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Research Areas
Research in Algebra and Representation Theory at SMSS investigates the structure and properties of algebraic systems and their symmetries. Faculty in this area work on commutative and homological algebra, Hopf algebras, Lie algebras and superalgebras, operator theory, and non-associative algebra, often motivated by connections to geometry, topology, and mathematical physics. This research contributes to understanding abstract mathematical ideas that underlie diverse areas of modern mathematics.
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Research in Applied and Computational Mathematics at SMSS focuses on the development and implementation of advanced mathematical models and computational techniques to explore complex physical, biological, and engineering systems. Faculty in this area work on numerical algorithms, scientific computing, and applied analysis involving ordinary and partial differential equations. Their work often bridges theory and application, combining rigorous mathematics with simulation and high-performance computation to address real-world challenges in science, engineering, and industry.
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Research in Analysis, Differential Equations, and Dynamical Systems at SMSS explores the fundamental mathematical structures underlying continuous and dynamic processes. Faculty in this area study analysis in different spaces, differential equations, stochastic equations, nonlinear systems, quantization, and the qualitative and geometric behavior of their solutions. Their work connects deep theoretical analysis with applications in physics, biology, and applied sciences, contributing to advances in mathematical modeling, stability theory, and geometric analysis, among other areas.
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Research in Geometry, Combinatorics, and Topology at SMSS examines the structures and relationships that arise from spatial, discrete, and topological configurations. Faculty in this area study discrete and computational geometry, sphere packings, polyhedral theory, differential geometry, algebraic and complex geometry, topological combinatorics, and fractal structures. Their work connects pure and applied mathematics, revealing deep links between geometric form, algebraic structure, and combinatorial complexity.
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Research and Scholarship in Mathematics Education and Pedagogy at SMSS focuses on advancing the teaching and learning of mathematics across K-16 settings. Research areas include studying how students develop mathematical understanding, reasoning, and proof skills, as well as how teachers can be better prepared to support these learning processes. Additionally, our scholarly work addresses teacher preparation, students’ mathematical identity, informal learning and family-based mathematics learning, curriculum design, alternative grading methods, instructors’ pedagogical practices, use of technology in mathematics education, and STEM education initiatives. Our work also examines how teachers engage families and local communities to support mathematics learning that connects with students’ backgrounds and everyday experiences. Collectively, this research seeks to improve mathematics learning outcomes and promote effective, evidence-based instructional practices that help all students participate meaningfully in mathematics.
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Research in Mathematical Physics at SMSS focuses on the mathematical foundations of physical theories and the analysis of models describing natural phenomena. Faculty in this area investigate topics such as partial differential equations in physics, integrable systems, soliton theory, models of complex systems, quantum field theory, theories of turbulent flows, and cosmology. Their work bridges pure mathematics and theoretical physics, combining analytical, geometric, and computational techniques to study wave propagation, quantum systems, elastic and porous media, dynamics of complex physical processes, and other phenomena.
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Research in Mathematical and Statistical Modeling at SMSS focuses on developing and analyzing quantitative models that describe complex phenomena in science, engineering, and society. Faculty in this area create and apply mathematical, statistical, and computational frameworks to understand and predict the behavior of systems ranging from biological, epidemiological, and environmental processes to physical and industrial applications. In particular, experts in this area work on models from both mathematical and statistical perspectives. Their work integrates theory, computation, and data to provide insights and solutions for real-world problems.
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Postdoctoral Fellows
Research in Number Theory and Special Functions at SMSS explores the properties of integers, partitions, and related analytic and combinatorial structures. Faculty in this area study topics such as q-series, modular forms, and special functions, along with their interconnections to combinatorics, algebra, and mathematical physics. This research advances both the theoretical understanding and computational aspects of number theory and its many modern applications.
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Research in Probability, Statistics, and Data Science at SMSS focuses on understanding uncertainty, variability, and data-driven decision-making through rigorous mathematical and statistical methods. Faculty in this area work on stochastic modeling, Bayesian inference, biostatistics with focus in health research, high-dimensional data analysis, machine learning and data science, among other innovative directions. Their research supports applications in medicine, health sciences, environmental sciences, and quantitative modeling, bridging theoretical statistics with real-world data challenges.
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