T. Brazelton

activity

20172026

A^{1}

-degree

7 citations · 15 across the 15 of their papers we have counts for

collaborators

17 papers

math.AG2026

Symmetry and solvability: Galois groups of equivariant enumerative problems

Thomas Brazelton, Alberto Landi, Sidhanth Raman

At the genesis of Galois theory at the end of the 19th century, enumerative geometers were concerned with the solvability of various problems: for instance whether one can express…

math.AG2025★ 1 cited

The Evolution of Enumerative Geometry: A Narrative from Classical Problems to Enriched Invariants

Candace Bethea, Thomas Brazelton

Enumerative geometry, the art and science of counting geometric objects satisfying geometric conditions, has seen a resurgence of activity in recent years due to an influx of new t…

math.AG2025

On algebraic vector bundles of rank $2$ over smooth affine fourfolds

Thomas Brazelton, Morgan Opie, Tariq Syed

The classification of algebraic vector bundles of rank 2 over smooth affine fourfolds is a notoriously difficult problem. Isomorphism classes of such vector bundles are not uniquel…

math.AG2024

Bitangents to symmetric quartics

Candace Bethea, Thomas Brazelton

Recall that a non-singular planar quartic is a canonically embedded non-hyperelliptic curve of genus three. We say such a curve is symmetric if it admits non-trivial automorphisms.…

math.AT2024

There is no Cazanave's Theorem for punctured affine space

Thomas Brazelton, William Hornslien

In his thesis, Cazanave proved that the set of naive $A^{1}$ -homotopy classes of endomorphisms of the projective line admits a monoid structure whose group completion is gen…

math.AG2024

Monodromy in the space of symmetric cubic surfaces with a line

Thomas Brazelton, Sidhanth Raman

We explore the enumerative problem of finding lines on cubic surfaces defined by symmetric polynomials. We prove that the moduli space of symmetric cubic surfaces is an arithmetic…

math.AT2022

Equivariant enumerative geometry

Thomas Brazelton

We formulate an equivariant conservation of number, which proves that a generalized Euler number of a complex equivariant vector bundle can be computed as a sum of local indices of…

math.AT2022

An enriched degree of the Wronski

Thomas Brazelton

Given $m p$ different $p$ -planes in general position in $(m + p)$ -dimensional space, a classical problem is to ask how many $p$ -planes intersect all of them. For example when $m = p =…

math.AG2021

Lifts, transfers, and degrees of univariate maps

Thomas Brazelton, Stephen McKean

One can compute the local $A^{1}$ -degree at points with separable residue field by base changing, working rationally, and post-composing with the field trace. We show that f…

math.AG2021★ 6 cited

Bézoutians and the $A^{1}$ -degree

Thomas Brazelton, Stephen McKean, Sabrina Pauli

We prove that both the local and global $A^{1}$ -degree of an endomorphism of affine space can be computed in terms of the multivariate Bézoutian. In particular, we show that…

math.NT2021

Residue sums of Dickson polynomials over finite fields

Thomas Brazelton, Joshua Harrington, Matthew Litman +1

Given a polynomial with integral coefficients, one can inquire about the possible residues it can take in its image modulo a prime $p$ . The sum over the distinct residues can somet…

math.AT2021★ 1 cited

Homotopy Mackey functors of equivariant algebraic $K$ -theory

Thomas Brazelton

Given a finite group $G$ acting on a ring $R$ , Merling constructed an equivariant algebraic $K$ -theory $G$ -spectrum, and work of Malkiewich and Merling, as well as work of Barwick,…

math.RA2021

A note on twisted group rings and semilinearization

Thomas Brazelton

In this short note, we construct a right adjoint to the functor which associates to a ring $R$ equipped with a group action its twisted group ring. This right adjoint admits an int…

math.AG2020

An Introduction to $A^{1}$ -Enumerative Geometry

Thomas Brazelton

We provide an expository introduction to $A^{1}$ -enumerative geometry, which uses the machinery of $A^{1}$ -homotopy theory to enrich classical enumerative geometry qu…

math.AT2019★ 7 cited

The trace of the local $A^{1}$ -degree

Thomas Brazelton, Robert Burklund, Stephen McKean +2

We prove that the local $A^{1}$ -degree of a polynomial function at an isolated zero with finite separable residue field is given by the trace of the local $A^{1}$ -deg…

math.AT2018

Constructing the Unstable Motivic Homotopy Category Using $(\infty, 1)$ -Categories

Thomas Brazelton

This is an expository paper providing an overview of the unstable motivic homotopy category using the theory of $(\infty, 1)$ -categories. In this paper, we examine two constructions…

math.NT2017

Zeros of Newform Eisenstein Series on $Γ_{0} (N)$

Thomas Brazelton, Victoria Jakicic

We examine the zeros of newform Eisenstein series $E_{χ_{1}, χ_{2}, k} (z)$ of weight $k$ on $Γ_{0} (q_{1} q_{2})$ , where $χ_{1}$ and $χ_{2}$ are primitive characters modulo $q_{1}$ and $q_{2}$ , respect…

Symmetry and solvability: Galois groups of equivariant enumerative problems

The Evolution of Enumerative Geometry: A Narrative from Classical Problems to Enriched Invariants

On algebraic vector bundles of rank 2 over smooth affine fourfolds

Bitangents to symmetric quartics

There is no Cazanave's Theorem for punctured affine space

Monodromy in the space of symmetric cubic surfaces with a line

Equivariant enumerative geometry

An enriched degree of the Wronski

Lifts, transfers, and degrees of univariate maps

Bézoutians and the A1-degree

Residue sums of Dickson polynomials over finite fields

Homotopy Mackey functors of equivariant algebraic K-theory

A note on twisted group rings and semilinearization

An Introduction to A1-Enumerative Geometry

The trace of the local A1-degree

Constructing the Unstable Motivic Homotopy Category Using (∞,1)-Categories

Zeros of Newform Eisenstein Series on Γ0​(N)

On algebraic vector bundles of rank $2$ over smooth affine fourfolds

Bézoutians and the $A^{1}$ -degree

Homotopy Mackey functors of equivariant algebraic $K$ -theory

An Introduction to $A^{1}$ -Enumerative Geometry

The trace of the local $A^{1}$ -degree

Constructing the Unstable Motivic Homotopy Category Using $(\infty, 1)$ -Categories

Zeros of Newform Eisenstein Series on $Γ_{0} (N)$