### 2017 – 2018

This year 18 seniors graduated with a major in statistics and 75 graduated with a major in mathematics, making it a record-breaking year for the number of math majors. We are currently located in Bascom House, our temporary home, and we are looking forward to moving into our new building in early 2021.

Two of our Math/Stat faculty members are leaving Williams. Brianna Heggeseth, assistant professor of statistics at Williams since 2013, accepted a position at Macalester College. Cory Colbert, a Gaius C. Bolin Fellow in Math/Stat for the last two years, accepted an assistant professor position at Washington and Lee University. We will miss both of them, and we wish them the best! We hired two new statisticians who will be joining us this fall: Xizhen Cai, a Postdoctoral Fellow Research Associate at Temple University for the last two years, and Anna Plantinga, who earned her Ph.D. in 2018 from the University of Washington.

Three faculty, Andrew Bydlon, Haydee Lindo ’08 and Chad Topaz all completed their first year as a professor at Williams. We were thrilled to have hired them last year! We celebrated many faculty accomplishments over the year, including: Steve Miller was promoted to full professor, Lori Pedersen’s contract was renewed, Mihai Stoiciu won the Northeastern Section of the Mathematical Association of America’s 2018 award for Distinguished College or University Teaching, and Dick De Veaux was elected Vice President of the American Statistical Association.

Professors Dick De Veaux, Leo Goldmakher (fall), and Allison Pacelli (spring) were on leave for 2017-2018. Professors Bernhard Klingenberg, Allison Pacelli (fall), and Mihai Stoiciu will be on leave in 2018-2019.

We are very proud of the accomplishments of our majors: Rosenberg prize for outstanding senior: Sumun Iyer ’18, Arjun Kakkar ‘18, and Daishiro Nishida ‘18; Goldberg award for outstanding colloquium: Chris D’Silva ’18 for math and Yolanda Zhao ’18 for stat; Wyskiel award for teaching: Ned Lauber ’18; Morgan prize in applied math: Daniel Maes ’18; Kozelka award for outstanding student in statistics: Anna Neufeld ’18 and Hallee Wong ‘18; Beaver prize for service to the department and math/stat community: Isabella Huang ’18; Benedict prize for outstanding sophomore: Michael Curran ‘20 and Alessandra Miranda ’20 (first prize) and Xiwei Yang ’20 and Teresa Yu ‘20 (second prize); Witte problem solving prize: Minh Tuan Tran ’19; Colloquium attendance prize: Isabella Huang ’18 for math and Daniel Maes ’18 for stat.

Three of our seniors won Fulbright Scholarships: Molly Knoedler ’18, Nohemi Sepulveda ’18, and Darla Torres ’18. Sumun Iyer ’18 was awarded a National Science Foundation Graduate Research Fellowship, and Sarah Fleming ’18 received an honorable mention for the national Alice T. Schafer award, given by the Association for Women in Mathematics. The 40th Green Chicken contest, a problem-solving exam between Williams and Middlebury students was held at Middlebury in October. The Williams team successfully defended their title. The top five scorers for Williams were Ian Banta ’19, Michael Curran ’20, Markus Feng ‘21, Will Howie ‘20, and Richard Wu ’21. In December, fifteen Williams students took the notoriously difficult national Putnam exam. Williams’ top scorers were Daishiro Nishida ’18, Minh Tuan Tran ’19, Hunter Wieman ’20 and Richard Wu ’21 who all placed in the top 500.

Finally, we thank the members of our student advisory board, SMASAB, who organized many Math/Stat events including ice cream socials, Math/Stat snacks, and dinners for job candidates: Isabella Huang ’18, Ned Lauber ’18, Austin Vo ’18, Yolanda Zhao ’18, Anya Michaelsen ’19, Grace Mabie ’19, Izzy Ahn ’19, Eli Cytrynbaum ’20, Alessandra Miranda ’20, and Sofie Netteberg ‘20.

In summer 2017, Professor Colin Adams worked with six students as part of the SMALL Summer Research Project on hyperbolic knots. They traveled to Chicago in August for Mathfest, where the students gave talks and produced a paper on “Hyperbolicity of Knots and Links in Thickened Surfaces.” Over the academic year, he gave a variety of talks at conferences and schools, including research talks, expository talks and even a talk on knots and dance. He submitted a variety of papers, including research papers, expository papers and even a story imagining what would happen if Donald Trump was the president of the American Mathematical Society. Adams advised a thesis by Daishiro Nishida 18, who generalized classical braid theory to multi-crossing braids.

