Transgender and Nonbinary Mathematics Pride

Pride month is a time for LGBTQIA+ (Lesbian, Gay, Bisexual, Transgender, Queer, Intersex, & Asexual inclusive) people to celebrate community, raise awareness of oppression, and work towards full human rights. It originates in the Stonewall riots of June 1969, led by Black and Latina transgender women.

This essay consists of eight consensual “elevator pitch” summaries of recent research of transgender and nonbinary mathematicians. Consent is important here as these are frightening times. Anti-trans bills and policies are working through legislatures and school/medical boards. Popular and political discourse includes transphobic hate speech, labeling us as mutilators and groomers of children. Sadly, conferences continue to be held in states where many of us feel unsafe or unwelcome Ree23.

My goal is to inspire aspiring or practicing trans/nonbinary mathematicians, by featuring a proud and visible group of us. I also seek to make cis mathematicians aware of us, so they can work towards making conferences, classrooms, and other mathematics spaces more welcoming; see the article by Buckmire, et al. in this issue for concrete suggestions.

Jessamyn Dukes (any pronouns) is a genderqueer, nonbinary, transgender, nontraditional undergraduate math major at Rutgers (USA) with very broad mathematical interests. Their joint work ABB$^+$22, arising from the Polymath Jr 2022 summer program, investigates lattice models: discrete dynamical systems studied in statistical mechanics where one can evaluate local interactions, or states, at each vertex, in order to reconcile probabilities of the global multistate system. She uses the Yang–Baxter equation to determine if any given lattice model is solvable; such solutions are rare, with many applications. His work provides explicit algebraic conditions such that given two local states of an $n$-color lattice model, a third state or solution can be determined. Furthermore, they show that all solutions to the $n$-color lattice model can be reduced to this 3-color subcase, and give an explicit parametrization of all solutions accordingly. With $n=2$ her result specializes to the “six-vertex” or “ice” model, which recovers Baxter’s classical conditions for solvability of a lattice model.

Stacey G. Harris (she/her/hers) is a trans woman full professor at Saint Louis University (USA) working in the interface of geometry and mathematical physics. She investigates the geometry of spacetime: a manifold $M$ with a notion of “causality” where points of $M$ are events in the universe. Harris researches possible boundaries on $M$ to understand its global behavior. One example, the Future Causal Boundary, consists of the sets of events that causally precede other events. This construction yields a future-limit in the boundary for every physically endless causal curve of each particle and relies only on intrinsic properties of $M$. Until now, the Future Causal Boundary has been calculable only for $M$ with a high degree of symmetry or special algebraic construction. Harris’s paper Har22 assumes only that $M$ is foliated by a field of observers and offers up what physical properties those observers would need to measure so that the Future Causal Boundary is fairly simple topologically and so that the geometry of $M$ has a continuous limit at the boundary for each observer.

Faye Jackson (she/her/hers) is a trans woman undergraduate math major at the University of Michigan (USA) whose research is in combinatorics and number theory. She is a lesbian and the 2023 winner of the Alice T. Schafer Prize. Her recent preprint JO23, with Otgonbayar from the UVA Number Theory REU, explores the arithmetic statistics of parts in partitions of $n$ as $n$ becomes large. It uses the circle method to derive an asymptotic formula for the number of parts congruent to $r$ modulo $t$ among all $k$-indivisible partitions, i.e., partitions where no part is divisible by $k$. The main term of this asymptotic does not depend on $r$, and so, in a weak asymptotic sense, the parts are equidistributed among congruence classes. However, inspection of the lower order terms indicates a bias towards different congruence classes modulo $t$. For large $k$, these biases are similar to work of Beckwith and Mertens for the class of all partitions, but they differ wildly for small $k$, and numerical evidence has led to several conjectures she is still working on.

Astra Kolomatskaia (she/her/hers) is a trans woman PhD student at Stony Brook University (USA) researching homotopy type theory and higher category theory.

