My Research Life

The Research

I consider myself an algebraic topologist!

In this area, I am interested in studying operads and there many applications and uses.  Some key words I would use to describe the math I think about and do are: homotopy theory, equivariant homotopy theory, homotopical combinatorics, coalgebraic models, Koszul duality.

Below are some papers I have on the arXiv (most recent first): 

• Left and Right Bousfield Localizations on Lattices

• Equivariant Homotopy Theory Via Simplicial Coalgebras

• Transplanting Trees: Chromatic Symmetric Function Results through the Group Algebra of $S_n$

• Spiders and their Kin: An Investigation of Stanley's Chromatic Symmetric Function for Spiders and Related Graphs

Below are some talks I have given (most recent first):

• Stay in the Loop and the Fun Group at the Claremont Center for the Mathematical Sciences Colloquium Spring 2025

• Left and Right Bousfield Localizations on Lattices at the 5 College Geometry and Topology Seminar Fall 2025

• Transfer Systems and Model Structures at INI Workshop: Operads and Calculus (recording) Spring 2025

• Model Structures On Lattices at the Joint Mathematics Meetings 2025

• Modeling Equivariant Simplicial Sets with Simplicial Coalgebras at the UPenn Geometry and Topology Seminar Fall 2024

• Coalgebraic Structures Describing G-Spaces at the ECOGYT Summer 2024

• Coalgebraic Models for G-Spaces at the Algebraic Structures in Topology II Summer 2024

• Coalgebraic Models of for G-Spaces at the Joint Mathematics Meetings 2024

• Equivariantly Equivalent (According to Elmendorf) at the University of Washington for USTARS Spring 2023 

• The Algebraic Structure of Loop Spaces at JMM 2023 in the AMS EDGE Session

• Understanding the Elmendorf Construction at eCHT for the Fall 2022 Kan Seminar 

• Algebraic Azaleas: the Algebraic Structure of Loop Spaces at the University of Oxford for the  EDGE 2022 Mentor Colloquium 

• Let's Talk Alge Top at Spelman College for the EDGE 2022 Symposium 

Below are some notes I have written (most recent first):

• I compiled each document below after passing  my oral advanced topics exam. These notes summarize concepts I have understood and related to my dissertation topic. 

• The Surjection Operad

• Advanced Topics Oral Exam Notes

• Defense Notes

This is what my academic family looks like and I am grateful to be apart of it!