Brin Postdoctoral Fellow Hannah Hoganson’s love of mathematics inspired her to study geometric group theory and to rethink the way math can be taught. 

Hannah Hoganson’s passion for math took her across the U.S.—from her hometown in Pennsylvania to Ohio to Utah—before she finally arrived at the University of Maryland as a postdoc in fall 2022.

“Even though I always liked math and was pretty good at it, I wasn’t always in the highest-level classes as a kid. In fact, I even struggled with a couple math classes in college,” Hoganson recalled. “But after I attended more classes and experienced more opportunities, I realized that sometimes, you just need more time and more exposure to content to really understand it. Having different perspectives or different teachers can make difficult things finally click.”

Hoganson brought this philosophy with her as she conducts research and teaches courses at UMD as a National Science Foundation Postdoctoral Fellow and one of five Brin Postdoctoral Fellows who are supported by a generous gift from Mathematics Professor Emeritus Michael Brin. The Brin Postdoctoral program supports young mathematicians whose research shows remarkable promise for up to three years. 

Hoganson works with Assistant Professor of Mathematics Lei Chen in the field of geometric group theory, a branch of math that involves using geometric tools and objects to study algebraic groups (such as a set of functions). By examining geometric symmetries or other behaviors like a geometric object’s possible transformations, Hoganson and Chen can learn more about the structure and properties of algebraic groups. 

“Think back to the algebra classes you used to take—you have symbols and equations that you’re manipulating to find answers. It’s all fairly abstract,” Hoganson explained. “Now add in what you learned in geometry class, like measuring shapes and angles. Those are more physical interpretations or visualizations of the abstract. I’m interested in finding connections between the two, kind of like creating a ‘dictionary’ that translates one concept by using the other.”

Similar to how she finds connections between two different concepts in her research, Hoganson has a knack for finding ways to connect her work to people as well. Her experience partnering with peers, leading discussions and organizing conferences with mathematicians from across the country helped her become an effective communicator. She thrives when she’s bouncing ideas off collaborators, often moving her research forward after considering different perspectives and possibilities as she takes on intricate problems. 

“Even if we’re all in the same field of study, we don’t always have the same ideas, understanding of concepts or conclusions,” she explained. “We have to know how to explain our findings and theories with each other in a way that we can all understand. And that requires the ability to tweak what you’re saying to different people and communicate well.”

And Hoganson practices what she preaches. She works to improve her teaching every semester, adjusting her lessons to each new batch of students by relying on feedback and her own positive experiences with allowing students to revise and resubmit assignments. Chen, who is Hoganson’s mentor, believes that these efforts are the reason why Hoganson is an effective teacher—and that sentiment is shared by the many undergraduate students who have taken her introductory calculus classes at UMD. 

“Hannah is a super enthusiastic and talented mathematician,” Chen said. “She likes to work with other people, often communicating with various mathematicians and organizing new research activities with them. This love for collaboration and communication is also why she is a fantastic teacher. I cannot wait to see her as a professor.” 

The path to math

Hoganson’s journey to UMD began when she attended a summer research experience for undergraduates program held at Miami University. 

“I didn’t have much experience that first summer there, but I thought it was cool how math research worked. It was complex and dynamic. As an undergrad, you don’t usually get the chance to see that,” said Hoganson, who was a math major at Lehigh University at the time. "The program left such a big impression on me that I went again—this time, as the graduate student mentor for the undergraduate participants. It ignited my interest in continuing this sort of work."

Inspired by her undergraduate research experiences, Hoganson completed a master’s degree in mathematics at Miami University and later earned a Ph.D. in mathematics at the University of Utah. She found her research calling in low dimensional topology (a branch of math that studies shapes and spaces that can be visualized in two or three dimensions) and geometric group theory. She also resolved to bring that same exhilarating experience she had as an undergrad to other young mathematicians. 

As she neared the end of her doctoral studies, Hoganson wanted to explore new research opportunities, and that eventually led her to UMD.

