# Research

## Preprints

Matroids in OSCAR with Lukas Kühne and Benjamin Schröter (2023).

Singular matroid realization spaces with Dante Luber (2023). code

The virtual Euler characteristic for binary matroids with Madeline Brandt and Juliette Bruce (2023).

Counting tropical curves in P1 x P1 : computation and polynomiality properties with Hannah Markwig and Dhruv Ranganathan (2022). code

Initial degenerations of flag varieties with Jorge Alberto Olarte (2022). code

The Ceresa class and tropical curves of hyperelliptic type, with Wanlin Li (2022). code

## Publications

Initial degenerations of spinor varieties. Accepted to European Journal of Mathematics. (2023) (code)

The Ceresa class: tropical, topological, and algebraic, with Jordan Ellenberg and Wanlin Li. Accepted to Journal of the Institute of Mathematics of Jussieu. (2023)

The Grassmannian of 3-planes in C8 is schön with Dante Luber. Algebraic Combinatorics, Volume 6 (2023) no. 5, pp. 1273-1299. (arXiv, code)

(Extended Abstract for FPSAC 2023).

Syzygies of P1 x P1 : Data and Conjectures, with Juliette Bruce, Daniel Erman, Steve Goldstein, Robert Laudone, and Jay Yang. Journal of Algebra, 593: 589-621. (2022) (arXiv)

Tropical moduli spaces as symmetric Delta-complexes, with Daniel Allcock and Sam Payne, Bulletin of the London Mathematics Society, 54: 193-205. (2022) (code, arXiv).

Initial degenerations of Grassmannians, Selecta Mathematica New Series 27, 57 (2021). (code).

Tropical curves of hyperelliptic type, Journal of Algebraic Combinatorics 53, 1215–1229 (2021).

Khovanskii bases of Cox-Nagata rings and tropical geometry, with Martha Bernal, Maria Donten-Bury, Naoki Fujita, and Georg Merz. In: Smith G., Sturmfels B. (eds) Combinatorial Algebraic Geometry. Fields Institute Communications, vol 80. Springer, New York, NY.

Continuity properties of vectors realizing points in the classical field of values, with Charles Johnson, Ryan Kirk, Brian Lins, and Ilya Spitkovsky. Linear Multilinear Algebra 61 (2013), no. 10, 1329–1338.

The product field of values, with Charles Johnson, Ryan Kirk, Brian Lins, and Ilya Spitkovsky. Linear Algebra and its Applications 438 (2013), no. 5, 2155–2173.

## Talks

Singular matroid realization spaces, Minisymposium "MS16: Combinatorial algebraic geometry and rigidity theory" at SIAM TX-LA 2023, University of Louisiana at Lafayette, Nov 2023.

The tropical Ceresa class, A Tropical Panorama, Trinity College Dublin, Sept 2023.

Singular matroid realization spaces, Combinatorial algebraic geometry reunion event, ICERM, August 2023.

Counting (tropical) curves in P1 x P1, Minisymposium "MS12 Matroidal and Tropical Methods in Algebraic and Enumerative Geometry" at SIAM Conference on Applied Algebraic Geometry, TU Eindhoven, July 2023.

Degenerations of spinor varieties and even Delta-matroids, Algebraic Geometry seminar, University of Versailles Saint-Quentin-en-Yvelines, June 2023

Matroids and their realizations, Universität des Saarlandes, May 2023 (notes)

Degenerations of flag varieties and subdivisions of generalized permutahedra, Oberseminar Groups and Geometry, Universität Bielefeld, April 2023.

An invitation to OSCAR, Machine Assistance for Algebra, University of Wisconsin-Madison, March 2023. (jupyter notebook)

Degenerations of flag varieties and subdivisions of generalized permutahedra, Algebra and Algebraic Geometry Seminar, University of Wisconsin-Madison, March 2023.

Tropical Geometry through the lens of algebraic geometry, Colloquium, University of Nevada, Las Vegas, Feb. 2023 (slides)

Degenerations of flag varieties and subdivisions of generalized permutahedra, Oberseminar Darstellungstheorie, RWTH Aachen University, Dec. 2022. (slides)

Initial degenerations of flag varieties, Combinatorics Seminar, Brown University, Oct 2022.

