## Research

I study the distribution of algebraic numbers, mathematical statistical physics and roots/eigenvalues of random polynomials/matrices.

### Projects in Progress

1The distribution of values of the non-archimedean absolute Vandermonde determinant and the non-archimedean Selberg integral (with Jeff Vaaler). The Mellin transform of the distribution function of the non-archimedean absolute Vandermonde (on the ring of integers of a local field) is related to a non-archimedean analog of the Selberg/Mehta integral. A recursion for this integral allows us to find an analytic continuation to a rational function on a cylindrical Riemann surface. Information about the poles of this rational function allow us to draw conclusions about the range of values of the non-archimedean absolute Vandermonde.

2Non-archimedean electrostatics. The study of charged particles in a non-archimedean local field whose interaction energy is proportional to the log of the distance between particles, at fixed coldness $\beta$. The microcanonical, canonical and grand canonical ensembles are considered, and the partition function is related to the non-archimedean Selberg integral considered in 1. Probabilities of cylinder sets are explicitly computable in both the canonical and grand canonical ensembles.

3Adèlic electrostatics and global zeta functions (with Joe Webster). The non-archimedean Selberg integral/canonical partition function are examples of Igusa zeta functions, and as such local Euler factors in a global zeta function. This global zeta function (the exact definition of which is yet to be determined) is also the partition function for a canonical electrostatic ensemble defined on the adèles of a number field. The archimedean local factors relate to the ordinary Selberg integral, the Mehta integral, and the partition function for the complex asymmetric $\beta$ ensemble. The dream would be a functional equation for the global zeta function via Fourier analysis on the idèles, though any analytic continuation would tell us something about the distribution of energies in the adèlic ensemble.

4Pair correlation in circular ensembles when $\beta$ is an even square integer (with Nate Wells and Elisha Hulbert). This can be expressed in terms of a form in a grading of an exterior algebra, the coefficients of which are products of Vandermonde determinants in integers. Hopefully an understanding of the asymptotics of these coefficients will lead to scaling limits for the pair correlation function for an infinite family of coldnesses via hyperpfaffian/Berezin integral techniques. This would partially generalize the Pfaffian point process arising in COE and CSE. There is a lot of work to do, but there is hope.

5Martingales in the Weil height Banach space (with Nathan Hunter). Allcock and Vaaler produce a Banach space in which $\overline{\mathbb Q}^{\times}/\mathrm{Tor}$ embeds densely in a co-dimension 1 subspace, the (Banach space) norm of which extends the logarithmic Weil height. Field extensions of the maximal abelian extension of $\mathbb Q$ correspond to $\sigma$-algebras, and towers of fields to filtrations. Elements in the Banach space (including those from $\overline{\mathbb Q}^{\times}/\mathrm{Tor}$) represent random variables, and the set up is ready for someone to come along and use martingale techniques—including the optional stopping time theorem—to tell us something about algebraic numbers.

## Instruction

I have three current PhD students and one current departmental Honors student. I have supervised two completed PhDs and six completed honors theses. You can find a list of current and completed PhD and honors students on my CV.

My teaching load has been reduced for the last five years (or so) due to an FTE release for serving on the Executive Council of United Academics. As President of United Academics, and Immediate Past President of the University Senate I am not teaching in the 2018 academic year. In AY2019, I am scheduled to teach a two-quarter sequence on mathematical statistical physics.

I take my teaching seriously. I prepare detailed lecture notes for most courses (exceptions being introductory courses, where my notes are better characterized as well-organized outlines). When practical and appropriate I use active learning techniques, mostly through supervised group work. I am a tough, but fair grader.

## Service

Service encompasses pretty much everything that an academic does outside of teaching and research. This includes advising, serving on university and departmental committees, reviewing papers, writing letters of recommendation, organizing seminars and conferences, serving on professional boards, etc. The impossibility of doing it all allows academics to decide what types of service they are going specialize based on their interests and abilities.

I have spent the last three years heavily engaged in university level service. I currently serve as the president of United Academics of the University of Oregon, and I am the immediate-past president of the University Senate. Before that I was the Vice President of the Senate and the chair of the Committee on Committees. All of these roles are difficult and require a large investment of thought and energy. The reward for this hard work is a good understanding of how the university works, who to go to when issues need resolution, and who can be safely ignored.