Over the past year, Assistant Professor Julie Blackwood has continued several ongoing projects in mathematical ecology. For example, she continues to work on mathematical models that describe the dynamics of periodical cicadas to better understand their synchronous behavior. She also continues to work on modeling the dynamics of infectious diseases, exploring questions related to identifying the drivers of spatiotemporal patterns of epidemics. Several Williams students have worked with her this past year, including thesis students Molly Knoelder ’18 and Jackson Barber ’18. Several papers have also been published that have student co-authors (A Neufeld ’18, E Matt ’18, A Meyer ’16, and R Vargas Jr ’16).

Professor Dick De Veaux continued his work in data mining, writing textbooks and gave a variety of keynote addresses, talks and workshops on teaching and data mining throughout the world. He finished his term as Chair of the section on Statistical Learning and Data Science of the American Statistical Association, but was elected Vice President of the American Statistical Association for the term 2019-2021. He served as tutorial chair for the IEEE Data Science conference (IEEE DSAA) in Turin Italy (Oct 2018) and was appointed program chair of the 2019 conference in Washington D.C. In June 2018 he was a Summer at Census fellow at the U.S. Census.

Professor Tom Garrity has continued his research in number theory. His paper “Generalizing the Minkowski Question Mark Function to a Family of Multidimensional Continued Fractions,” written with Peter McDonald ’16, has been accepted for publication in The International Journal of Number Theory.

In June of 2017, he gave an invited talk at Project Dyna3S, Université Caen, titled “On Transfer Operators for Triangle Partition Maps.” Also in June, he spoke “On a Thermodynamic Classification for Real Numbers,” in the Automata Seminar at the Institut de Recherche en Informatique Fondamentale (IRIF), Université Paris-Diderot. In July of 2017, he gave a talk on Mathematical Maturity at the Park City Mathematics Institute. In September, 2017, he gave the Martha Davenport Heard Lecture at Wellesley College. In November, 2017, he gave the Keynote Lecture at the Mathematics Conference and Competition of Northern New York (MCCNNY), Clarkson University.

Assistant Professor Leo Goldmakher continued his research in number theory and additive combinatorics, spending the Fall semester on sabbatical and returning to teaching during the Spring. During the course of the year he had four papers accepted for publication (one written jointly with Elijah Fromm ’17, now a math Ph.D. student at Yale.) In the Spring semester he taught a course on Galois theory and a tutorial on analytic number theory, and also gave the Spring 2018 Sigma Xi lectures.

Professor Goldmakher also gave invited talks at the Heilbronn Institute/University of Bristol (UK), TU Graz (Austria), Tufts (MA), University of Michigan-Ann Arbor (MI), Rice (TX), and Yale (CT). He also delivered a talk to the Yale Math Society, an undergraduate organization. Finally, he gave two invited talks at conferences: one at the Mathematical Congress of the Americas (in Montreal, QC, Canada) and the other at Canadian Math Society Summer Meeting (in Fredericton, NB, Canada).

Assistant Professor Pamela E. Harris developed two new courses for the Mathematics and Statistics Department: MA328 Combinatorics and MA392T Undergraduate Research Topics in Graph Theory. In honor of her continued mentoring activities at Williams College, Professor Harris was selected as the Outstanding Mentor of 2018 by the Davis Center.

Professor Harris continued her work in algebraic combinatorics focusing on problems at the intersection of the representation theory of Lie algebras and combinatorics. Of note is her new article co-authored with Erik Insko and Mohammed Omar, which answers a very natural question regarding the number of ways to express the highest root of a classical Lie algebra as a sum of the positive roots. The article “The q-analog of Kostant’s partition function and the highest root of the simple Lie algebras” appeared in the Australasian Journal of Combinatorics Volume 71(1) (2018) 68–91. This is one of 7 accepted papers this academic year.

Professor Harris was awarded six grants or travel awards this year. This was also the second year of support under the National Science Foundation (award DMS-1620202). Professor Harris presented 23 lectures, 21 of which were invited lectures, including an international invitation to present her research in Quito, Ecuador. In addition, Professor Harris attended 8 conferences, including trips to England, Ecuador, and Mexico.

