Mathematical Computer Science

Matthew Harrison-Trainor works in mathematical logic and computability theory. His work can be broadly described as using computability-theoretic techniques to measure complexity in mathematics. Much of his work is on the complexity of classifying mathematical structures and characterizing their properties, but he has also worked in algorithmic randomness, effective descriptive set theory, and modal logic.

Vishesh Jain is broadly interested in probability, combinatorics, and theoretical computer science. His work often involves techniques from high-dimensional probability. Specific recent projects include work on universality in random matrix theory, algorithmic applications of Markov chains, regularization phenomena in numerical analysis, and the mean-field approximation in statistical physics.

Marcus Michelen works in probability, combinatorics and classical analysis. Much of his work involves using complex- and Fourier-analytic techniques in discrete settings. Specific recent projects include random algebraic structures such as matrices, polynomials and partitions; the relationship between zero-free regions and probability theory; and Gibbs point processes.

Dhruv Mubayi works primarily on extremal and structural questions on graphs and hypergraphs, with applications to computer science. Much of his work involves the use of probabilistic and algebraic methods. His focus in the past five years lies in Turan and Ramsey type questions, particularly on hypergraphs. Specific recent projects include: the forbidden intersection problem in extremal set theory, the supersaturation phenomenon in extremal graph and hypergraph theory, extending the spectral theory of quasirandom graphs to hypergraphs, and using semi-random, or nibble methods in hypergraph coloring.

Lev Reyzin's work focuses on foundational questions in computational and statistical learning theory, but he is more broadly interested a variety of topics, ranging from theoretical computer science to more practical issues in machine learning. His research also intersects with various areas of combinatorics and optimization.

Caroline Terry works at the intersection of combinatorics and model theory, a branch of mathematical logic.

Gyorgy Turan works in theoretical computer science, artificial intelligence and related areas in discrete mathematics and logic. Recently he worked on combinatorial, probabilistic, algorithmic and belief revision aspects of propositional Horn formulas, and on experimental aspects of commonsense reasoning. In the past he also worked on complexity theory (circuit complexity, decision trees, proof complexity) and computational learning theory (query learning, theory revision, learnability in logic).

Jan Verschelde's research interests are mainly computational algebraic geometry, with a focus on numerical and symbolic methods to solve polynomial systems. He is also interested in mathematical software, parallel algorithms, and supercomputing.