Ren uses statistics to make sense of a messy world.

Joan Jian-Jian Ren is a problem-solver. The University of Maryland mathematics professor develops tools to analyze large, messy biomedical datasets. Although much of her work delves deep into theoretical statistics, her research has real-world applications for helping make sense of the enormous volumes of data collected today.

“There are many situations where we don’t have methods to analyze the data that we have,” Ren said. “People are collecting huge volumes of data, but if we can’t analyze it properly, then we can’t really get useful information out of it or come to the most accurate possible conclusions.”

Take vaccination data, for example. The U.S. Department of Health and Human Services houses a database with more than a half-million reports on the adverse effects of vaccines but extracting a clear story from the data isn’t easy. 

“The structure of this data is very complex,” Ren said. “For example, when you take your kid to get vaccines, they will get maybe three or four shots at one time. So, when they get a fever or some other adverse reaction, how do we know which vaccine triggered it? Or, if the reaction comes three days or four later, how do we know what variables are involved in causing that reaction?”  

To answer those questions, Ren applies statistics and data visualization tools she develops with colleagues from the University of Michigan Medical School and the University of Maryland School of Medicine. They are beginning to find patterns that indicate which vaccines cause which types of reactions. Ren also develops statistical methodologies to better analyze and understand data on AIDS and certain cancers. Their findings may eventually help regulatory agencies set medical standards and make recommendations for treatments and preventions. 

That’s exactly what happened when Ren dug into the data on breast cancer screenings two decades ago. Scientists had been struggling to determine how frequently women needed to have mammograms and at what age to detect the earliest stages of breast cancer. Ren and colleagues from the University of Nijmegen in the Netherlands concluded that mammogram screenings once every two years was sufficient for early detection of breast cancer in women over 70 years of age, but not in women under 70. 

“Our research concluded that every two years was not frequent enough for detecting primary cancer in women under 70,” Ren said. “And it opened the debate about the appropriate frequency of screening mammograms in women under 70.”

Guidelines still vary widely among different institutions and agencies, but Ren’s work had real-world applications, because most recommendations suggest less frequent mammograms for women over 70. 

“I find it very exciting to use mathematics in a meaningful way that can really help people,” Ren said. “It is always rewarding to work on a challenging mathematics problem, and it makes me happy to see the significance and importance of the results.” 

Ren discovered the rewards of solving difficult math problems when she was still in high school in Beijing, China. She did well in mathematics competitions and often found herself helping friends work through challenging math problems. She enjoyed the feeling of being good at math, but when she realized it was something she wanted to pursue as a career, Ren had to navigate a critical non-mathematical problem.

“My mother really didn’t want me to study math,” Ren recalled. “In China, girls were not encouraged to do math. It was seen as something girls didn’t do.”

Ren was good at foreign languages and writing, and her mother tried to persuade her to become a translator or something more traditionally associated with women’s jobs in China. 

“That was a huge fight. It was a very difficult decision for me,” Ren remembered. “Then my high school math teacher got involved. He had a meeting with my mother, and she laid off after that.”

Thanks to her math teacher, Ren studied mathematics at Peking University. In 1985, she moved to the United States to earn her Ph.D. in theoretical statistics from the University of North Carolina at Chapel Hill. There, she found very different attitudes toward women in mathematics.

“One of the biggest differences when I came to this country is I felt that, overall, they supported women much more,” Ren said. “All my professors were very supportive, and I don’t feel that they treated me differently as a girl or that I didn’t belong in math because I was a girl.”

After earning her Ph.D. in 1990, Ren joined the faculty at the University of Nebraska–Lincoln and then moved to Tulane University and the University of Central Florida. She earned tenure in Nebraska and was a professor before coming to UMD in 2011.

“Her work in biostatistics was very exciting, and she was really an expert at what she was doing,” said UMD Mathematics Professor Benjamin Kedem, who recruited Ren to UMD. They met when she was giving an invited talk at an international statistics conference in Washington, D.C. 

“Jian-Jian’s work refined a well-known statistical model called the Cox proportional hazards model, and with her expertise and talent I knew it would be a benefit to the department to have her here,” Kedem said.

The Cox proportional hazards model is used in medicine to determine survival rates or hazard risks (such as a person’s risk of dying of cardiovascular disease over the next five or 10 years) based on different variables. 

The move to Maryland turned out to be a good decision for Ren and her young son. The department welcomed her warmly and supported her work, and her son was able to excel in the local school system. He will soon graduate from UMD with a B.S. in mathematics at just 19 years old. 

As a soon-to-be empty-nester, Ren may have more time for playing tennis and piano. But one thing is certain, she will continue to be motivated by the big questions that lie hidden in biomedical data, just waiting for someone like her to help tease out the answers. 

“Statistics is only going to become more and more important in the era of big data,” Ren said. “I would love to see more statisticians here at Maryland working with experts from other departments to understand how to analyze and understand the data. There are a lot of problems big data can help solve but only with the right tools.”

Written by Kimbra Cutlip

An internationally renowned mathematician in probability theory, Freidlin was once a Russian “refusenik.”

