Michael Monaco
Table of Contents
| Affiliation | Purdue University |
| monacom@purdue.edu | |
| Office | MATH 405 (West Lafayette) |
| ET 314 (Indianapolis) | |
| Office Hours | 3:30pm – 4:30pm MWF |
Research
I study algebraic applications of profunctors (also known as bimodules or distributors) with a particular interest in studying algebraic structures that are useful in algebraic topology from this perspective. Lately, I am considering homological aspects of these structures especially the interaction between cubical structures in the sense of Kaufmann–Ward, plethysm bar constructions, and Koszul duality. I am also interested in Hopf algebraic aspects of these structures.
Papers
- The plethysm product, plus and element constructions (PDF) with Ralph Kaufmann,
Published in Comptes Rendus–Mathématique, Volume 362, p.357-411 (2024) - Calculations for plus constructions
Published in Contemporary Mathematics Volume 802, p.139-160 (2024) - Plus constructions, plethysm, and unique factorization categories with applications to graphs and operad–like theories with Ralph Kaufmann,
Algebraic Geometry and Physics, Int. Press (to appear).
Dissertation work
In my dissertation, I developed a general formalism for defining operads and related structures as plethysm monoids and characterized which structures can be defined this way using a generalization of the Baez–Dolan plus construction. Most of this was published in the first paper. The details of this generalized plus construction were written up in the third paper where we give a generalization of the Baez–Dolan plus construction to arbitrary categories and monoidal categories.
Talks
- A plethysm formalism for operadic structures and homological applications
- Purdue University, Topology seminar, November 2024
- Ohio State University, Homotopy seminar, November 2024
- A formalism for operadic structures with applications to Hopf algebras and \(B_+\) operators
- University of Louisiana at Lafayette, Topology seminar, February 2024
- Princeton University, Topology seminar, February 2024
- The Plus Construction and Monoid Definitions of Operad-Like Structures
- Penn Deformation theory seminar, October 2022
- University of Minnesota Topology seminar, October 2022
- Generalized plethysms and homological applications (contributed)
- Algebraic structures in Topology (San Juan, Puerto Rico), June 2024
- Equivariant bimodule algebras and their representations (contributed)
- Maurice Auslander International Conference, April 2023
- The Plus Construction on Monoidal Categories (contributed)
- AMS Central Sectional Meeting Special Session on Higher Structures in Topology, Geometry and Physics, March 2022
Teaching
Currently, I am teaching two sections of Linear algebra (MA 265) at the Indianapolis location. I have also taught the following courses at Purdue in previous semesters:
- Instructor of record
- MA 26600 Ordinary Differential Equations
- MA 26500 Linear algebra
- MA 15800 Precalculus — Functions And Trigonometry
- Recitation instructor
- MA 16500 Analytic Geometry And Calculus I
- MA 16600 Analytic Geometry And Calculus II
- MA 16200 Plane Analytic Geometry And Calculus II
- MA 26100 Multivariate Calculus