Professor Harris is highly committed to fostering the success of underrepresented scientists and to improving diversity and retention rates among women and minorities in the mathematical sciences. To do so Professor Harris is highly involved with the Society for the Advancement of Chicanos/Hispanics and Native Americans in Science (SACNAS) and organizes multiple scientific symposia and professional development sessions at the society’s annual national conference. This year, in collaboration with Alexander Diaz-Lopez, Alicia Prieto-Langarica and Gabriel Sosa, Professor Harris secured grant funding to support the website www.lathisms.org whose mission is to provide an accessible platform that features prominently the extent of the research and mentoring contributions of Latin@ s and Hispanics in different areas of the Mathematical Sciences.

Lastly Professor Harris and her work has been featured in

• Vanguard STEM feature for women of color in STEM, June 27, 2017.

• Association for Women in Mathematics ADVANCE website on Women do Math.

• London Mathematical Society Success Stories project celebrates the diversity of successful careers and mathematicians: https://www.lms.ac.uk/content/pamela-e-harris

• Featured mathematician in “Power in Numbers: The Rebel Women of Mathematics” by Talithia Williams

Assistant Professor Brianna Heggeseth enthusiastically returned from sabbatical to teach Introduction to Statistics and Data Analysis, one of the core upper level courses called Regression and Forecasting, and a senior seminar called Data Mining and Computational Statistics that covered the methods, use, and ethics of modern statistical learning algorithms.

In her research, she submitted two methodological papers for review as well as co-authored collaborative papers. Additionally, she had two thesis students, Hallee Wong ‘18 and Anna Neufeld ‘18. Hallee’s work focused on methodological development for predicting 30-day hospital readmissions and Anna studied, implemented, and compared methods for fitting regression trees to longitudinal data. The review of the literature will be written as a review paper and her code will be developed into a publicly available R package with an accompanying paper. Dr. Heggeseth presented their work at an invited session at the ENAR Biometrics 2018 conference and will be presenting it at the Joint Statistical Meetings 2018.

Additionally, Dr. Heggeseth acted as a statistical consultant and then collaborator on a project of implicit and explicit bias with a colleague in the psychology department and a project of timing of cricket mating with a colleague in the biology department.

She left Williams at the end of the academic year to take a position at Macalester College in the Department of Mathematics, Statistics, and Computer Science.

Professor Stewart Johnson remains active in dynamical systems, focusing on massively parallel computing methods for scientific modeling. He is developing tools for assessing chaotic attractors in high dimensional spatial systems, and adapting classic methodologies to better understand how the spatial component of these dynamics impact our notions of chaos and predictability. This basic research furthers our understanding of spatially organized systems such as systems of neurons, grain boundaries in crystal formation, and cellular tissue growth.

Prof. Johnson supervised a senior thesis by Cody Cao ‘18, where he studied the spatial implementation of the replicator equation from evolutionary dynamics, using highly parallel computation to establish the direction and properties of travelling waves, extending the ground-breaking work of Hudson, Vickers, and Cressman to higher dimensional models.

Professor Bernhard Klingenberg published a couple of papers in collaboration with scientists in medicine and biology and provided statistical consulting to faculty and students at Williams on a variety of projects. He also programmed new web apps published on his website ArtofStats.com that help students understand statistical concepts and carry out data analysis in the cloud. In March, he presented some of these at the Conference on Technology in Collegiate Mathematics. At the department, Prof. Klingenberg served as associate chair of statistics. He also continued as associate editor for the Journal of Statistical Modelling.

Professor Susan Loepp completed her second year of a three-year term as chair of Math/Stat. In addition to her chair duties, she enjoyed teaching and her research in commutative algebra. She helped organize the first commutative algebra seminar at Williams which met every two weeks. Four faculty and five students participated. She especially enjoyed her research collaborations with her three thesis students, Sarah Fleming ’18, Alex Semendinger ’18, and Weitao Zhu ’18.

In summer 2017, Loepp advised the Commutative Algebra research group as part of the department’s SMALL program. The group included the two Williams students Timothy Kostolansky ’18, and Alex Semendinger ’18. A paper based on the group’s original results has been submitted to a refereed research journal to be considered for publication. Loepp gave a talk in April at an American Mathematical Society Sectional Meeting based on the results in the paper.

In January, Loepp attended the Joint Mathematics Meetings in San Diego. She is serving in her second 5-year term as an associate editor for the Mathematical Monthly, and she continues to serve on committees for the American Mathematical Society, and the Mathematical Association of America.

