## Ph.D. Candidate, University of Iowa

Peninsula State Park, WI, 2016

I am originally from River Forest, IL, which is a close suburb of Chicago. After high school, I went to St. Olaf College in Northfield, MN. In 2016, I graduated with a Bachelor of Arts in Mathematics and Physics.

Photo from University of Iowa Currently, I am graduate student in the Department of Mathematics at the University of Iowa. My research interests are in representation theory and, in particular, representations of finite groups over fields of positive characteristic. My advisor is Professor Frauke Bleher. I enjoy helping students understand mathematics and, most semesters, I am a teaching assistant in the Mathematics department. I have also served in the Graduate Student Senate and on the Math Graduate Board, striving to make a difference in the mathematical and larger university community.

Photo from Cedar Rapids Gazette When I am not thinking about math, I enjoy running, traveling and spending time in nature, listening to organ music by J.S. Bach, and cooking. If you can't find me at my desk working on math, you can probably find me on a gravel road in the middle of a long run.

Pontresina, Switzerland, 2013
Link to more pictures from travelling.

## Teaching

Current Teaching

Information about the current semester. I am not teaching during Fall 2019.

Experience

Teaching Assistant
University of Iowa
Calculus for the Biological Sciences
Fall 2018
Calculus II
Summer 2018
Introduction to Abstract Algebra
Spring 2018
Calculus and Matrix Algebra for Business
Fall 2017
Engineering Math II
Spring 2017
Calculus and Matrix Algebra for Business
Fall 2019
St. Olaf College
Calculus with Review
Fall 2014

Teaching Practicum Experience, University of Iowa
Introduction to Linear Algebra
Fall 2019
Engineering Math III: Matrix Algebra
Summer 2019

Tutoring
Math Tutorial Lab, University of Iowa
2016-present
Private Tutoring
2016
Math Clinic, St. Olaf College
2014-2016

Awards and Certifications

Outstanding Teaching Assistant Award, Council on Teaching, University of Iowa, 2018-2019
Graduate Certificate in College Teaching, Pending

Files

To be updated.

## Research

My research interests are in algebra and representation theory. In particular, I am interested in representations of finite groups over fields of prime characteristic. Most recently, I have been looking at representations defined geometrically.

For a curve $$X$$ over a field $$k$$ with an action of a group $$G$$, one can consider the sheaf of relative differentials of $$X$$ over $$k$$, denoted by $$\Omega_X$$. Then, for $$m>1$$, taking the global sections of $$\Omega_X^{\otimes m}$$ yields the space of holomorphic polydifferentials. One can also consider a $$G$$-invariant divisor $$D$$ on $$X$$. Taking the global sections of the invertible sheaf $$\mathcal O_X(D)$$ yields the so-called Riemann-Roch spaces. Both of these spaces are representations of $$G$$. I am studying these representations for certain groups and for certain conditions on the curve $$X$$.

Selected Publications and Presentations

"Groups, Representation Theory, and Curves"
MAA MathFest, August 3, 2019

"Representation Theory and Geometry via the Space of Holomorphic Polydifferentals"
Undergraduate research seminar, University of Iowa, May 2, 2019

"Representation Theory and Holomorphic Polydifferentials"
Research seminar, St. Olaf College, April 26, 2019

Jacob Forster, Kristina Garrett, Luke Jacobsen and Adam Wood. A bijective proof of a $$q$$-analogue of the sum of cubes using overpartitions. Involve, 10, no. 3:523-530, 2017.