arXiv subjects

Drew Lewis

Publications and source records attributed to Drew Lewis.

14 recordsLinked to original sources

arXiv2026

Community-driven data science practices

Mathematics researchers are becoming more involved with research questions at the interface of data science and social justice. This type of research needs to be grounded in the needs of the community in order to have significant impact. In this paper, we examine two examples of community-research partnerships in data science for social justice co-authored by both community members and mathematical researchers. The first, VECINA, is a place-based community-research partnership focused on environmental justice. VECINA introduces a framework for developing fruitful local collaborations. The second example, SToPA, originates in citizens' request for an analysis of their town's policing data, but focuses on how to scale this work beyond that place-based setting. SToPA's research helps us imagine how we can continue to actively collaborate with community members even when working to scale projects beyond a single community. In both of these case studies, we examine the harmonies between established principles of power, process, and perspective with our framework for research-community partnerships. We use a duoethnography approach, directly illustrating the experiences of researchers. We also offer a set of reflections on the impact of these research-community partnerships.

math.HO↗

arXiv2025

Instruction Set Migration at Warehouse Scale

Migrating codebases from one instruction set architecture (ISA) to another is a major engineering challenge. A recent example is the adoption of Arm (in addition to x86) across the major Cloud hyperscalers. Yet, this problem has seen limited attention by the academic community. Most work has focused on static and dynamic binary translation, and the traditional conventional wisdom has been that this is the primary challenge. In this paper, we show that this is no longer the case. Modern ISA migrations can often build on a robust open-source ecosystem, making it possible to recompile all relevant software from scratch. This introduces a new and multifaceted set of challenges, which are different from binary translation. By analyzing a large-scale migration from x86 to Arm at Google, spanning almost 40,000 code commits, we derive a taxonomy of tasks involved in ISA migration. We show how Google automated many of the steps involved, and demonstrate how AI can play a major role in automatically addressing these tasks. We identify tasks that remain challenging and highlight research challenges that warrant further attention.

cs.SE↗

arXiv2023

Quantifying and Documenting Inequity in PhD-granting Mathematical Sciences Departments in the United States

We provide an example of the application of quantitative techniques, tools, and topics from mathematics and data science to analyze the mathematics community itself in order to quantify and document inequity in our discipline. This work is a contribution to the new and growing interdisciplinary field recently termed "mathematics of Mathematics," or "MetaMath." Using data about PhD-granting institutions in the United States and publicly available funding data from the National Science Foundation, we highlight inequalities in departments at U.S. institutions of higher education that produce PhDs in the mathematical sciences. Specifically, we determine that a small fraction of mathematical sciences departments receive a large majority of federal funding awarded to support mathematics in the United States. Additionally, we identify the extent to which women faculty members are underrepresented in mathematical sciences PhD-granting institutions in the United States. We also show that this underrepresentation of women faculty is even more pronounced in departments that received more federal grant funding.

math.HO↗

arXiv2023

The Mathematics of Mathematics: Using Mathematics and Data Science to Analyze the Mathematical Sciences Community and Enhance Social Justice

We present and discuss a curated selection of recent literature related to the application of quantitative techniques, tools, and topics from mathematics and data science that have been used to analyze the mathematical sciences community. We engage in this project with a focus on including research that highlights, documents, or quantifies (in)equities that exist in the mathematical sciences, specifically, and STEM (science, technology, engineering, and mathematics) more broadly. We seek to enhance social justice in the mathematics and data science communities by providing numerous examples of the ways in which the mathematical sciences fails to meet standards of equity, equal opportunity and inclusion. We introduce the term ``mathematics of Mathematics" for this project, explicitly building upon the growing, interdisciplinary field known as ``Science of Science" to interrogate, investigate, and identify the nature of the mathematical sciences itself. We aim to promote, provide, and posit sources of productive collaborations and we invite interested researchers to contribute to this developing body of work.

math.HO↗

arXiv2023

On definitions of "mathematician"

The definition of who is or what makes a ``mathematician" is an important and urgent issue to be addressed in the mathematics community. Too often, a narrower definition of who is considered a mathematician (and what is considered mathematics) is used to exclude people from the discipline -- both explicitly and implicitly. However, using a narrow definition of a mathematician allows us to examine and challenge systemic barriers that exist in certain spaces of the community. This paper explores and illuminates tensions between narrow and broad definitions and how they can be used to promote both inclusion and exclusion simultaneously. In this article, we present a framework of definitions based on identity, function, and qualification and exploring several different meanings of ``mathematician". By interrogating various definitions, we highlight their risks and opportunities, with an emphasis on implications for broadening and/or narrowing participation of underrepresented groups.

math.HO↗

arXiv2022

A unified approach to embeddings of a line in 3-space

While the general question of whether every closed embedding of an affine line in affine $3$-space can be rectified remains open, there have been several partial results proved by several different means. We provide a new approach, namely constructing (strongly) residual coordinates, that allows us to give new proofs of all known partial results, and in particular generalize the results of Bhatwadekar-Roy and Kuroda on embeddings of the form $(t^n,t^m,t^l+t)$.

math.AG↗

arXiv2019

Comparing demographics of signatories to public letters on diversity in the mathematical sciences

