Research Areas
Actuarial Science
Actuarial Science explores how to model, manage, and mitigate risk in financial, insurance, and healthcare settings. Our faculty investigate topics ranging from retirement planning and longevity risk to enterprise risk management and capital requirements. Their work integrates advanced statistical methods, predictive analytics, and stochastic modeling to tackle complex real-world problems, with applications that span individual decision-making to organizational strategy.
Algebra and Number Theory
Research in algebra and number theory focuses on the study of mathematical structures, symmetries, and relationships between numbers. Our faculty work in areas such as algebraic geometry, combinatorics, number theory, representation theory, and commutative and homological algebra. Their research uncovers fundamental patterns that connect different branches of mathematics and drive progress across the field.
Analysis
Analysis investigates the behavior of functions, operators, and spaces, providing tools that reach across mathematics and its applications. Our faculty study topics ranging from Banach spaces, ergodic theory, and non-linear functional analysis to Fourier analysis, wavelets, and approximation theory. Their work connects abstract structures with practical challenges, including inverse problems, tomography, and differential equations on groups and fractals.
Applied Mathematics
Faculty working in applied mathematics explore differential equations arising in continuum mechanics and material science, combining qualitative analysis with large-scale numerical simulations. Research also spans applied functional analysis for tomography and remote sensing, as well as numerical linear algebra for stochastic processes and nonnegative matrices, with a focus on high-performance computing. Additional interests include variational methods, such as the Mountain Pass Theorem, and questions in mathematical physics and space-time structure.
Geometry and Topology
The geometry and topology group explores the shape, structure, and underlying spaces of mathematics from many perspectives. Research in differential geometry and geometric analysis examines topics such as complex geometry, foliations, geometric flows, and mathematical relativity. Faculty also study geometric and functional inequalities on manifolds and metric measure spaces, as well as geometric topology with applications to computer animation, visualization, and engineering. The group thrives on connections, linking geometry and topology to areas such as algebra, analysis, physics, and probability.
Mathematics Education
Our group in mathematics education focuses on improving the teaching and learning of mathematics across the K–20 spectrum and in connection with other disciplines. Faculty are active in curriculum design, pedagogy, outreach, and research, often in collaboration with the Neag School of Education and campus partners such as the Quantitative Learning Center. Current initiatives include redesigning calculus courses, training graduate teaching assistants, strengthening peer tutoring, and developing professional programs for in-service and high school teachers. Through these efforts, the group combines innovation in the classroom with broader contributions to mathematics education.
Mathematical Finance
Mathematical finance develops rigorous tools for understanding risk, investment, and decision-making in financial markets. Faculty research includes the theory of stochastic processes, pricing and hedging of contingent claims, and optimal investment in incomplete markets. They also study portfolio optimization, anticipations in financial markets, and the statistical foundations that support modern financial modeling.
Mathematical Logic
Our mathematical logic group investigates the foundations of mathematics, exploring computability, proof theory, reverse mathematics, and algorithmic randomness. Faculty study the computational power of programs, computable models of algebraic and combinatorial structures, and the axiomatic strength required to prove mathematical theorems. The group engages in interdisciplinary work through the UConn Logic Group and serves as the administrative home of the Association for Symbolic Logic.
Numerical Analysis
Numerical analysis focuses on developing and studying algorithms for solving mathematical problems with precision and efficiency. Our faculty work on numerical solutions of partial differential equations, particularly using finite element methods, and on fast algorithms for structured matrices with applications in engineering, signal processing, and control theory. A key emphasis of their research is understanding error and ensuring numerical accuracy in computational methods.
Partial Differential Equations
The partial differential equations group studies equations that arise across the sciences, combining theory, modeling, and applications. Research spans linear PDEs and Brownian motion, nonlinear analysis including the Mountain Pass Theorem, and models such as Gierer–Meinhardt and Bose–Einstein condensates. Faculty also investigate geometric PDEs from general relativity, fully nonlinear equations with connections to differential and algebraic geometry, and elliptic and parabolic equations from materials science and continuum mechanics.
Probability Theory
Probability theory explores the behavior of random phenomena across a variety of settings. Our faculty study stochastic processes with jumps, stochastic analysis on fractals and in infinite dimensions, and Harnack inequalities. Their work blends rigorous theory with applications, uncovering patterns and structures in complex probabilistic systems.