I know what academic initiatives are underway, being involved in several of them. I am spearheading, with the new Core Education Council, the reform of general education at UO. I am working on the New Faculty Success Program—an onboarding program for new faculty—with the Office of the Provost and United Academics. I am currently on the Faculty Salary Equity Committee and its Executive Committee. I have been a bit player in many other projects and initiatives including student evaluation reform, the re-envisioning of the undergraduate multicultural requirement, and the creation of an expedited tenure process to allow the institution alacrity when recruiting imminent scholars. This list is incomplete.

Next year, with high probability, I will be the chair of the bargaining committee for the next collective bargaining agreement between United Academics and the University of Oregon (this assumes I am elected UA president). I will also be working with the Core Ed Council to potentially redefine the BA/BS distinction, with a personal focus on ensuring quantitative/data/information literacy is distributed throughout our undergraduate curriculum. I will also be working to help pilot (and hopefully scale) the Core Ed “Runways” (themed, cohorted clusters of gen ed courses) with the aspirational goal of having 100% of traditional undergraduates in a high-support, high-engagement, uniquely-Oregon first-year experience within the next 3-5 years.

As important as the service I am doing, is the service I am not doing. I do little to no departmental service (though part of this derives from the CAS dean’s interpretation of the CBA) and I avoid non-required departmental functions (for reasons). I do routinely serve on academic committees for graduate/honors students, etc. I decline most requests to referee papers/grants applications, and serve on no editorial boards. The national organizations for which I am an officer are not mathematical organizations, but rather organizations dedicated to shared governance.

## Diversity & Equity

The two principles which drive my professional work are truth and fairness.

I remember after a particularly troubling departmental vote, a senior colleague attempted to assuage my anger at the department by explaining that “the world is not fair.” I hate this argument because it removes responsibility from those participating in such decisions, and places blame instead on a stochastic universe. And, while there is stochasticity in the universe, we should be working toward ameliorating inequities caused by chance, and in instances where we have agency, making decisions which do not compound them.

I do not think the department does a very good job at recognizing nor ameliorating inequities. Indeed, there are individuals, policies and procedures that negatively impact diversity. See my recent post Women & Men in Mathematics for examples.

My work on diversity and equity issues has been primarily through the University Senate and United Academics. As Vice-president of the UO Senate, I sat on the committee which vetted the Diversity Action Plans of academic units. I also worked on, or presided over several motions put forth by the University Senate which address equity, diversity and inclusion. Obviously, the work of the Senate involves many people, and in many instances I played only a bit part, but nonetheless I am proud to have supported/negotiated/presided over the following motions which have addressed diversity and equity issues on campus:

Besides my work with the Senate, I have also participated in diversity activities through my role(s) with United Academics of the University of Oregon. United Academics supports both a Faculty of Color and LGBTQ* Caucus which help identify barriers and propose solutions to problems affecting those communities on campus. United Academics bargained a tenure-track faculty equity study, and I am currently serving on a university committee identifying salary inequities based on protected class and proposing remedies for them.

I have attended in innumerable rallies supporting social justice, and marched in countless marches. I flew to Washington D.C. to attend the March for Science. I’ve participated in workshops and trainings on diversity provided by the American Federation of Teachers, and the American Association of University Professors.

I recognize that I am not perfect. I cannot represent all communities nor emulate the diversity of thought on campus. I have occasionally used out-moded words and am generally terrible at using preferred pronouns (though I try). I recognize my short-comings and continually work to address them.

There are different tactics for turning advocacy into action, and individuals may disagree on their appropriateness and if/when escalation is called for. My general outlook is to work within a system to address inequities until it becomes clear that change is impossible from within. In such instances, if the moral imperative for change is sufficient then I work for change from without. This is my current strategy when tackling departmental diversity issues; I work with administrative units, the Senate and the union to put forth/support policies which minimize bias, discrimination and caprice in departmental decisions. I ensure that appropriate administrators know when I feel the department has fallen down on our institutional commitment to diversity, and I report incidents of bias, discrimination and harassment to the appropriate institutional offices (subject to the policy on Student Directed Reporters).

Fairness is as important to me as truth, and I look forward to the day where I can focus more of my time uncovering the latter instead of continually battling for the former.

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## Diversity and Equity

Notice

This post is part of my post-tenure review. If it seems self-serving, that is because it is.

The two principles which drive my professional work are truth and fairness.