In its December 2019 edition, the \textit{Notices of the American Mathematical Society} published an essay critical of the use of diversity statements in academic hiring. The publication of this essay prompted many responses, including three public letters circulated within the mathematical sciences community. Each letter was signed by hundreds of people and was published online, also by the American Mathematical Society. We report on a study of the signatories' demographics, which we infer using a crowdsourcing approach. Letter A highlights diversity and social justice. The pool of signatories contains relatively more individuals inferred to be women and/or members of underrepresented ethnic groups. Moreover, this pool is diverse with respect to the levels of professional security and types of academic institutions represented. Letter B does not comment on diversity, but rather, asks for discussion and debate. This letter was signed by a strong majority of individuals inferred to be white men in professionally secure positions at highly research intensive universities. Letter C speaks out specifically against diversity statements, calling them "a mistake," and claiming that their usage during early stages of faculty hiring "diminishes mathematical achievement." Individuals who signed both Letters B and C, that is, signatories who both privilege debate and oppose diversity statements, are overwhelmingly inferred to be tenured white men at highly research intensive universities. Our empirical results are consistent with theories of power drawn from the social sciences.

math.HO↗

arXiv2018

An algorithmic approach to the Polydegree Conjecture for plane polynomial automorphisms

We study the interaction between two structures on the group of polynomial automorphisms of the affine plane: its structure as an amalgamated free product and as an infinite-dimensional algebraic variety. We introduce a new conjecture, and show how it implies the Polydegree Conjecture. As the new conjecture is an ideal membership question, this shows that the Polydegree Conjecture is algorithmically decidable. We further describe how this approach provides a unified and shorter method of recovering existing results of Edo and Furter.

math.AG↗

arXiv2017

Normal subgroups generated by a single polynomial automorphism

We study criteria for deciding when the normal subgroup generated by a single polynomial automorphism of $\mathbb{A}^n$ is as large as possible, namely equal to the normal closure of the special linear group in the special automorphism group. In particular, we investigate $m$-triangular automorphisms, i.e. those that can be expressed as a product of affine automorphisms and $m$ triangular automorphisms. Over a field of characteristic zero, we show that every nontrivial $4$-triangular special automorphism generates the entire normal closure of the special linear group in the special tame subgroup, for any dimension $n \geq 2$. This generalizes a result of Furter and Lamy in dimension 2.

math.AG↗

arXiv2017

Co-tame polynomial automorphisms

A polynomial automorphism of $\mathbb{A}^n$ over a field of characteristic zero is called co-tame if, together with the affine subgroup, it generates the entire tame subgroup. We prove some new classes of automorphisms, including $3$-triangular automorphisms, are co-tame. Of particular interest, if $n=3$, we show that the statement "Every $m$-triangular automorphism is either affine or co-tame" is true if and only if $m \leq 3$; this improves upon positive results of Bodnarchuk (for $m \leq 2$, in any dimension $n$) and negative results of the authors (for $m \geq 6$, $n=3$). The main technical tool we introduce is a class of maps we term 'translation degenerate automorphisms'; we show that all of these are co-tame, a result that may be of independent interest in the further study of co-tame automorphisms.

math.AG↗

arXiv2014

The affine automorphism group of A^3 is not a maximal subgroup of the tame automorphism group

We construct explicitly a family of proper subgroups of the tame automorphism group of affine three-space (in any characteristic) which are generated by the affine subgroup and a non-affine tame automorphism. One important corollary is the titular result that settles negatively the open question (in characteristic zero) of whether the affine subgroup is a maximal subgroup of the tame automorphism group. We also prove that all groups of this family have the structure of an amalgamated free product of the affine group and a finite group over their intersection.

math.AG↗

arXiv2013

Some Families of Polynomial Automorphisms III

We prove that the closure (for the Zariski topology) of the set of polynomial automorphisms of the complex affine plane whose polydegree is (cd-1,b,a) contains all triangular automorphisms of degree cd+a, where a,b >1 and c>0 are integers and d=ab-1. When b=2, this result gives a family of counterexamples to a conjecture of Furter.

math.AG↗

arXiv2013

Strongly residual coordinates over A[x]

For a domain A of characteristic zero, a polynomial f over A[x] is called a strongly residual coordinate if f becomes a coordinate (over A) upon going modulo x, and f becomes a coordinate upon inverting x. We study the question of when a strongly residual coordinate is a coordinate, a question closely related to the Dolgachev-Weisfeiler conjecture. It is known that all strongly residual coordinates are coordinates for n=2 . We show that a large class of strongly residual coordinates that are generated by elementaries upon inverting x are in fact coordinates for arbitrary n, with a stronger result in the n=3 case. As an application, we show that all Venereau-type polynomials are 1-stable coordinates.

math.AG↗

arXiv2010

Venereau-type polynomials as potential counterexamples

We study some properties of the Venereau polynomials b_m=y+x^m(xz+y(yu+z^2)), a sequence of proposed counterexamples to the Abhyankar-Sathaye embedding conjecture and the Dolgachev-Weisfeiler conjecture. It is well known that these are hyperplanes and residual coordinates, and for m at least 3, they are C[x]-coordinates. For m=1,2, it is only known that they are 1-stable C[x]-coordinates. We show that b_2 is in fact a C[x]-coordinate. We introduce the notion of Venereau-type polynomials, and show that these are all hyperplanes, and residual coordinates. We show that some of these Venereau-type polynomials are in fact C[x]-coordinates; the rest remain potential counterexamples to the embedding and other conjectures. For those that we show to be coordinates, we also show that any automorphism with one of them as a component is stably tame. The remainder are stably tame, 1-stable C[x]-coordinates.

math.AC↗