Professor Allen’s research lies at the intersection of homotopy theory and algebraic geometry. His current work revolves around certain aspects of Quillen’s conjecture which roughly speaking, seeks to determine if some higher order algebraic structures vanish after a certain degree. His research uses objects called quasitoric manifolds-mathematical objects that are very rich combinatorially and algebraically–to make progress resolving this conjecture. From an applied perspective, Professor Allen is interested in topological data analysis and networking analysis.
Professor Lee is interested in combinatorial and additive number theory. He has published papers on additive bases, geometry of sumsets, and class activities using Fibonacci sequence for students, winning numerous grants for these works. He is also interested in other related areas, such as number theory, group theory, combinatorics, dynamical systems, etc.
Professor McCarthy’s research interests in applied math include mathematical models of chemical and biological processes, such as adsorption kinetics (chemistry) and evolution of treatment resistant pathogens (biology). His pure math research interests include the Hilbert Projective Metric and its applications. In the field of math education research, he is involved in peer mentoring and incorporating mathematical modeling into the teaching of math (especially in association with Simiode.org).
Professor Muzician’s areas of expertise are in complex analysis and complex dynamical systems. He works with conformally natural extensions of circle maps and their rigidity. He also studies the dynamics of rational maps with half-symmetries.
Professor Offenholley’s current research interests include gaming in mathematics education, part of the developing field of games-based learning. She is currently working on a $875,794 NSF grant to create a game-based developmental math course for aspiring STEM majors.
Professor Wladis’ current research interests are online learning and developmental mathematics education. In particular, she focuses on issues of access and retention in higher education, with a particular interest in students who have traditionally been underrepresented in higher education and in STEM (science, technology, engineering, and mathematics) fields. She is currently directing a $719,108 NSF grant focused on exploring how student-level factors relate to online course outcomes. She is also in the process of developing and testing an elementary algebra concept inventory, and piloting new approaches to teaching conceptually in elementary algebra.