After more than 30 years at the University of Maryland, Distinguished University Professor Emeritus of Mathematics Mark Freidlin retired on July 1, 2021. After being barred from leaving his home country 40 years ago and shut out of academic life for nearly a decade, Freidlin moved to Maryland and traveled the world as an invited speaker at prestigious mathematical conferences and research institutions. 

Freidlin was born in Moscow and began his career in mathematics during the Cold War between the United States and the former Soviet Union. As a professor of mathematics at Moscow State University in the 1960s and ’70s, Freidlin earned both privilege and status in a country that valued higher education and revered rigorous intellectual pursuits. 

But as a person of Jewish descent, Freidlin was also subjected to government harassment, discrimination and policies that limited his professional and economic opportunities. He applied for an exit visa in 1979 with hopes of leaving the Soviet Union with his wife, Lera, who was also a mathematician, and their two children. They were denied an exit visa without an explanation, and they were promptly fired from their jobs and barred from publishing papers in the Soviet Union or attending scientific conferences. 

During those years, the Soviet Union ran a brutal political campaign to separate its citizens and citizens from other East bloc countries from the Western world behind what Winston Churchill called the Iron Curtain. Scientists and mathematicians were often denied permission to leave the country. After Freidlin and his wife requested permission to emigrate, they were labeled “refuseniks”—Soviet citizens denied the freedom to leave their country by the Soviet government. Freidlin was 41 years old.

For eight years, Freidlin and his wife made a living as tutors. Lera also got work translating documents, and Freidlin continued working on mathematics on his own. But he had already earned an international reputation, in part because of a book he and his colleague Alexander Wentzell published right before he was shut out of academia.

“I waited until after the book was published to apply for an exit visa, because I knew if I applied before, the book would never be published,” Freidlin recalled.

The book was first published in Russian in 1979 and was translated into English in 1984. Several editions followed, with the latest published in 2012. The book introduced a theory, now known as the Freidlin-Wentzell theory, which explains how small, seemingly insignificant, perturbations in complicated systems can create critical changes in the system over long time periods. The theory is widely used in mathematical modeling in fields as diverse as physics, biology, economics, and the social sciences.

The Freidlin-Wentzell theory laid the groundwork for much of his later research that seeks to describe the effects of small random fluctuations on dynamical systems. 

“In many mathematical models, if you don’t take into account random perturbations in the system, that may work fine over certain time intervals,” Freidlin explained. “But over longer time intervals, these perturbations can become critical enough to cause a transition from one stable behavior to another stable behavior, and our goal is to describe these transitions.” 

Freidlin would eventually work with Wentzell again, years after the Soviet Union fell and they were both in the U.S., but in the eight years between publication of his first book and his arrival in Maryland, Freidlin was forced to work largely on his own. During that time, his western colleagues helped Freidlin communicate with the outside world. 

Visiting colleagues smuggled Freidlin’s letters and academic papers out of the country, and he remained an important figure in the world of mathematics, publishing several papers in academic journals outside of the Soviet Union during his time as a refusenik.

But those papers represented just a fraction of Freidlin’s work during those years, so he compiled his unpublished works into a second book that his wife translated into English. They had it smuggled out of the country, and his former Ph.D. advisor Eugene Dynkin arranged for it to be published through Princeton University Press. Dynkin left the Soviet Union in 1977 and was teaching mathematics at Cornell University. 

“A colleague carried it out of the country,” Freidlin recalled. “We changed the cover page to make it look as if he was the author of the book so that if he was caught it would not appear to be mine.”

Freidlin’s second book “Functional Integration and Partial Differential Equations” was published in 1985. Two years later, under pressure from the international community, the Soviet government granted Freidlin and his family permission to leave. He and Lera packed up their two children and moved to Maryland in 1987.

“I had some other offers from different countries,” Freidlin recalled, “but various colleagues including Dynkin convinced me to go to Maryland.” 

Lera took a job as a statistician at the National Institutes of Health. And after waiting so many years to leave his homeland, Freidlin embarked on a few years of travel to share his mathematical ideas as an invited speaker in France, Israel, Germany, Italy, England, Canada, and all over the U.S. He was even an invited speaker at the International Congress of Mathematicians in 1998.   

“After eight years, we were happy to come to the United States,” he said. “I had liked to teach students, and I enjoyed teaching again and being able to travel and talk with colleagues openly. I was very happy.” 

During his tenure at UMD, Freidlin mentored more than a dozen Ph.D. students and several postdoctoral associates. He has given more than 170 invited talks around the world and published nearly 100 refereed papers (making a combined total exceeding 150 papers over the course of his career). 

Through these works, Freidlin made prolific contributions to the field of stochastics, which is the study of complex processes that can be analyzed and predicted statistically but defy prediction of precise outcomes. 

“I was very lucky to be a mathematician,” Freidlin said. “It is very interesting work, and it’s a world where you can live outside these other problems you know. There is always something interesting in mathematics that you can be challenged to think about and to solve.” 

Freidlin will continue to work on mathematical theories in his retirement and spend more time with his grandchildren. He also looks forward to resuming travel once the threat of COVID-19 is in the rearview mirror. Hopefully, he should not have to wait eight years.

