Three out of the 40 coveted Simons Fellowships in Mathematics for 2018 have been awarded to Cornell mathematics faculty members: Professor Marcelo Aguiar, Associate Professor Lionel Levine and Professor Alex Vladimirsky. The Simons Fellows Programs in both Mathematics and Theoretical Physics provide funds to faculty for up to a semester long research leave from classroom teaching and administrative obligations. The program is intended to make sabbatical leaves more productive by extending them to a full academic year.
Aguiar specializes in algebra, combinatorics and category theory. His research interests include topics in noncommutative algebra, category theory and algebraic combinatorics, with Hopf algebras and their generalizations appearing prominently. A goal of his past work has been to build a conceptual framework for the study of Hopf algebraic structures in combinatorics and to clarify its significance to concrete applications. Part of his current work is devoted to enlarging the scope of classical Hopf-Lie theory.
Levine focuses on probability and combinatorics in his work. The broad goal of his research is to understand how and why large-scale forms and complex patterns emerge from simple local rules. His approach is to analyze mathematical models that isolate just one or a few features of pattern formation. Recently he has been exploring abelian networks, a generalization of the Bak-Tang-Wiesenfeld abelian sandpile model.
Vladimirsky’s research is in numerical methods, dynamical systems, nonlinear PDEs and control theory. He studies the effects of anisotropy and inhomogeneity on analytic properties of differential equations and the computational efficiency of numerical methods. He is interested in a variety of discrete and continuous nonlinear problems that have some causal properties defining the direction of “information flow.” Much of his work also exploits the often underutilized connections between computer science/operations research and “continuous” numerical analysis.