# Research

## Preprints and Papers

- Preprint: Maximal skew sets of lines on a Hermitian surface and a modified Bron-Kerbosch algorithm with Haoyu Du, Madhav Krishna, Sandra Nair, Janet Page, and Tim Ryan
- This came out of a LoG(M) project done by Haoyu and Madhav, where Janet and Tim were the faculty advisors, and Sandra and I were the grad mentors.

- Preprint: The Cartier core map for Cartier algebras
- See my KUMUNU poster for an overview.

- Preprint: Geometry of Smooth Extremal Hypersurfaces with Janet Page, Tim Ryan, and Karen E. Smith
- Parametrizations of k-Nonnegative Matrices: Cluster Algebras and k-Positivity Tests with Sunita Chepuri and Alex Mason, Journal of Combinatorial Theory, Series A [arXiv]
- See my JMM poster for an overview.

Or, go directly to my arXiv site: https://arxiv.org/a/brosowsky_a_1.html.

## Presentations

A list of talks and poster presentations I've given:

- Talks and presentations on my work on the Cartier core map.
- Talk in the Special Session on Recent Developments in Commutative Algebra at the AMS Spring Southestern Sectional Meeting at Georgia Tech in March 2023.
- Poster presentation at the JMM in January 2023.
- Talk in the Special Session on Commutative Algebra at the AMS Fall Western Sectional Meeting at University of Utah in October 2022.
- Talk at the UIC Commutative Algebra seminar in October 2022.
- Talk at the (virtual) UM Commutative Algebra seminar in September 2022.
- Talk at the (virtual) UNM Algebra and Geometry seminar in September 2022.
- Poster presentation at KUMUNU in May 2022. [Poster]

- Expository talks at the UM Student Commutative Algebra Seminar.
- "Using Macaulay2" (an interactive workshop on using Macaulay2!) in February 2023.
- "How to tell when an ideal is homogeneous" in January 2023.
- "Using volumes to compute properties of ideals" in October 2022.
- "An Introduction to Determinantal Rings" in February 2022.
- "Cluster Algebras" in November 2021.
- "Introduction to Strong F-regularity" in October 2020 (virtual).
- "Primary Decomposition" in November 2018.

- An expository talk at the UM Student Combinatorics Seminar.
- "Spectral Properties of Graph Laplacians" in December 2020 (virtual).

- Talks on work done at the UMN Twin Cities combinatorics REU. Our REU project on k-positivity tests was joint work with Sunita Chepuri and Alex Mason; Sunita also supervised a closely related project on parametrizations for k-nonegative matrices done by Neeraja Kulkarni, Joe Suk, and Ewin Tang.
- Poster presentation on k-positivity tests (joint work with Sunita Chepuri and Alex Mason) at the MAA Undergraduate poster session at the JMM on January 12, 2018. I also won an outstanding poster award! [Poster]
- Final presentation on both related projects for the Twin Cities REU on August 1, 2017. Jointly presented with Neeraja and Alex. [Slides]

- Expository talks for the Cornell undergraduate math club.
- Talks on work done at the MAPS REU at the University of Maryland, College Park; all joint work with Nathaniel Gillman and Murray Pendergrass.
- Women in Mathematics in the Northeast conference at Smith College on September 24, 2016. [Slides]
- Young Mathematicians Conference at Ohio State University on August 20, 2016. Jointly presented with Nate and Murray. [Slides]
- Final presentation for the MAPS REU. [Slides]