Written by Kimbra Cutlip

We welcomed six new faculty members and five Novikov postdocs to the Math family this fall!

Faculty:

Lei Chen (Assistant Professor). Lei received a B.S. from Peking University and a Ph.D. from the University of Chicago (2018) under the supervision of Benson Farb. She was then a Noether Instructor at CalTech. Lei works in the area of low dimensional topology and geometric group theory.  She made major contributions in the areas of group actions on manifolds and homomorphisms between transformation and mapping class groups. Her work is also related to complex geometry and topological dynamics.

Dan Cristofaro-Gardiner (Assistant Professor). Dan received his A.B. degree from Harvard (2007) and Ph.D. from Berkeley (2013). He then worked as an assistant professor at UC Santa Cruz and was a von Neumann Fellow at the Institute for Advanced Study. Dan works in symplectic topology/geometry/dynamics. He is a leader in the field of “quantitative symplectic geometry,” an area that focuses on questions about symplectic embedding of symplectic manifolds with boundary, and Reeb dynamics on the boundaries of symplectic manifolds. He has contributed in substantial ways to a variety of hard problems. Most recently, together with Humiliere and Seyfaddini, he posted on the arXiv a surprising proof of the simplicity conjecture showing that the group of compactly supported area-preserving homeomorphisms of the two-disc is not simple.

Bassam Fayad (Professor, Brin Chair). Bassam received his Ph.D. from the École Polytechnique (2000) and a Habilitation from the University of Paris 13 (2006). Recently, he worked as a Directeur de Recherche 1ère class at the CNRS. Bassam is a distinguished mathematician, working in the area of dynamical systems. He is mostly known for his work on the Kolmogorov-Arnold-Moser (KAM) theory. Bassam’s work is centered on Hamiltonian dynamics and on smooth ergodic theory. He has important results in many other areas including rigidity theory, number theory and mathematical physics. Bassam made substantial contributions to the KAM theory of analytic systems by proving stability results and obtaining optimal bounds for the stability time. Among other areas, he obtained significant results in the study of positive entropy systems and to zero entropy systems. Throughout his career, Bassam has received many distinctions and honors, including an invited lecture at the 2018 International Congress of Mathematics in Rio de Janeiro. Bassam joins our department as the Michael and Eugenia Brin Distinguished Chair of Mathematics.

Yu Gu (Associate Professor). Yu received a B.S. in mathematics and physics from Tsinghua, an M.S. from Brown and a Ph.D. from Columbia under the direction of Guillaume Bal. He then spent three years as a Szegö Assistant Professor at Stanford before moving to Carnegie Mellon University as an assistant professor (2017). Yu works in the area of mathematical and asymptotic analysis of random dynamics and random partial differential equations. He made fundamental contributions to the theory of homogenization and provided the first results on random fluctuations in high dimensions. Recently, he obtained breakthrough results in the study of a Hamilton-Jacobi type equation driven by a spacetime white noise, the so-called KPZ equation. Last year, Yu received a National Science Foundation CAREER Award.

Huy Nguyen (Assistant Professor). Huy received a Ph.D. from the University of Paris-Sud 11 (with Nicolas Burg, 2016). Then, he was a postdoc in Princeton and a Tamarkin Assistant Professor at Brown. Huy works in the area of analysis, somewhere between pure analysis, harmonic analysis, and PDEs.  Huy made substantial contributions to many problems including the proof of modulation instability of Stokes waves, optimal Strichartz estimate for water waves, and the global well-posedness for the one-phase Muskat problem (a free boundary problem in a porous medium that describes two flows separated by a free boundary).

Christian Rosendal (Professor). Christian received a Ph.D. from the University of Paris 6 under the direction of Alain Louveau. He then worked at CalTech, the University of Illinois at Urbana-Champaign, and more recently at the University of Illinois at Chicago. In the past two years, he has been working as a program director at the National Science Foundation. Christian works in the area of mathematical logic. His research belongs to four interconnected topics: rigidity of Polish groups, geometry of topological groups, descriptive set theory, and the geometry of Banach spaces. In 2020, he was named Fellow of the AMS.

Novikov Postdocs:

James Hanson. A student of Uri Andrews at Wisconsin. James works in continuous logic and applications of logic to topology and analysis. He also has a background in theoretical physics. His mentor is Chris Laskowski.

Xiaoqi Huang. A student of Chris Sogge at Johns Hopkins. Xiaoqi works in harmonic and geometric analysis and partial differential equations. His mentor is Manos Grillakis.

Hussain Ibdah. A student of Edriss Titi at Texas A&M. Hussain is interested in theoretically analyzing nonlinear, nonlocal PDEs, in particular, those of fluid mechanics and transport-diffusion systems. His mentor is Eitan Tadmor.

Rigoberto Zelada. A student of Vitaly Bergelson at Ohio State. Rigoberto works in ergodic theory. His mentor is Adam Kanigowski.

Lutian Zhao. A student of Sheldon Katz at Illinois. Lutian works in enumerative algerbraic geometry with applications to mathematical physics. His mentor is Amin Gholampour.