### 2016 – 2017

This year 29 seniors graduated with a major in statistics and 71 graduated with a major in mathematics, making it a record-breaking year for both majors. We continue to see a large number of majors in the department with 79 rising seniors who have declared a math major and 17 rising seniors who have declared a statistics major. In summer 2017, Math/Stat moved into Bascom House, where we will be until we move into the newly constructed building in 2020.

We have three outstanding visiting professors who are leaving this year: *Diana Davis ’07*, Alejandro Sarria, and Peyam Tabrizian. We hired two new mathematicians who will be joining us this fall: *Haydee Lindo ’08*, a commutative algebraist who has been a Bolin Fellow in our department for the last two years, and Chad Topaz, an applied mathematician who has spent the last ten years on the faculty at Macalester College.

Four new assistant professors did a great job in their first year at Williams: Pamela Harris and *Ralph Morrison ‘10* in Math and Laurie Tupper and Daniel Turek in Stats. Leo Goldmakher was reappointed, Mihai Stoiciu has been promoted to full professor, and Lori Pedersen, who has been a visiting faculty member for several of the past few years, is now a regular faculty member in our department.

Professors Colin Adams, Julie Blackwood, Tom Garrity, Leo Goldmakher (spring), Brianna Heggeseth, and Cesar Silva (spring) were on leave in 2016-2017. Professors Dick De Veaux, Leo Goldmakher (fall), and Allison Pacelli (spring) will be on leave for 2017-2018.

We are very proud of the accomplishments of our majors: Rosenburg prize for outstanding senior: *David Burt ’17*; Goldberg award for outstanding colloquium: *Connor Mulhall ’17* for stats and *Molly Siebecker ’17* for math; Wyskiel award for teaching: *Si Young Mah ’17*; Morgan prize in applied math: *Anand Hemmady ’17* and *Intekhab Hossain ’17*; Kozelka award for outstanding student in statistics: *Hae-Min Jung ’17*; Beaver prize for service to the department and math/stat community: *Nina Pande ’17* and *Troy Sipprelle ’17*; Benedict prize for outstanding sophomore: *Anya Michaelsen ’19* (first prize) and *Anthony Simpson ’19* (second prize); Witte problem solving prize: *Elijah Fromm ’17*; Colloquium attendance prize: *David Burt ’17* for math and *Dongheon Lee ’17* for stat.

Seven of our seniors won Herchel Smith Fellowships: *Megumi Asada ’17, Osama Brosh ’17, David Burt ’17, Nikolaus Howe ’17, Alexander Kastner ’17, Aaditya Sharma ’17, *and* Vidya Venkatesh ’17.* *Sarah Fleming ’18* was runner-up for the national Alice T. Schafer award, given by the Association for Women in Mathematics. The Green Chicken contest, a problem-solving exam between Williams and Middlebury students was held at Williams in November. The Williams team successfully defended their title. The top three scorers for Williams were *Ian Banta ’19, Elijah Fromm ’17*, and *Abe Leite ’20*. In December, twenty-seven Williams students took the notoriously difficult national Putnam exam. *Tuan Tran ’18* placed in the top 200, *Elijah Fromm ’17* and *Hunter Wieman ’20* were in the top 500 and *Osama Brosh ’17*, *Ian Banta ’19, Matthew Davis ’20, Canvas Li ’19*, and *Alina Shubina ’19* were in the top 1000.

Finally, we thank the members of our student advisory board, SMASAB, who did a great job this year: *David Burt ’17, Nina Pande ’17, Reidar Riveland ’17, Troy Sipprelle ’17, Stephanie Stacy ’17, Sarah Fleming ’18, Jay Habib ’18, Kiran Kumar ’18, Haley Lescinsky ’18, Claudia Reyes ’18, Zihan Ye ’18, Anya Michaelsen ’19, Aesha Siddiqui ’19*, and *Anthony Simpson ’19*.

In summer, 2016, Professor Colin Adams led a group of SMALL students who produced a paper on cusp densities of hyperbolic 3-manifolds. He co-organized the Knots in Hellas conference in Ancient Olympia, Greece, where he spoke and put on theater. He also co-organized and obtained funding for the UnKnot Conference at Denison University, where he and his students spoke (and put on theater). And he co-organized a special session on knots at MathFest in Columbus, OH.