“I was drawn to UMD because I wanted a chance to work with Lei Chen, whose work shares many overlaps with my own research interests,” Hoganson said. “Another big attraction was the Brin Mathematics Research Center, which was brand new when I first learned about it. Having a big research center dedicated to pure math research was something that really set UMD apart from other schools and I knew I wanted to be a part of that.”

Since landing the postdoctoral position at UMD, Hoganson has gone on to teach several introductory math classes at UMD and publish several papers on mapping class groups with longtime collaborators and friends. She’s taking a break from teaching this semester to focus more on her research but hopes to return with new teaching tactics and an updated approach to conveying new ideas. 

“It’s definitely a good time to be here at UMD,” said Hoganson. “There’s a lot going on right now in terms of research, workshops and collaborations that I look forward to exploring.”  

Written by Georgia Jiang

The overarching goal of his research is to improve predictive data science and scientific computing via intelligent computation.

From navigating with map apps and streaming new music to virtual personal assistants like Alexa and Siri, machine learning is a valuable tool that has become an intrinsic part of our daily lives. Yet these systems are not always reliable because they sometimes provide inaccurate information.

Haizhao Yang, an associate professor in the University of Maryland’s Department of Mathematics, is paving the way for more dependable machine learning systems by advancing its subset of deep learning. Deep learning is a method that uses three or more layers of neural networks to learn information and has led to tremendous breakthroughs in the field by providing more interpretable and precise outcomes.

The overarching goal of his research is to improve predictive data science and scientific computing via intelligent computation, which could have significant impacts on several fields, like weather prediction and health care.

Because deep learning is still in its infancy, establishing mathematical and statistical principles is an important step in improving its ability to obtain reliable results in these applications, Yang explained.

However, there are several challenges that he must overcome to make deep learning more reliable. The first obstacle is gaining a better understanding of how physical processes, like weather phenomena for example, can be applied to his research.

The second challenge involves lowering the expensive computational costs associated with the creation of deep learning. In order to overcome these challenges, Yang will utilize artificial intelligence to examine historical data and develop numerical strategies to make fast computations.

Yang, who recently started a new affiliate appointment at the University of Maryland Institute for Advanced Computer Studies (UMIACS), is looking forward to collaborating with fellow faculty members—especially those in the University of Maryland Center for Machine Learning—and utilizing the institute’s state-of-the-art computing infrastructure.

“The unique, interactive environment and powerful resources provided by UMIACS will accelerate my research on advancing intelligent computation,” he explained.

Yang has received several prestigious awards, including the award for Maryland Research Excellence in 2023, the Office of Naval Research Young Investigator Award in 2022, the Teaching for Tomorrow Award at Purdue University in 2021 and a National Science Foundation CAREER Award in 2020.

Before coming to UMD, Yang was an assistant professor of mathematics at Purdue University. He also held an affiliate position at the Institute of Data Science at the National University of Singapore. He earned his Ph.D. in mathematics from Stanford University in 2015.

Adapted from an article written by Ethan Cannistra, UMIACS communications group

As chair, Levy launched the Brin Mathematics Research Center, expanded undergraduate and graduate program offerings, and hired 22 new faculty members.

Professor Doron Levy has been reappointed chair of the University of Maryland’s Department of Mathematics for a five-year term, effective July 1, 2023. He has been chair for the last four years.

“Doron has extended the Department of Mathematics’ reach and enhanced its already strong academic and research programs,” said Amitabh Varshney, dean of UMD’s College of Computer, Mathematical, and Natural Sciences (CMNS). “I know the department will continue to flourish with him at the helm, and I look forward to our continued work together.”

Levy, who joined UMD in 2007, will continue to lead the department, which has over 100 tenured/tenure-track and professional-track faculty members, over 600 undergraduate majors and 200 graduate students, and teaches over 10,000 students a semester.

“I am looking forward to continue working with all members of the Math Department and the University of Maryland to further improve the department’s research program and strengthen our undergraduate and graduate programs,” Levy said. “I am fully committed to improving student success and strengthening our efforts to build an inclusive department where everyone can thrive. I would like to thank Dean Varshney and Provost Rice for their ongoing support of the Department of Mathematics.” 

