Marcelo Aguiar

Cornell University


"I studied Mathematics at the Universidad de la Republica in Uruguay and then at Cornell University in Ithaca. I was fortunate to be mentored by great people such as Walter Ferrer-Santos, Steve Chase, and Andre Joyal. Other influential people have been Lou Billera, Ken Brown, Persi Diaconis and Gian-Carlo Rota. I taught at Texas A&M University and I am now a full professor at Cornell University. I regard my prior and ongoing monographs with Swapneel Mahajan as my most valuable contributions to the field.

My research interests include topics in noncommutative algebra, category theory and algebraic combinatorics, with Hopf algebras and their generalizations appearing prominently. A goal of my past work has been to build a conceptual framework for the study of Hopf algebraic structures in combinatorics and to clarify its significanceto concrete applications. Part of my current work is devoted to enlarging the scope of classical Hopf-Lie theory. The new theory includes hyperplane arrangements and idempotent semigroups as part of the fundamental data. I am developing it in joint work with my colleague and friend Swapneel Mahajan."