I remember after a particularly troubling departmental vote, a senior colleague attempted to assuage my anger at the department by explaining that “the world is not fair.” I hate this argument because it removes responsibility from those participating in such decisions, and places blame instead on a stochastic universe. And, while there is stochasticity in the universe, we should be working toward ameliorating inequities caused by chance, and in instances where we have agency, making decisions which do not compound them.

I do not think the department does a very good job at recognizing nor ameliorating inequities. Indeed, there are individuals, policies and procedures that negatively impact diversity. See my recent post Women & Men in Mathematics for examples.

My work on diversity and equity issues has been primarily through the University Senate and United Academics. As Vice-president of the UO Senate, I sat on the committee which vetted the Diversity Action Plans of academic units. I also worked on, or presided over several motions put forth by the University Senate which address equity, diversity and inclusion. Obviously, the work of the Senate involves many people, and in many instances I played only a bit part, but nonetheless I am proud to have supported/negotiated/presided over the following motions which have addressed diversity and equity issues on campus:

Besides my work with the Senate, I have also participated in diversity activities through my role(s) with United Academics of the University of Oregon. United Academics supports both a Faculty of Color and LGBTQ* Caucus which help identify barriers and propose solutions to problems affecting those communities on campus. United Academics bargained a tenure-track faculty equity study, and I am currently serving on a university committee identifying salary inequities based on protected class and proposing remedies for them.

I have attended in innumerable rallies supporting social justice, and marched in countless marches. I flew to Washington D.C. to attend the March for Science. I’ve participated in workshops and trainings on diversity provided by the American Federation of Teachers, and the American Association of University Professors.

I recognize that I am not perfect. I cannot represent all communities nor emulate the diversity of thought on campus. I have occasionally used out-moded words and am generally terrible at using preferred pronouns (though I try). I recognize my short-comings and continually work to address them.

There are different tactics for turning advocacy into action, and individuals may disagree on their appropriateness and if/when escalation is called for. My general outlook is to work within a system to address inequities until it becomes clear that change is impossible from within. In such instances, if the moral imperative for change is sufficient then I work for change from without. This is my current strategy when tackling departmental diversity issues; I work with administrative units, the Senate and the union to put forth/support policies which minimize bias, discrimination and caprice in departmental decisions. I ensure that appropriate administrators know when I feel the department has fallen down on our institutional commitment to diversity, and I report incidents of bias, discrimination and harassment to the appropriate institutional offices (subject to the policy on Student Directed Reporters).

Fairness is as important to me as truth, and I look forward to the day where I can focus more of my time uncovering the latter instead of continually battling for the former.

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## Post-tenure Reviews

As I wrote in Women & Men in Mathematics, tenure is a platform to change the world. I encourage all newly-tenured individuals to pause and reflect on what is important to them—to take a break from the academic conveyer belt, assess their skills and passions, and determine for themselves how best to change the world.

For many, this will involve a short pause to recoup from the trauma of hoop-jumping, before hopping back on the academic conveyer. Others may reflect and decide that their passion lies in one of the other official job-duties of tenured professors: teaching and service. Still others may decide to jump fields, angle for an administrative position or use their accumulated academic and political capital to work on social issues. Academics are legion, and there are lots of ways to change the world!

Post-tenure reviews work great for those happy to hop back on the academic conveyer belt, and those whose passion truly lies in their scholarship. But what is their use for individuals who want to reinvent themselves? How do we reconcile the narrow standards put forward by department heads and associate deans, with the lofty dreams and ideals of those who have moved beyond them? How does a university harness the passion and energy of these diverted academics without relegating them to the insulting, false category of dead wood?

I do not have an answer for these questions, except to say that the answer does not lie a hastily written summary of activity ending in the words Meets Expectations, Exceeds Expectations or the dreaded Does Not Meet Expectations.

The diverted academic has transcended your expectations, and any assessment based on narrow, metrics-driven criteria is more apt to drive them farther from the academic milieu than bring them back to the fold.

One possible path forward is to use a post-tenure review to identify all faculty activities that support the university mission (hint: that’s most of them) and to determine what resources are available to support that work.

Occasionally, though I suspect much less frequently than associate deans would have you believe, individuals are not fulfilling the required parts of the job. Independent of their dreams and ideals, most tenured faculty still have to teach and sit on committees. This is real work, and it should be done well. For those individuals falling down on this portion of their job, a suggested course correction is necessary and appropriate.

