Research

My research is within an area of math called algebraic topology. What is topology? Topology is the study of spaces (think shapes, maybe of higher dimensions), specifically properties of shapes that aren't changed as one stretches, bends, shrinks, or smoothly deforms them. The algebra (here talking about abstract algebra, where one generalizes operations like multiplication and addition for integers or real numbers) comes in when one wants to quantify these different topological properties. 

I'm interested in using tools of algebraic topology and higher categories to model quantum field theories. 

I'm also interested in finding ways to introduce the ideas of topology to undergraduate students in a liberal arts college setting. I've mentored a couple of undergraduate research projects during my time at Providence College; for more details about those projects and for further areas of inspiration for future projects, see here. 

Publications:

• • (submitted) Nested cobordisms, Cyl-objects and Temperley-Lieb algebras, joint with M. E. Calle, R.S. Hoekzema, N. Pacheco-Tallaj, C. Rovi, S. Sridhar-Shapiro; https://arxiv.org/abs/2403.01067

  • Flat principal 2-group bundles and flat string structures, joint with D. Berwick-Evans, E. Cliff, A. Nakade and E. Phillips, Contempory Mathematics, 2024. Available here.  

  • Cut and paste invariants of manifolds via algebraic K-theory, joint with R. Hoekzema, M. Merling, C. Rovi, J. Semikina, Topology and its Applications, 2022; arxiv.org/abs/2001.00176 

  • Homological perspective on edge modes in linear Yang-Mills and Chern-Simons theory, joint with P. Mathieu, A. Schenkel and N. Teh, Letters in Mathematical Physics, 1-26, 2020; arxiv.org/abs/1907.10651 

  • Why surplus structure is not superfluous, joint with J. Nguyen and N. Teh, The British Journal for the Philosophy of Science, axy026, 2018; doi.org/10.1093/bjps/axy026 

In Preparation:

• Equivariant factorization algebras

• The Freed-Quinn line bundle in terms of group cohomology, joint with D. Berwick-Evans, E. Cliff.

Invited Talks and Selected Research Activities:

• Center for Mathematics at Notre Dame, Thematic Program in Field Theory and Topology; talk: Principal 2-group Bundles and the Freed-Quinn Line Bundle; Summer 2024. 

• Co-organizer for AIM SQuaRES project, Pasadena, CA, Spring 2024. 

• Co-mentor for Women in Topology IV Workshop, Hausdorff Institute, Bonn, Germany, Summer 2023. 

• Summer Research for Women in Mathematics, Mathematical Sciences Research Institute, Berkeley; Summer 2020 (postponed to 2021).

• Women in Topology III Workshop, Hausdorff Institute, Bonn, Germany, Summer 2019; junior participant.

• AMS Mathematical Research Community: Geometric Representation Theory and Equivariant Elliptic Cohomology, Summer 2019; participant.

• 'Comparing G-equivariant factorization algebra to G-factorization algebras'; junior research talk at Séminaire de mathématiques superérieures, Derived Geometry & Higher Categorical Structures in Geometry and Physics, The Fields Institute, Summer 2018.