John Abou-Rached - Robert Riley Visiting Assistant Professor
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Laura Anderson - Associate Professor
Focus areas: Combinatorics, Topology
Description: My research focuses on interactions between combinatorics and topology, particularly those involving oriented matroids, convex polytopes, and other concepts from discrete geometry. Much of my work involves combinatorial models for topological structures such as differential manifolds and vector bundles. The aims of such models include both combinatorial answers to topological questions (e.g., combinatorial formulas for characteristic classes), and topological methods for combinatorics (e.g. on topology of posets).


Robert Bieri - Visiting Professor
Focus areas: Geometric, homological, combinatorial and asymptotic methods in group theory
Description: My original interest in homological methods for infinite groups (cohomological dimension and Poincare type duality) shifted towards geometric and -- more recently -- asymptotic methods. I find it interesting to relate geometric properties at infinity of groups and G-spaces with algebraic properties of these groups, their group rings and their modules. The focus is on familar groups like metabelian, soluble, free and linear ones, or fundamental groups of 3-manifolds, but I also met Thompson's group F and other PL-homeomorphism groups on the way, and had an encounter with tropical geometry.


Alexander Borisov - Associate Professor
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Description: My general research area is algebraic geometry and number theory, broadly interpreted. Particular topics of interest include birational geometry, toric geometry and convex discrete geometry, polynomial morphisms, integer polynomials, Arakelov geometry.


Walter Carlip - Visiting Associate Professor
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Zeyu Ding - Assistant Professor
Focus areas: Data privacy, machine learning
Description: My research lies in the intersection of data privacy, software security, machine learning and algorithmic fairness. The overarching goal of my work is to protect sensitive personal information from being leaked in unintended ways. My current research focuses on differential privacy and its interactions with software security, formal verification, numerical optimization, statistical inference and machine learning.


Michael Dobbins - Associate Professor
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Description: My research is primarily on discrete geometry, particularly geometric problems arising from computer science. I also work in computational geometry, complexity, convexity, combinatorics, and topology.


Yuan Fang - Assistant Professor
Focus areas: Statistics, bioinformatics
Description: My current research focuses on studying lipid profiles for ceramide pathways in boys with Duchenne Muscular Dystrophy using multi-omics statistical and bioinformatics approaches. I am also interested in extending existing models and statistical approaches for clustering longitudinal data.


Alex Feingold - Professor
Focus areas: Algebra, Lie algebras, conformal field theory
Description: Finite dimensional semisimple Lie algebras, tensor product decomposition of irreducible modules, representation theory of the infinite dimensional Kac-Moody Lie algebras, bosonic and fermionic creation and annihilation operators, affine and hyperbolic Kac-Moody algebras, topics in combinatorics, power series identities, modular forms and functions, Siegel modular forms, conformal field theory, string theory, and statistical mechanical models, vertex operator algebras, their modules and intertwining operators, the theory of fusion rules.


Guifang Fu - Associate Professor
Focus areas: Statistics, high-dimensional inference, functional data analysis
Description: My main focus is to develop advanced statistical models and computational methodologies to unravel the genetic and environmental mechanisms that regulate complex biological traits, including morphology/shape, biomedical problems and disease. I am particularly interested in high-dimensional, “big data” modeling, and functional data analysis. My genetic leaf shape project was awarded a three-year NSF grant. I enjoy collaborating on interdisciplinary projects, working with researchers from the application domains and addressing real-life data analysis questions.


James Hyde - Assistant Professor
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Quaid Iqbal - Robert Riley Visiting Assistant Professor
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Dikran Karagueuzian - Associate Professor
Focus areas: Algebraic topology, representation theory, group cohomology
Description: My research for the past few years has been primarily in the representations and cohomology of finite groups. For the past few years I have been studying problems in algebra that arise from techniques of algebraic topology. Sometimes there is a theorem hidden behind the feasibility of a well-known method. An example of this phenomenon is my most recent preprint, written in collaboration with Peter Symonds of the University of Manchester Institute of Science and Technology. In this case the theorem was uncovered through exploration with the computer algebra package Magma, which is well worth checking out. Often such software lets us investigate mathematical phenomena which would be very difficult to understand otherwise.


