I am a fifth year PhD student in Mathematics and an NSF Graduate Research Fellow at the University of Pennsylvania. I am on the job market this fall. I am co-advised by Mona Merling and Kirsten Wickelgren. I am interested in enumerative geometry and algebraic topology, particularly $\textbf{A}^1$-homotopy theory and equivariant homotopy theory. My CV is here.

tbraz at math.upenn.edu

I co-founded the Penn chapter of the Directed Reading Program with Mona Merling, which I now co-organize with Marielle Ong. We were recently featured in an article in Omnia.

### Papers and Preprints:

1. Equivariant enumerative geometry,
Preprint.
2. An enriched degree of the Wronski,
23 pages, 2021. Submitted.
3. Lifts, transfers, and degrees of univariate maps, with S. McKean,
29 pages, 2021. To appear in Math. Scand.
4. Bézoutians and the $\mathbb{A}^1$-degree, with S. McKean, S. Pauli,
30 pages, 2021. Submitted.
5. Residue sums of Dickson polynomials over finite fields, with J. Harrington, M. Litman, T.H.W. Wong,
18 pages, 2021. Submitted.
6. Homotopy Mackey functors of equivariant algebraic $K$-theory,
Journal of Pure and Applied Algebra 226(8), 2022.
7. An introduction to $\mathbb{A}^1$-enumerative geometry,
In: Neumann F., Pál A. (eds) Homotopy Theory and Arithmetic Geometry – Motivic and Diophantine Aspects. Lecture Notes in Mathematics, vol 2292. Springer, Cham. 2021.
8. A note on twisted group rings and semilinearization,
Communications in Algebra, 49:8, 3380-3386, 2021.
9. The trace of the local $\mathbb{A}^1$-degree, with R. Burklund, S. McKean, M. Montoro, M. Opie,
Homology, Homotopy and Applications 23(1):243-255, 2021.
10. Zeros of newform Eisenstein series on $\Gamma_0(N)$, with V. Jakicic,
J. Number Theory (190):109-130, 2018.
11. On consecutive $n$th roots of unity modulo $q$, with J. Harrington, S. Kannan, M. Litman,
J. Number Theory (174):494-504, 2017.

### Notes:

Attached are expository sets of notes from various talks I've given. They are likely riddled with errors - please email me if you find any.

### Conference and course notes:

Disclaimer: Any errors found in these notes should be attributed to me, not the original lecturer. If you find any typos or have suggestions, please feel free to contact me.

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