Dylan Shepardson works on mathematical problems that are motivated by applications in other disciplines, like biology, epidemiology, sociology, or archaeology. He is especially interested in new and unusual applications of optimization theory. In most physical, biological, and economic systems, a property is being optimized (like energy or entropy in physical systems, or reproductive success in evolutionary biology), and optimization techniques offer interesting insights into these systems. Shepardson's recent projects include voting theory and its connections to combinatorial geometry, infectious disease modeling, and the problem of using collections of radiocarbon data to estimate dates of the earliest human settlements of Pacific islands.
Chassidy Bozeman’s research interests lie in graph theory and linear algebra. She is currently working on eigenvalue problems of matrices and graph coloring/graph covering problems. She particularly enjoys graph domination problems and their variants. As a teacher, she devotes much energy to current and effective pedagogy. A main goal of hers is to create an inclusive classroom environment via innovative teaching techniques such as the use of recorded video lectures. Bozeman enjoys combining her passion for research and teaching by supervising undergraduate research students.
Tim Chumley is a probabilist interested in working on models that arise in physics, engineering, and other areas. In the past, much of his work has focused on Markov chain models which can be generically called random billiards. His work on probabilistic limit theorems for these models aims to provide a framework for detailed study of realistic physical models of phenomena in kinetic theory of gases and classical statistical mechanics. In addition, he is interested in random walks in random media, differential geometry, and stochastic processes on manifolds.
Alanna Hoyer-Leitzel does research in applications of dynamical systems. Her projects include classifying relative equilibria in the n-vortex problem (configurations of swirls in fluids that maintain their shape while translating and rotating) by looking at symmetry of their structures. Her more recent work applies the ideas of bifurcation, tipping, and disturbance to modeling resilience in climate and ecosystems. Alanna's other interests include bad scifi, cross stitching, taking pictures of her cats, and riot grrl punk music.
Lidia Mrad’s research focuses on applying analytical and computational techniques to solve problems in materials science, specifically in the area of liquid crystals. She is particularly interested in liquid crystal behavior relevant to creating higher-efficiency optical displays, as well as understanding biological phenomena such as DNA packing. Specific methods she uses fall under calculus of variations, nonlinear partial differential equations, and mathematical modeling. In addition to problems from materials science, she works on problems related to public health applications, such as modeling and simulation of mosquito flight for the purpose of controlling disease spread.
Amy Nussbaum is interested in the study of latent variables, which, like happiness or stress, cannot be measured directly. Specifically, she studies the assessment of personality traits. In addition to academia and research, she encourages understanding the use of statistics in government and industry. After graduation, she spent a year as the inaugural American Statistical Association Science Policy Fellow, working to promote the practice and profession of statistics by advocating for evidence-based policymaking and the federal statistical agencies. In addition, she worked for a small medical device company developing a novel imager that detects diseased human tissue using artificial intelligence.
Marie Ozanne '12 is a biostatistician who focuses broadly on statistical methodology to address public health concerns. Her primary interest is infectious disease modeling, where she focuses on extending and tailoring statistical approaches to neglected tropical diseases, as defined by the World Health Organization. Ozanne enjoys the collaborative nature of public health research; she works closely with epidemiologists and medical professionals to ensure statistical models are practical and useful. She also is excited about a new project involving applying statistical models to evaluate homelessness reduction approaches in Connecticut.
Mark Peterson is a physics theorist who teaches in both the physics and mathematics departments. His research includes modelling fluid dynamics in biophysical settings, innovative mathematical methods for elasticity theory, and the history of physics and mathematics, especially the life and work of Galileo.
Margaret Robinson is a number theorist whose work combines analysis, algebra, and topology to understand number theoretic objects, in particular zeta functions. For Robinson, the research is addictive because objects from other areas of mathematics arise like strange outcrops revealing unexpected constituents in the rock of number theory. Tracking down and explaining why these startling connections exist is tantalizing, sometimes frustrating, but never boring.
Peter Rosnick is Professor Emeritus from Greenfield Community College. He has a Bachelor Degree from Tufts University and his Ed.D from the University of Massachusetts. He has been teaching College Mathematics since 1977. In "retirement", in addition to teaching at Mount Holyoke, Dr. Rosnick continues to teach at GCC and also directs its Sustainable Agriculture and Green Energy Education Center. His avocations include bicycling, theater, cinema, and hiking and snowshoeing in search of the elusive Conway moose.
Shan Shan is an applied mathematician and statistician. Her research and teaching focus on extracting stable and interpretable information from high-dimensional data. On the theory side, she builds algorithms and probabilistic models on geometric objects for data analysis tasks, e.g. dimension reduction, inference, regression. On the applied side, she uses her work on anatomical surfaces (typically, teeth and bones of primates) to gain insights about evolutionary processes. On the implementation side, she develops robust and easy-to-use software to bridge the gap between research and practice.
Jessica Sidman works at the intersection of algebra, geometry, and computation. In particular, she is interested in applications of computational algebraic geometry, which is a fancy way of saying that she likes seeing how to use a computer to solve problems with polynomials. Her current research is focused on using algebraic methods to analyze systems of geometric constraints that arise in rigidity theory, a subject with many applications including robotics, protein folding, and computer-aided design.
Rebecca Tramel studies algebraic geometry. This is the study of the geometry of objects which are built out of polynomial equations. She is particularly interested in ways in which different fields can inspire questions in one another. For example, Tramel's main area of study, Bridgeland stability conditions, started out as an idea in physics (string theory), then was translated into an idea in algebra (cohomology and category theory), and has now been used to answer classical questions in algebraic geometry.
Ashley K. Wheeler's primary work is in principal minors of a generic matrix. The topic was motivated by old questions in Invariant Theory. In her thesis, Wheeler showed that unlike the well-studied determinantal and Pfaffian ideals, principal minor ideals do not arise from rings of invariants. Rather, their structure is less organized and for the most part, mysterious. Wheeler has also recently become interested in connections between Hilbert's axioms (his modern reworking of Euclid's axioms), the classical Pappus's Theorem in projective geometry, and the Gorenstein property of rings.
Derek Young's research is in combinatorial matrix theory. Young uses linear algebra and mathematical software to construct matrices that realize the maximum nullity over a set of matrices. Young also uses graph theory to describe the maximum nullity. For instance, each set of matrices that are of interest corresponds to a unique graph. That graph has parameters which bound the maximum nullity above and below.