Vladislav Kargin - Associate Professor
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Description: I am particularly interested in random matrices and its applications, in particular, statistical analysis of large data, zeroes of zeta functions, statistical mechanics of random media, and free probability.


Tae Young Lee - Robert Riley Visiting Assistant Professor
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Paul Loya - Associate Professor
Focus areas: Global and geometric analysis, Elliptic theory of differential operators on manifolds with singularities, Partial differential equations
Description: The underlying theme of my research is the investigation of topological, geometric, and spectral invariants of (singular) Riemannian manifolds using techniques from partial differential equations. For example, the Euler characteristic of a surface is a topological invariant based its usual definition in terms of a triangulation of the surface. However, it may also be considered geometric in view of the Gauss-Bonnet theorem or spectral in view of the Hodge theorem. I am interested in such relationships on general singular Riemannian manifolds.


Cary Malkiewich - Assistant Professor
Focus areas: Algebraic topology, especially stable homotopy theory, algebraic K-theory, applications to manifolds and cell complexes.
Description: My general research interest is in algebraic topology, and my work is broadly motivated by the study of manifolds and cell complexes by algebraic techniques. I have recently been focusing on topological Hochschild homology, algebraic K-theory, transfers, and stable homotopy theory. There is also an emerging connection between my work and homotopy-invariant properties of topological dynamical systems.


Marcin Mazur - Professor
Focus areas: Algebraic number theory, group theory
Description: My research interests concentrate around areas where number theory and group theory intersect. Topics of particular interest are group rings, group schemes over rings of algebraic integers, Galois module structures and Galois representations.


Ryan McCulloch - Visiting Associate Professor
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Pedro Ontaneda - Distinguished Professor
Focus areas: Topology and differential geometry
Description: My general interest is the geometry and topology of aspherical spaces. I have done some work in the study of the relationship between exotic structures and (negative, non-positive) curvature, and its applications to the limitations of PDE methods in geometry. Other interests: geometric group theory, K-theory, mechanics.


Aleksey Polunchenko - Associate Professor
Focus areas: Statistics, sequential analysis.
Description: Mathematical statistics and specifically the problem of sequential (quickest) change-point detection, currently focusing on the case of composite hypotheses.


Xingye Qiao - Professor and Chair
Focus areas: Statistics, machine learning, causal inference
Description: My research interests encompass statistics, machine learning, and data science. I develop and analyze predictive and inferential tools for complex data problems such as imbalanced classes, high-dimensional data, transfer learning, and observational studies. My focus is on designing theoretically sound and efficient learning algorithms that address sample, time, and space complexity challenges. I aim to enhance the trustworthiness and reliability of statistics and machine learning methods, particularly in critical domains like healthcare. My work includes developing user-friendly prediction tools with built-in confidence measures and methods for individualized estimation, prediction, and recommendation from observational and interventional data.


David Renfrew - Assistant Professor
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Description: My research lies in Probability and Random Matrices. I am particularly interested in non-Hermitian random matrices and the interplay between random matrices and free probability. I am also interested in applications to biologic systems.


Minghao Rostami - Associate Professor
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Lorenzo Ruffoni - Assistant Professor
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Eugenia Sapir - Assistant Professor
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Anton Schick - Professor
Focus areas: Statistics, probability
Description: Uses of large sample theory in statistics, the characterization and construction of efficient estimators and tests for semiparametric and nonparametric models, statistical inference for Markov chains and stochastic processes, estimation and comparison of curves, the behavior of plug-in estimators, optimal inference for bivariate distributions with constraints on the marginal, modelling with incomplete data, and the theory and application of finite and infinite order U-statistics.


Rakhi Singh - Assistant Professor
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Daniel Studenmund - Assistant Professor
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Description: My research addresses questions arising at the intersection of geometric group theory and the study of discrete subgroups of Lie groups. I am particularly interested in invariants associated to the collection of finite-index subgroups of a given group G. One example is the abstract commensurator Comm(G), the group of all isomorphisms between finite-index subgroups of G, modulo equivalence. Other examples are growth rates of various functions associated to the collection of finite-index subgroups, which can be thought of as helping to “quantify” residual finiteness of G. I also study other invariants of groups, such as superrigidity and cohomology of arithmetic groups, using algebraic and geometric methods.


