Faculty Profiles

Highlighted below are faculty from each of the four PhD areas of concentration. Please see  MSCS Faculty page for more information on individual faculty research programs.

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Dima Sinapova: Associate Professor

My research is in mathematical logic and set theory. My main interests are infinitary combinatorics, forcing, and large cardinals.

Many natural questions cannot be answered by the standard mathematical axioms (ZFC) alone. Most famously, in 1963 Cohen invented forcing and used it to show that  the continuum hypothesis (CH) is independent of ZFC, resolving Hilbert’s first problem. Since then, a major theme in modern set theory is relative consistency results via forcing and large cardinals, which are ZFC-strengthenings.  We are motivated by two  complementary notions: what is necessary? what is sufficient? Infinitary combinatorics i.e. analyzing the structure of higher infinite objects is used to address these questions.

I came to UIC in 2012. Since then I have graduated two Ph.D. students (in 2017 and 2018), and currently I am advising two more. I look forward to welcoming new graduate students. Our department has a diverse selection of graduate classes and prominent research groups in both pure and applied mathematics, computer science and statistics. We have many areas of research in the Department, including algebraic geometry, geometry and topology, combinatorics, logic, to name a few. There are always seminars and workshops taking place. For example, in logic we have our research weakly seminar, and also a couple of working seminars, some run by graduate students.  I have also organized some workshops myself, and plan to do more in the future.

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Jie Yang: Associate Professor

I work in the fields of experimental design, big data analysis, bioinformatics, and financial mathematics. On experimental design, I focus on optimal design theory and efficient algorithms, which require both optimization theory and practice. On big data analysis, I focus on developing methods and algorithms for model-based statistical analysis. On bioinformatics, I mainly focus on high-dimensional classification and clustering problems in genomic data and microbiome data. On financial mathematics, I work on estimating risk-neutral densities and pricing financial assets. Since 2013, I have supervised 7 PhD students including 1 in experimental design, 1 in big data analysis, 2 in bioinformatics, and 3 in financial mathematics.

The whole MSCS department is like a big family. Welcome to join us!

*Jie is pictured with statistic PhD candidates Yanxi Liu, Hani Aldirawi, Keren Li (alum), and Nurlan Abdukadyrov.

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Mimi Dai: Assistant Professor

My research concerns analysis of nonlinear partial differential equations arising in fluid and complex fluid dynamics. Fluid is the most omnipresent substance on our planet; understanding the behaviors of solutions to fluid equations is important not only from the mathematical perspective, but also for comprehending classical issues in physics. Theoretical aspects can also cast light on real-life applications like designing aircraft and predicting weather. I have been concerned with issues in fluid and complex fluid dynamics that form a constellation of related problems to the global regularity problem. For instance, my recent results include justifying Kolmogorov’s 1941 conjecture on phenomenological turbulence theory, building grounds for the study of finite dimensionality of turbulent flows, improving regularity criteria for supercritical equations, and discovering dramatic ill-posedness behaviors of solutions.

In recent work with PhD student, Han Liu, we have completed a few projects on some complex fluid models, focusing on the low modes regularity criterion for a Chemotaxis-Navier-Stokes system. This describes the dynamics of bacterial swimming (example: Bacillus Subtilis) and oxygen transport in a liquid medium. We confirmed that under the low modes part of the solution only, a blow-up will not happen, and the bacteria will not concentrate at one point in the space.

Currently, Han is working on the well/ill-posedness problem for the magneto-hydrodynamics with Hall effect, which is a fundamental model to capture the fast magnetic reconnection phenomena in astrophysics. Our analytical study involves applications of various classical energy methods, Calderon-Zygmund techniques, and modern harmonic analysis tools.

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Lev Reyzin: Associate Professor

My work focuses on foundational questions in computational and statistical learning theory, but I am more broadly interested a variety of topics, ranging from practical issues in machine learning to theoretical computer science. My research also intersects with various areas of combinatorics and optimization. Some of my specific recent projects include work on adaptive data analysis, noise-tolerant algorithms, active and interactive learning, network optimization, boosting and ensemble methods, and multiarmed bandits.

Much of my research is done with Ph.D. students, and I work with them across all of my areas of research interest.  A few of my recent students have written their dissertations in areas that involve the intersection of theoretical computer science and new challenges posed in the era of “big data.”

Theoretical computer science is thriving and growing at UIC, both within the Math department and in the Computer Science department.  Please visit theory.cs.uic.edu to learn more about the theoretical computer science efforts here.