Tropical Ceresa class, AMS Fall Eastern Sectional Meeting, UMass Amherst, Oct 2022. (slides)

Initial degenerations of flag varieties, Tropical Geometry in Frankfurt (TGiF), Goethe University Frankfurt am Main, July 2022.

Tropical Ceresa class, Universität Tübingen, April 2022. (slides)

Tropical curves, Retreat 2022 of the SFB-TRR 195, Ebernburg in Bad Münster am Stein, March 2022.

Initial degenerations of Grassmannians and spinor varieties, Fifth annual conference of the SFB-TRR 195, RWTH Aachen University, Sept. 2021.

Initial degenerations of Grassmannians and spinor varieties, Discrete Mathematics and Geometry seminar, Technische Universität Berlin, April 2021.

Initial degenerations of Grassmannians, Algebraic Geometry and Polyhedra, Combinatorial Algebraic Geometry at ICERM, April 2021. (video).

The Ceresa class: tropical, topological, algebraic, Tropical Geometry in Zoom (TGiZ), Goethe University Frankfurt am Main, March 2021 (video).

The Ceresa class: tropical, topological, algebraic. Algebraic Geometry Seminar, University of Warwick, Feb 2021.

Initial degenerations of Grassmannians, Geometry Seminar, University of Texas at Austin, Oct 2020.

Topology of moduli spaces of tropical curves in low genus. Algebra and Algebraic Geometry Seminar, University of Wisconsin-Madison, Nov 2019.

Tropical curves of hyperelliptic type. Algebra seminar, Georgia Institute of Technology, Nov 2019.

Topology of moduli spaces of tropical curves in low genus. Graph complexes in algebraic geometry and topology, University of Manchester, Sept 2019.

The Tropical Ceresa Class, Topology, Analysis and Geometry Seminar, Central Michigan University, Sept 2019.

Tropical curves of hyperelliptic type, SIAM Conference on Applied Algebraic Geometry, Bern, July 2019.

Initial degenerations of Grassmannians, University of Kentucky Algebra and Number Theory Seminar, University of Kentucky, Oct 2018.

Initial degenerations of Grassmannians, Tropical Geometry and Moduli Spaces, ICM Satellite Conference in Cabo Frio, Brazil. August 2018.

Initial degenerations of Grassmannians, Algebra and Algebraic Geometry Seminar, University of Wisconsin-Madison, April 2018.

Initial degenerations of Grassmannians, AMS Spring Central Section Meeting, Ohio State University, March 2018 (slides).

Initial degenerations of Grassmannians, Geometry, Combinatorics, and Integrable Systems, Ohio State University, Jan 2018.

A primer on toric degenerations, BATMOBYLE, Yale University, Nov. 2018.

Initial degenerations of Grassmannians, Valley Geometry Seminar, UMass Amherst, Sept. 29 2017.

Initial degenerations of Grassmannians, SIAM Conference on Applied Algebraic Geometry, Georgia Institute of Technology, August 2017 (slides).

Initial degenerations of Grassmannians, AMS Graduate Student Conference, Brown, May 2017.

Homology of the boundary complex, STAGS, Brown, April 2015.

### Posters

Initial degenerations of Grassmannians, AGNES, Northeastern University, Oct. 2017 (poster).

Initial degenerations of Grassmannians, GAeL, University of Bath, June 2017 (poster).

The compact tropical Grassmannian, Combinatorial Algebraic Geometry (Introductory Workshop), Fields Institute, Sept. 2016 (poster).

## Conferences/seminars/workshops (co)-organized

Tropical methods for moduli spaces with Leonid Monin, minisymposium at SIAM AG23.

Discrete Mathematics/Geometry seminar with Michael Joswig and Marta Panizzut at TU Berlin. webpage.

Algebraic and Tropical Online Meetings with many contributors. webpage.

Matroids day with Jose Israel Rodriguez. webpage.

Matroids seminar Together with Jose Israel Rodriguez, Colin Crowley, Connor Simpson at University of Wisconsin-Madison. webpage.

Student Tropical and Algebraic Geometry Seminar Together with Jeremy Usatine at Yale University webpage.