Professor Steven Miller is on year two of a three year individual NSF grant to continue his investigations in number theory and probability (he is also a co-PI on three grants to support the 32nd Automorphic Forms Workshop, which ran from March 18th to 22nd at Tufts), and served as co-Director of the Williams SMALL REU (as well as being co-PI on a successful three-year renewal grant for the program from NSF). He and his students published 20 papers and gave 38 talks (thesis students: Hallee Wong ‘18 (health care), Alyssa Epstein ‘18 (game theory; research students (academic year): Bryan Woolley, George Carroll, William Gearson, Charles Ide, Jay Habib ‘18; summer students (mentored with Ezra Waxman, visiting graduate student): Alexandre Gueganic, Alina Shubina ‘19, Eric Winsor, Granger Carty, Jared Lichtman, Jianing Yang, Ryan Chen, Shannon Sweitzer, Yujin Kim). He has continued his mathematical outreach activities, ranging from his successful math riddles page (http://mathriddles.williams.edu/), which is used in schools around the world, to writing computational modules for high school classes, to giving continuing education lectures to junior high and high school teachers, to writing a textbook/study guide on Operations Research, and to working with many math camps. With Mihai Stoiciu he ran math puzzle night and continued our streak of over 1% campus participation on the Putnam exam. He also expanded his involvement in using online resources in teaching; all of his course lectures are available online through YouTube, as are many of his talks. In addition to giving many math talks at Williamstown Elementary School, he is the faculty advisor to the Rubik’s Cube Club at Mt. Greylock Regional High School, where he serves as an elected school committee member. He serves on many editorial boards (Managing Editor of the Journal of Number Theory, Editor of the Notices of the American Mathematical Society, Problem Editor of the Pi Mu Epsilon Journal, Member (and then chair) of the Arnold Ross Lecture Series Committee, Member of the Fibonacci Association Board, AMSTEXT Editorial Committee, and the Carus Editorial Committee). He is also a mentor for the Math Alliance, and a Senator-at-Large for Phi Beta Kappa (and faculty president of Williams Chapter).

Professor Frank Morgan spent his second year of retirement as Editor-in-Chief of the Notices of the American Mathematical Society, the largest publication in higher mathematics. His travels included trekking in Nepal, with views of Mt. Everest.

Assistant Professor Ralph Morrison completed his second year at Williams College. He continued his research on tropical, algebraic, and discrete geometry. He was a guest at the Mittag-Leffler Institute for their program on Tropical Geometry, Amoebas, and Polytopes in January and February 2018, where he presented on his research. He attended and presented at the 2017 SIAM Conference on Applied Algebraic Geometry, the 2018 Joint Mathematics Meetings, and the 2018 AMS Spring Central Sectional Meeting. He led a research group in tropical geometry in the department’s summer SMALL REU in both 2017 and 2018, working with nine undergraduates on embedded and abstract tropical geometry, including Williams students Andrew Scharf ‘18, Franny Dean ‘19, Sammy Rosofsky ‘19, and Teresa Yu ‘20. He took both groups to conferences to present on their work: in 2017, to the Young Mathematicians’ Conference, and in 2018, to the MAA’s Mathfest conference. He advised two senior honors theses in mathematics: Higher distance commuting matrices by Madeleine Elyze ‘18 and Intersections of tropical surfaces by Andrew Scharf ‘18. He taught two sections of Discrete Mathematics (Math 200) in the fall, and introduced two new upper level courses in the spring: a senior seminar on Tropical Geometry (Math 474), and a tutorial on Discrete Geometry (Math 329T).

Professor Allison Pacelli continued her work in algebraic number theory, including a project with a student about the geometry of modular arithmetic. She also supervised Ned Lauber’s ‘18 thesis in math education about effective teaching methods. Pacelli is on sabbatical during 2018.

Professor Cesar Silva started the summer of 2017 by teaching in the Summer Science Program. In fall 2017, Silva taught Real Analysis (Math 350) and Measure and Ergodic Theory (Math 403). In spring 2018, he also taught Real Analysis (Math 350) and then Chaos and Fractals (Math 306). During the academic year, Silva had two thesis students, Beatrix Haddock ‘18 and Sumun Iyer ’18, who worked in ergodic theory. During January of 2018 he taught a travel Winter Study course in photography, in collaboration with Richard Washburne. He and his students travelled to the cities of Lima and Cuzco, and visited Machu Picchu, in Peru.

His professional activities included participating in a National Science Foundation panel, and being an associate editor for Notices, a monthly publication of the American Mathematical Society. He also published four papers, three of them with his former students. He attended a group research meeting at American Mathematics Institute, in San Jose, California, in November, 2017.

