty Wood Knapp Professor for Innovation and Creativity.

The research was supported by the National Science Foundation and the Simons Foundation.

Reposted excerpt – Read the full UCLA Newsroom article here.

UCLA mathematics professor Stan Osher, Cognitech Inc CEO Leonid Rudin and then PhD student Emad Fatemi, now sadly deceased, created a numerical algorithm that was instrumental in reconstructing the cleaned up image of the black hole captured in April 2017. Their work has been cited as the key regularization function in sparse modeling that has been applied to astronomical imaging (Akiyama et al. 2017) . 

In 1992, Rudin, Osher and Fatemi introduced a nonlinear total variation (TV) based noise removal algorithm which provided a simple and relatively fast way to achieve state-of-the-art results for very noisy images. In the original abstract, the technique is described as “a first step of moving each level set of the image normal to itself with velocity equal to the curvature of the level set divided by the magnitude of the gradient of the image, and a second step which projects the image back onto the constraint set” (Rudin et al. 1992).

The UCLA Myco-Fluidics Laboratory or “Roper’s Lab,” led by mathematics Professor Marcus Roper, is a semi-finalist in the National Science Foundation (NSF) We Are Mathematics Video Competition. This contest aims to “bring mathematics to life in a way that can help to break down barriers for those who may not otherwise understand what it means to do advanced mathematics or conduct research in the mathematical sciences.” 

The video submitted by Roper’s Lab is focused on the mathematics of fungal highways.

The final winner is decided by public voting! To support Roper’s Lab, please vote for the “MycoFluidics: Math & Fungi” video before Tuesday, April 30th

UCLA mathematics professor Tim Austin has published a proof of the “weak Pinsker conjecture,” first posed in the 1970s. Austin’s work provides the building blocks for a better understanding of the mathematical descriptions of random change. In a recent article, Quanta magazine praised Austin’s research, highlighting its importance in the field. Below, Austin gives a detailed explanation of the theorem:

A `stationary stochastic process’ is a mathematical model of a sequence of changing outcomes that are individually random, but with probabilities governed by an underlying law which does not change with time.  Such models are ubiquitous in probability theory, and also arise naturally in many other parts of math.  In large part, `ergodic theory’ studies the broad, long-run features that different stationary processes can exhibit.

One key quantity of interest is the `entropy’ of a stationary stochastic process, which quantifies how `unpredictable’ it is.  If the entropy is zero, this means that the past of the process determines its future completely — then the process is called `deterministic’.  If the entropy is positive, then this quantifies how much `fresh randomness’ the process exhibits per unit time, on the average over a long period. The simplest example of positive entropy is an `independent process’, in which the state of the process is newly random at each time-step, with no influence from the past at all: imagine new tosses of a coin that are not influenced by the outcomes of any previous tosses.

An old conjecture of Pinsker (1960) asks whether, through a suitable `encoding’, any stationary process can be separated into a two components, running independently of each other, one deterministic and the other independent (`purely random’).  (Technicality: the processes must be assumed `ergodic’, else one needs to re-phrase the conjecture slightly.)  Ornstein showed in 1973 that this is false.  Then, in 1977, Thouvenot proposed a weaker conjecture: the same as Pinsker’s, except allowing a process with arbitrarily small positive entropy in place of the strictly deterministic component.  The new result is that this `weak Pinsker property’ does, indeed, hold for all ergodic stationary processes.

The Society for Industrial and Applied Mathematics (SIAM) has selected 28 members, including Professor Mason Porter (University of California, Los Angeles), to join the 2019 Class of SIAM Fellows. According to SIAM, these distinguished members were nominated for their exemplary research as well as outstanding service to the community. Through their contributions, SIAM Fellows help advance the fields of applied mathematics and computational science.

“I first became a member of SIAM as an undergraduate. I figured it would be a good thing for a young applied mathematician to do. Among all professional societies I am in, SIAM is the one in which I am most heavily involved, so it’s nice to be recognized by them, ” says Porter, whose research focuses on networks, complex systems, and nonlinear systems. 

The 2019 Class of SIAM Fellows will be recognized at the 2020 SIAM Annual Meeting in Toronto, alongside the Class of 2020. Read here to learn more about the SIAM Fellowship program.