The department saw unprecedented levels of energy and enthusiasm over the past four years with Levy as chair. A major accomplishment was establishing the Brin Mathematics Research Center (Brin MRC), which will host 18 workshops, four summer schools and eight distinguished speakers during its first two years. Levy serves as the founding director of the center, which brings over 300 mathematicians from around the world to UMD each year.

A wave of faculty retirements provided opportunities for Levy to recruit top talent to the department. He hired 16 tenured/tenure-track faculty members (including three who hold endowed chairs), two long-term visiting professors and four lecturers. The new faculty members conduct research in many different areas, including number theory, algebraic geometry, geometric analysis, low dimensional topology, symplectic topology, dynamical systems, probability, analysis, logic, partial differential equations, mathematical biology, statistics, numerical analysis and data sciences.

As chair, Levy secured the department’s role in leading the new data science minor, a joint initiative with the Department of Computer Science. He oversaw the creation of new courses and the revision of STAT 100 and STAT 400 to include modern content and technology. Levy expanded the department’s role in the CMNS Science Academy, which offers professional master’s degree programs in data science, machine learning, bioinformatics and computational biology, and quantum computing. The department also sponsors the EDGE Program, which is designed to strengthen the ability of women and minority students to successfully complete graduate programs in the mathematical sciences. 

To expand outreach to high school students, Levy co-led a joint project between the Department of Mathematics and the College of Education to offer calculus courses to students in Prince George’s County high schools that don’t offer the courses. Levy and Larry Washington, the department’s associate chair for undergraduate studies, also created the Maryland High School Credit by Exam program, which offers final exams in advanced topics to students at eight local high schools. Students who perform well on the exam and then enroll at UMD can move on to more advanced courses.

Levy boosted the department’s fundraising efforts, securing over $12 million in gifts including the largest single gift in department history: an estate gift from Carol Fullerton, daughter of the late Nobel Laureate Herbert A. Hauptman (Ph.D. ’55, mathematics), to establish the Herbert A. Hauptman Endowed Graduate Fellowship Program. Additional gifts provided undergraduate scholarships and graduate student awards and travel, as well as $4.75 million from Mathematics Professor Emeritus Michael Brin and his wife Eugenia and the Sergey Brin Family Foundation to launch the Brin Mathematics Research Center.

Levy secured funding to double the size of the department’s postdoctoral program. The department attracts more than 500 applications annually and supports more than 20 postdocs, including 15 Brin and Novikov Postdocs.

“Over the next five years, I will continue to prepare for the expected retirement of faculty members and identify exceptional targets for recruitment,” Levy said. “I will also continue facilitating the rise of the Brin MRC as one of the most prominent mathematics research centers.”

Levy plans to develop summer bridge programs for undergraduate students and graduate students, increase research opportunities for high school and undergraduate students within the department, and lead a comprehensive revision of the department’s honors program. He will also continue to prioritize raising scholarship and fellowship funding to support undergraduate and graduate students.

An active leader in the mathematics community, Levy served on the board of governors for the Institute for Mathematics and its Applications and the board of directors for the Society for Mathematical Biology. Among his many distinctions, Levy was named a 2017-18 fellow in the Big Ten Academic Leadership Program, a Pauli Fellow of the Wolfgang Pauli Institute in Vienna and a Guggenheim Fellow. In 2013, he was named a UMD Distinguished Scholar-Teacher.

Levy’s research focuses on biomedical applications of mathematics with a particular interest in cancer dynamics, drug resistance, immunology, imaging and cell motility. He is a member of the Maryland Biophysics Graduate Program and the Applied Mathematics, Statistics, and Scientific Computation Graduate Program, and he serves as a co-director of the NCI-UMD Partnership for Integrative Cancer Research.

After earning his bachelor’s degree in mathematics and physics from Tel-Aviv University in 1991, Levy received both his master’s degree and Ph.D. in applied mathematics from Tel-Aviv University in 1994 and 1997, respectively. He then held visiting and faculty positions at the École Normale Supérieure (Paris), UC Berkeley, Lawrence Berkeley National Laboratory and Stanford University.