# Research

## Topological (co)Hochschild Homology

My dissertation work centered around an invariant called topological coHochschild homology (coTHH), which is constructed analogously to topological Hochschild homology (THH) but allows us to study coalgebra spectra. The diagram below gives an intuitive picture of the relationship between these tools for those who are familiar with homotopy theory.

More specifically, I developed the *relative coBökstedt spectral sequence *in order to compute the homotopy groups of coTHH of coalgebras over any commutative ring spectrum.

## (Topological) coHochschild Homology Shadows

As a part of my dissertation work, I studied coHochschild homology as a bicategorical shadow, in the sense of Ponto. In a current collaboration with Maximilien Péroux, we are extending this work to the setting of topological coHochschild homology.

## THH and the Loday Construction

I am a member of a Women in Topology research group studying the Loday construction and higher topological Hochschild homology. My collaborators are:

Ayelet Lindenstrauss, Indiana University

Birgit Richter, University of Hamburg

Alice Hedenlund, University of Oslo

Foling Zou, University of Chicago

Our paper, *Loday constructions on twisted products and on tori*, is available at arXiv:2002.00715.

## Dold-Kan Correspondence for Abelian Inverse Semigroups

In a collaboration with Ranthony Edmonds, Sanjeevi Krishnan, and Emily Rudman, we are developing a Dold-Kan theorem for simplicial abelian inverse semigroups.

## Conference and Seminar Talks

International Christian Community for Teacher Education Conference (May 2021)

*Graphic Novels and Teaching STEM: Science and Art and Understanding the Creation,*invited to speak at the ICCTE Conference

University of Pennsylvania (April 2021)

*Calculations in Topological CoHochschild Homology*, invited to speak in the Geometry-Topology Seminar

Michigan State University (March 2021)

*Mastery-Based Grading in Calculus*, invited to speak in the Conversations Among Colleagues Seminar

École Polytechnique Fédérale de Lausanne (December 2020)

*T**opological CoHochschild Homology**Calculations*, invited to speak in the Topology Seminar

University of Kentucky / Vanderbilt (November 2020)

*Computational Structure of**Topological CoHochschild Homology*, invited to speak in the Topology Seminar

Indiana University (October 2020)

*Computations in Topological CoHochschild Homology*, invited to speak in the Homotopy Theory Seminar

Society for Classical Learning Conference (June 2020)

*Transitioning Group-based Learning Online,*invited to speak in the Rapid Fire Roundtable on "Cultivating Mathematical Communities"

Joint Math Meetings (January 2020)

*Expanding Tools for Topological CoHochschild Homology*, invited to speak in the Special Session on Categorical and Computational Methods in Homotopy Theory

University of California, Los Angeles (November 2019)

*Computations in Topological CoHochschild Homology*, invited to speak in the Algebraic Topology Seminar

Geometry & Topology Student Seminar at MSU (November 2019)

*Computations in Topological CoHochschild Homology,*presented in the weekly seminar at Michigan State University

Christian Educators Association Convention (October 2019)

*Miss Smith, My Future Career and My Mom: Factors that Motivate Students to Learn Mathematics*, invited to speak at the CEA Convention

Calvin University (October 2019)

*Motivations to Learn Mathematics*, invited to speak as a co-presenter in Calvin University's math colloquium series

Redeemer University College (October 2019)

*Topology and its Applications*, invited to speak in a Modern Geometry lecture

AMS Fall Central Sectional Meeting (September 2019)

*Topological CoHochschild Homology Computations*, invited to speak at University of Wisconsin-Madison in the Special Session on Homotopy Theory

MAA MathFest (August 2019)

*Tools for Studying Topological CoHochschild Homology*, presented in the Great Talks for a General Audience: Coached Presentations by Graduate Students session

Young Topologists Meeting (July 2019)

*Computations in Topological CoHochschild Homology*, presented at Ecole Polytechnique Federale de Lausanne

ACMS Conference (May 2019)

*Computations in Topological CoHochschild Homology*, presented at Indiana Wesleyan University

ACMS Conference (May 2019)

*Factors that Motivate Students to Learn Mathematics*, one of five co-presenters at Indiana Wesleyan University

Graduate Student Topology & Geometry Conference (March 2019)

*Computations in Topological CoHochschild Homology*, presented at University of Illinois at Urbana-Champaign

Calvin College (March 2019)

*Tools for Studying Topological CoHochschild Homology*, invited to speak in Calvin College's math colloquium series

Math in Action (February 2019)

*Why Learn Math: Intrinsic and Extrinsic Factors that Motivate Students*, invited as a co-presenter at the Math in Action conference at Grand Valley State University

Undergraduate Research Group at MSU (January 2019)

*(co)Hochschild Homology*, presented at Michigan State University for the undergraduate student researchers working in algebraic topology during the spring of 2019

Calvin College (November 2018)

*Harry Potter and Higher Dimensions*, co-presenter in Calvin College's math colloquium series

European Talbot (July 2018)

*Hochschild (co)homology basics and Operations in Hochschild (co)homology*, presented at the European Talbot Conference in Fischbach bei Dahn, Germany

Geometry & Topology Student Seminar at MSU (April 2018)

*Understanding Topological Hochschild Homology*, presented in the weekly seminar at Michigan State University

Algebraic K-theory Seminar at MSU (March 2018)

*Quillen's Q-construction*, presented in the weekly seminar at Michigan State University

Algebraic K-theory Seminar at MSU (February 2018)

*Topological Foundations and Classifying Spaces*, presented in the weekly seminar at Michigan State University

ACMS Conference (June 2017)

*The Topology of Harry Potter: Exploring Higher Dimensions in Young Adult Fantasy Literature*, co-presenter at Charleston Southern University

Math Teachers' Circle (May 2017)

*A focus on Strategies, Collaboration, and Explanation of Solutions*, invited as a co-presenter at Lewis University as a part of the Math Teachers' Circle in Southwest Chicago

Calvin College (December 2016)

*Topological Data Analysis of Rat Brains*, invited to speak in Calvin College's math colloquium series

MAA MathFest (August 2016)

*Reading, (W)Riting, Reflecting, and Reviewing: The Four "R's" of Formative Assessment in Mathematics*, co-presenter in the Formative Assessment Techniques for Undergraduate Math Courses session

To see other conferences and workshops that I've attended click here:

## Scholarship of Teaching and Learning

Graphic Novels in STEM

Together with Bill Boerman-Cornell, Josha Ho, and Dave Klanderman, we examine graphic novels in Science, Technology, Engineering, and Mathematics to supplement learning in the classroom and engage students more broadly.

Teaching practices advocating against gender bias and combatting imposter syndrome

Reshma Menon and I are contributing an essay to Teaching Gradually: Practical Pedagogy for Graduate Students, by Graduate Students about practices that can help overcome imposter syndrome in teaching.

Student Understanding of Proof

Building on the mentored teaching project from my Certification in College Teaching, Rani Satyam and I are interviewing students about the transition from calculus to proof-based courses and the ways in which students view math as a result.

Math Motivations

In a collaboration with Patrick Eggleton, Ben Gliesmann, Dave Klanderman, and Josh Wilkerson, we surveyed 645 students from middle schools, high schools, and universities in order to analyze factors that motivate students to study mathematics.

Engaging students in math through interest in young adult literature

In collaborations with Bill Boerman-Cornell, Dave Klanderman, and Lexi Schut we explored connecting ideas from math (and topology in particular) to analogies in young adult literature in order to pique student interest.