I understand the motivation for post-tenure reviews. I just wish they reflected the diversity of opinions on what it means to be an academic in the modern age. Instead, as currently envisioned, they drive us to the least-common-denominator of expectations as pushed by metrics-chasing administrators more worried about rankings than actually changing the world for good.

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## Women & Men in Mathematics

Mathematics has a diversity problem. This problem is far larger than just one of gender representation, but let’s start the conversation there. Only two of the thirty-five tenure-track professors in the Department of Mathematics at the University of Oregon are women. This is not an accident—the structure of the department, those empowered to make decisions, cultural factors (both as a discipline and the backgrounds of our faculty) and out-moded ideas of social gender roles have made our department the image of one from the 1960s (or earlier)!

I have heard tales of women students being told by male UO math professors that they were “good at math, for a girl”. Graduate students often ask faculty for advice, but the advice that “women should not have children during graduate school” is neither appropriate, welcoming, nor welcome. Off-hand musings that “the department was better when the wives [of faculty] organized and hosted social events” while questionably appropriate in 1960, are grossly inappropriate now. These are not hypothetical utterances—all have been said by UO math professors out loud, and in the presence of students.

Policies dictating the matriculation of graduate students through our program have been waived for male students—allowing them to continue unimpeded, having benefited from violating policy—while women in similar situations are summarily dismissed from the program in spite of comparable academic performance, and in spite of them following our policies to the letter. These decisions have been upheld by departmental leadership, even after the obvious structural bias has been pointed out.

In recent years, when reporting incidents of bias to departmental leadership—ostensibly empowered to uphold the institutional commitment to diversity—I have often been asked to ‘tone down’ my rhetoric, and steered toward the word ‘bias’ and away from ‘harassment’ or ‘discrimination.’ There are, apparently, different standards for reporting bias and discrimination, and it was more important to protect faculty from diversity trainings (which was explained to me by the same administrator as a waste of time and incapable of changing behavior) than to attempt to address the problem head-on. I have no doubt that the incidents I brought forward were not reported by those administrators to the appropriate offices on campus, though on several occasions I reported the incidents directly myself.

In faculty searches, committees routinely produce short-lists of candidates for interviews which are less diverse than the pools of applicants. Imagine a pool of 750 applicants (the approximate number we get for any tenure-track search) being winnowed down to 25—only three of which are women. (To be fair, faculty do not have easy access to demographics of individual applicants, so my assessment of these numbers is based on names and pronouns in application materials—not a good way to make such determinations but the best I can do with the information provided me).

If the department wanted to, out of 750 candidates for tenure-track positions, it could easily put forth 25 excellent woman for consideration. But the department does not want to. Indeed, it doesn’t even feel compelled to match the diversity of the candidate pools.

I should be clear, not everyone in the department (or the field) is a problem in this regard. There are excellent, inclusive, well-meaning individuals in the department who are supportive of all of our students and colleagues. There are individuals in the department who are working hard on initiatives that support diversity and students/colleagues from different backgrounds. The department has funded, and continues to support a local chapter of the Association of Women in Mathematics. Our graduate students by-and-large, are thoroughly modern when it comes to diversity and engage in more diversity work in total than our tenure-track faculty. To all those individuals, I say “Thank you”.

The problem is cultural. There is an ethos in mathematics that puts disproportionate weight on the opinions of those that are good at math. Somehow the expectation is that mathematical production is connected to good decision-making. It is not. All mathematicians have at least one bad decision in common, and alacrity in mathematical thinking does not translate to good decision-making on topics that involve tricky, non-idealized social considerations.

When it comes to diversity, the decorated but old-fashioned, stodgy and biased full professor should not be listened to disproportionately, or even at all. Tenure protects the opinions of those individuals, but we do not have to listen to them. Nor should we. Let’s hound them ceaselessly until they relent or we drive them to the dust bin of history.

Tenure is a platform from which to change the world. It is a privileged position that allows people to make unpopular or controversial statements. In a way, it’s an amped-up First Amendment that protects faculty not only from government interference in their speech, but also protects them from university interference in their speech. However, like the First Amendment, tenure does not protect professors from public outrage, nor does it keep the rest of the academic (and general) community from pointing out obvious moral failings in their arguments. If tenure is to survive in the modern academic world, then it is incumbent on us to ensure that those with the privilege are using it to change the world for good. We do this by loudly and vociferously speaking out against those holding us back from an excellent, diverse faculty representing the backgrounds and interests of our students.

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