Marcelo Aguiar

Visiting Scholar

509 Malott Hall

(607) 255-3443

Ph.D. (1997) Cornell Universtiy

Research Area

Algebra, Combinatorics, Category Theory

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 significance to 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.

Selected Publications

Hopf monoids in the category of species. Joint with Swapneel Mahajan. Contemporary Mathematics 585 (2013), 17-124.

Generalized Hopf Modules for bimonads. Joint with Steve Chase. Theory and Applications of Categories, Vol. 27 (2013), No. 13, 263-326.

Monoidal functors, species and Hopf algebras. Joint with Swapneel Mahajan. CRM Monograph Series, Vol. 29 (2010) AMS, Providence, RI. lii+784 pp.

Combinatorial Hopf algebras and generalized Dehn-Sommerville equations. Joint with Nantel Bergeron and Frank Sottile. Compositio Mathematica 142 (2006) 1-30.

On the associative analog of Lie bialgebras. Journal of Algebra 244 (2001) 492-532.