She describes her work to her friends as follows: Type theory is about putting math on a computer. Homotopy type theory is about letting the resulting system talk about shapes. In this setting, all I want to know is: “What is a triangle?”

A higher category has objects, morphisms, and higher morphisms between morphisms with a sophisticated interdependence. In homotopy type theory, the barriers to talking about infinitary structures are known as higher-coherence issues, and the prototypical problem exemplifying this is the construction of semisimplicial types, higher triangles.

The fundamental insight of Kolomatskaia’s work is that every definition of a mathematical structure should automatically induce a hierarchy of higher dependent structures living over it. In this framework, she is studying how such definitions can express cross-level interactions Kol22.

Seppo Niemi-Colvin (he/him/his) is a transgender man postdoc at Indiana University (USA). He studies homology of 3-manifolds and knots, especially links of singularity and generalized algebraic knots. Links of singularity are 3-manifolds capturing the local topology around a normal complex surface singularity, and traditional algebraic knots use a singular complex curve in the complex plane. Generalized algebraic knots combine these two by allowing the curve and surface to be singular. His invariant of interest is Ozsváth–Stipsicz–Szabó’s knot lattice homology which computes knot Floer homology combinatorially via resolutions of singularities. In his dissertation NC22, he proved knot lattice homology’s invariance under the choice of resolution for the singularity defining the knot, and he expressed this invariance on the level of a doubly filtered homotopy type. He hopes to compute this knot lattice homotopy type in more examples to better understand how these knots relate to each other and to knots in the 3-sphere.

Emily Quesada-Herrera (she/her/hers) is a Costa Rican trans woman postdoc at Graz University of Technology (Austria) working on the interface of number theory and harmonic analysis. Her recent paper CQH22 with Chirre investigates the classical problem of representing integers and primes by quadratic forms using tools from analytic and algebraic number theory and Fourier analysis to obtain new estimates in this area. As an application, for primes of the form $x^2+27y^2$ studied by Euler and Gauss, assuming the generalized Riemann hypothesis, she shows that there is always such a prime in the short interval $[x, x+5.52\sqrt {x}\log x]$, for $x\gg 0$. She uses a broad toolbox that includes lattices in $\mathbb{R}^2$, ideals of imaginary quadratic fields, and summation formulas that connect these objects to Fourier analysis.

J. Daisie Rock (she/her/hers) is a trans woman BOF Postdoc at Ghent University (Belgium) who was a first-generation college student working in representation theory informed by analysis and category theory. Broadly speaking, her research is about generalizing historically discrete structures to continuous structures. For instance, consider mutation in cluster algebras, which has applications in high energy physics. One begins with a set $\mathcal{X}$ of cluster variables and special subsets of $\mathcal{X}$ called clusters that have the same cardinality and satisfy the mutation property, which allows one to replace cluster variables in a cluster while respecting the cluster property. Classically, this is a discrete process. Choose an $x\in T$, replace it, choose the next $x'$, replace it, and so on. Her paper Roc22 introduces a way to mutate a continuum of variables in order, a process that has exciting possibilities even for the classical situation.

Theresa Simon (she/her/hers) is a butch transgender woman and non-tenure-track faculty member at WWU Münster (Germany), working in applied mathematics. In her joint paper MMSS22, she rigorously analyzes topologically nontrivial, particle-like patterns called magnetic skyrmions occurring in extremely thin magnets. They are modeled as minimizers of the harmonic map problem with a flat, 2D domain and target being the two-dimensional sphere, augmented by a lower order term and constant boundary conditions. She specifies the skyrmion’s topology by requiring it to be homeomorphic to the identity map of the sphere after collapsing the boundary to a point. She proves that if the limit of the lower order term vanishes, then the skyrmion indeed behaves like a particle, and she fully determines its relevant properties.