Together with his colleagues Colin Adams and Frank Morgan, Silva organized a Special Session at the annual meeting of the American Mathematical Society in San Diego, California, that took place on January 13, 2018. This was on the occasion of the 30th anniversary of the SMALL Undergraduate Research Program.

Professor Mihai Stoiciu taught “Foundations in Quantitative Skills” and two sections of “Applied Real Analysis” during the Fall Semester and “Calculus II” during the Spring Semester of the Academic Year 2017 – 2018. He also supervised the undergraduate thesis of Eliza Matt ‘18 and an independent study course on “Stochastic Calculus”, taken by William Chen ‘19. During the year, Stoiciu continued his research on spectral properties of random and deterministic operators and was invited to present his work and at the conference “NEAM 2017: Second Northeastern Analysis Meeting”, hosted by University at Albany in Albany, NY and at the AMS Special Session on “Spectral Theory”, hosted by Portland State University in Portland, OR.

During June-July 2017, Stoiciu participated in IAS-PCMI Summer School on the topic “Random Matrices”. There he taught a three-week course for advanced undergraduate students titled “Introduction to Random Matrix Theory”. At Williams College Stoiciu advised four students in the SMALL Undergraduate Research Program, who worked on several projects in Random Matrix Theory. He gave a seminar at Williams College in August 2018, where he presented their summer research.

During the academic year, Stoiciu served as a member of the LACOL (Liberal Arts Consortium for Online Learning) Faculty Advisory Council and worked on LACOL projects in Quantitative Skills. He represented Williams College at the 2018 LACOL Workshop, hosted by Carleton College, where he gave a presentation on the tutorial course on Numerical Analysis he developed at Williams.

Professor Chad Topaz greatly enjoyed his first year at Williams College! In the fall, he developed new courses in Computational Linear Algebra (Math 307) and in Applied Partial Differential Equations (Math 453), and in the spring, taught Discrete Mathematics (Math 200). He was privileged to advise two students on research, namely Daniel Maes ’18 who built Markov chain models of the college admissions pipeline in order to assess “critical mass” in affirmative action, and Arjun Kakkar ’18 who used nonlocal energy balance models to study vegetation pattern formation.

Professor Topaz submitted and was awarded a three-year National Science Foundation research grant on “Variational and topological approaches to complex dynamical systems” to support his research. This past year, he worked on three manuscripts, including one he submitted that stems from a collaborative data science project he launched to measure the diversity of artists in major U.S. museums. Speaking of collaboration, he co-organized an American Mathematical Society Mathematics Research Community which facilitated research groups for Ph.D. students and postdocs, and he began co-organizing a workshop on topological data analysis to take place in 2019 at the ICERM math institute. Active within his professional organizations, he was appointed to the editorial board of the SIAM Journal on Applied Dynamical Systems and invited to be a plenary speaker at the 2019 SIAM Conference on Applications of Dynamical Systems.

Assistant Professor Laurie Tupper continued her research in classification, similarity, and clustering approaches to complex data, and the effects of using different structures (spatial, temporal, spatio-temporal, high-dimensional) to represent such data. She submitted an NIH Small Business Innovation Research grant application with academic and industry collaborators, for work on distinguishing mammalian cell types using electrical behavior. She also continues to work with wind and climate applications, including presenting an invited poster at the IMA Workshop on Frontiers in Forecasting and four current projects with summer research students (Youngsoo Baek ’19, Alessandra Miranda ’20, Eric Rosenthal ’19, and Daniel Woldegiorgis ’20). She developed a new course on Design of Experiments in the fall, incorporating both classical and modern optimal-design methods, and taught Regression and Forecasting and two sections of Statistics and Data Analysis.

Assistant Professor Daniel Turek completed his second year at Williams. He continued his theoretical work in the area of computational statistical algorithms in which he developed highly efficient implementations of existing statistical methodology, or variations and hybrids of existing algorithms with the goal of improving computational performance. In addition, he continued his role as an active core developer of NIMBLE, an open-source statistical software project. The book “The Practice of Reproducible Research,” co-edited by Turek, was published by University of California Press in 2017.

Turek enjoyed advising the research of Daniel Maes ’18 during the summer of 2017. His research project was titled “Optimal Investment Strategies for Leveraged Exchange-Traded Funds,” where he analyzed statistical models for a variety of leveraged financial assets, and what properties of these assets led to profitable trading strategies.