Hung Tong-Viet - Professor
Focus areas: Representation theory and character theory of finite groups, permutation groups and abstract finite groups.
Description: My main research interests lie in the representation and character theory of finite groups, permutation groups and applications to number theory and combinatorics, and finite group theory in general. I am interested in studying groups or group structures using several important numerical invariants of the groups such as character degrees (ordinary and modular), p-parts of the degrees or character values such as zeros of characters. In permutation group theory, I study derangements, that is, permutations without fixed points, and their applications in number theory and graph theory, permutation characters and permutation polytopes. Recently, I am also interested in studying the influence of real conjugacy class sizes on the group structures.


Tan Nhat Tran - Robert Riley Visiting Assistant Professor
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Danika Van Niel - Robert Riley Visiting Assistant Professor
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Adrian Vasiu - Professor
Focus areas: Arithmetic Algebraic Geometry
Description: My area of research is Arithmetic Algebraic Geometry, which is the common part of Number Theory, Algebra, and Geometry. I am very much interested in moduli spaces, group schemes, Lie algebras, formal group schemes, representation theory, cohomology theories, Galois theory, and the classification of projective, smooth, connected varieties. My research is focused on:
  1. Shimura varieties of Hodge type (which are moduli spaces of polarized abelian varieties endowed with Hodge cycles),
  2. arithmetic properties of abelian schemes,
  3. classification of $p$-divisible groups,
  4. representations of Lie algebras and reductive group schemes,
  5. crystalline cohomology of large classes of polarized varieties, and
  6. Galois representations associated to abelian varieties.


Minjie Wang - Assistant Professor
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Emmett Wyman - Assistant Professor
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Description: I study Laplace-Beltrami eigenfunctions of large eigenvalue and how their asymptotics relate to the geometric or dynamical structure of the space in which they live. This area is related to classical and quantum physics and number theory.


Xiangjin Xu - Associate Professor
Focus areas: Harmonic Analysis and PDEs
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  1. Harmonic Analysis on Manifolds: eigenfunction estimates and multiplier problems on Riemannian manifolds, Gibbs' phenomenon and Pinsky's phenomenon for Fourier inversion and eigenfunction expansion.
  2. Nonlinear differential equations: Well-posedness problems for nonlinear hyperbolic differential equations on manifolds; Boundary stabilization, controllability problems for (linear and nonlinear) parabolic and hyperbolic PDE's on manifolds; Periodic solutions, subharmonics and homoclinic orbits


Qiqing Yu - Professor
Focus areas: Statistics
Description: My research interests are mainly in three fields.
  1. Survival analysis. Since 1987, I have been working in this field, in particular on modeling the interval censored data, studying consistency and asymptotic normality of the generalized maximum likelihood estimator (MLE) of survival function or the semi-parametric estimator under linear regression model.
  2. Statistical decision theory. My thesis was on admissibility and minimaxity of the best invariant estimator of a distribution function.
  3. Probability model and computing methods for pattern recognition in the Genome project.


Thomas Zaslavsky - Professor
Focus areas: Combinatorics, graph theory
Description: My research is in combinatorics, especially matroids and their connections with combinatorial geometry and graph theory. The main topic of my work is signed, gain, and biased graphs. These are graphs with additional structure that leads to new graphical matroids and other new kinds of graph theory, such as colorings and geometrical representations, of which ordinary graphical matroids, colorings, etc., are special cases. In combinatorial geometry I work on arrangements of hyperplanes and lattice-point counting. Other research interests are in graph theory and in generalizing Sperner's theorem.


Jia Zhao - Associate Professor
Focus areas: Mathematical modeling, numerical analysis, high-performance computations, machine learning
Description: I position myself as an applied and computational mathematician, aiming to strike a balance between mathematical modeling, numerical analysis, high-performance computations, and machine learning, while my application domains are life science and engineering. For further info, please check out my research website: www.zhaojia.net


Gang Zhou - Associate Professor
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  1. mathematical physics: the long time behavior of Schrodinger-type equations, relations between quantum and PDE models, non-equilibrium statistical mechanics,
  2. geometric analysis: mean curvature flow and Ricci flows by methods different from the classical ones, formation of singularities in finite time, flow through singularities.