References

[ABB$^+$22]

P. Addona, E. Bockenhauer, B. Brubaker, M. Cauthorn, C. Conefrey-Shinozaki, D. Donze, W. Dudarov, J. Dukes, A. Hardt, C. Li, J. Li, Y. Liu, N. Puthanveetil, Z. Qudsi, J. Simons, J. Sullivan, and A. Young, Solving the $n$-color ice model, arXiv:2212.06404, 2022.

[CQH22]

A. Chirre and E. Quesada-Herrera, Fourier optimization and quadratic forms, Q. J. Math. 73 (2022), no. 2, 539–577, DOI 10.1093/qmath/haab041. MR4439798,

Show rawAMSref

\bib{Emily}{article}{ author={Chirre, A.}, author={Quesada-Herrera, E.}, title={Fourier optimization and quadratic forms}, journal={Q. J. Math.}, volume={73}, date={2022}, number={2}, pages={539--577}, issn={0033-5606}, review={\MR {4439798}}, doi={10.1093/qmath/haab041}, }

[Har22]

S. G. Harris, Spacelike causal boundary at finite distance and continuous extension of the metric: A preliminary report, Developments in Lorentzian Geometry: GeLoCor 2021, Cordoba, Spain, February 1–5, Springer, 2022, pp. 143–157.

[JO23]

F. Jackson and M. Otgonbayar, Unexpected biases between congruence classes for parts in $k$-indivisible partitions, J. Number Theory 248 (2023), 310–342, DOI 10.1016/j.jnt.2023.01.006. MR4562070,

Show rawAMSref

\bib{Faye}{article}{ author={Jackson, F.}, author={Otgonbayar, M.}, title={Unexpected biases between congruence classes for parts in $k$-indivisible partitions}, journal={J. Number Theory}, volume={248}, date={2023}, pages={310--342}, issn={0022-314X}, review={\MR {4562070}}, doi={10.1016/j.jnt.2023.01.006}, }

[Kol22]

A. Kolomatskaia, Semi-simplicial types, https://github.com/FrozenWinters/SSTs, 2022.

[MMSS22]

A. Monteil, C. B. Muratov, T. M. Simon, and V. V. Slastikov, Magnetic skyrmions under confinement, arXiv:2208.00058, 2022.

[NC22]

S. Niemi-Colvin, Invariance of Knot Lattice Homology and Homotopy, ProQuest LLC, Ann Arbor, MI, 2022. Thesis (Ph.D.)–Duke University. MR4463331,

Show rawAMSref

\bib{Seppo}{book}{ author={Niemi-Colvin, S.}, title={Invariance of Knot Lattice Homology and Homotopy}, note={Thesis (Ph.D.)--Duke University}, publisher={ProQuest LLC, Ann Arbor, MI}, date={2022}, pages={118}, isbn={979-8802-70416-5}, review={\MR {4463331}}, }

[Ree23]

E. Reed, Updated anti-trans legislative risk assessment map, https://tinyurl.com/2pvh3a4j, 2023.

[Roc22]

J. D. Rock, Continuous quivers of type A (IV): Continuous mutation and geometric models of E-clusters, Algebras Rep. Thy. (2022), 34 pp.

Credits

Photo of Keri Ann Sather-Wagstaff is courtesy of Joy Sather-Wagstaff.

Photo of Jessamyn Dukes is courtesy of Jessamyn Dukes.

Photo of Stacey G. Harris is courtesy of Stacey G. Harris.

Photo of Faye Jackson is courtesy of Faye Jackson.

Photo of Astra Kolomatskaia is courtesy of Astra Kolomatskaia.

Photo of Seppo Niemi-Colvin is courtesy of Seppo Niemi-Colvin.

Photo of Emily Quesada-Herrera is courtesy of Emily Quesada-Herrera.

Photo of J. Daisie Rock is courtesy of J. Daisie Rock.

Photo of Theresa Simon is courtesy of Victoria Liesche.