Adams was on leave for the academic year 2016-2017. He worked on various papers, and wrote a math novel entitled “Lost in the Math Museum: A Survival Story.” He gave a variety of talks in various venues, some serious and some silly, but all with mathematical content. At the Joint Meetings in Atlanta in January, he put on theater and presented a minicourse on teaching applied topology. He continued to serve as the humor columnist for the expository math magazine the Mathematical Intelligencer.

Professor Julie Blackwood was on leave during the 2016-2017 academic year. She had two papers accepted for publication (one of which included two student co-authors, *Alexander Meyer ’16* and *David Stevens ‘14*) and submitted three manuscripts which are currently under review (two of which have undergraduate co-authors).

Over the past year, Blackwood continued several ongoing projects in mathematical ecology including her work on spatial synchrony in periodical cicadas as well as disease transmission dynamics in several infectious diseases. Blackwood expanded her research on white-nose syndrome in little brown bats and participated in a related working group sponsored by the US Fish and Wildlife Service.

In addition, Blackwood developed several new projects over the course of this year. For example, Blackwood, along with other collaborators, received funding to be hosted by the National Institute for Mathematical and Biological Synthesis (NIMBioS) in the form of a working group, which will bring together 13 researchers from multiple fields (including mathematics, agricultural and resource economics, ecology, and computer science). The topic of the working group is “ecosystem federalism,” in which the multi-disciplinary team will develop new mathematical and economic frameworks to optimally manage ecosystems that are both adaptive and account for multiple levels of government authority. The tools created by this work will be directly useful in her other ecological research.

Professor Dick De Veaux continued his work in data mining and writing textbooks and gave a variety of talks and workshops on teaching and data mining throughout the world. He served as Chair of the section on Statistical Learning and Data Science of the American Statistical Association. He also organized the Undergraduate Faculty Workgroup at the 2016 Park City Math Institute (PCMI), the result of which was a paper detailing curriculum guidelines for undergraduate data science programs.

Professor Thomas Garrity has continued his research in number theory. He has spent a delightful year in Paris on sabbatical at the Institut de Reserche en Informatique Fondamentale (IRIF) at l’Université Paris-Diderot (Paris 7). He is, though, looking forward to returning to Williams.

His paper: “Stern Sequences for a Family of Multidimensional Continued Fractions: TRIP-Stern Sequences”, with coauthors *Amburg ’14,* Dasaratha, Flapan, *Lee ’12*, Mihaila, *Neumann-Chun ’13*, Peluse and Stoffregen, has appeared in the Journal of Integer Sequences. With co-author *Ilya Amburg ’14*, he put “Functional Analysis behind a Family of Multi-dimensional Continued Fractions: Triangle Partition Maps” on the math arxiv preprint server, and, with co-author *Peter McDonald ‘16*, he put “Generalizing the Minkowski Question Mark Function to a Family of Multi-dimensional Continued Fractions” on the math arxiv.

He has spoken at least twice at Paris-Diderot, at l’Université de Liège in Belgium, at the l’Institut Fourier in Grenoble, at a special session on continued fraction at the joint meeting of the AMS-MAA in Atlanta and to alums in London.

Professor Leo Goldmakher continued his research in number theory and additive combinatorics with a number of collaborators, including Williams student *Elijah Fromm ’17*. He spent the Spring semester on sabbatical leave in Berkeley, where he participated in research programs on analytic number theory (at MSRI) and pseudorandomness (at the Simons Institute for the Theory of Computing). This was a productive time; in addition to starting a number of new research projects, he submitted one paper, is finishing up two more, and had two other papers accepted to journals. He spent a week at the (invitation-only) analytic number theory workshop at Oberwolfach, and also gave talks at the Williams faculty seminar and at the MSRI analytic number theory seminar. He was invited to give a number of research talks in the coming months, including at the Mathematical Congress of the Americas this July.

Professor Pamela E. Harris developed two new courses for the Mathematics and Statistics Department: Math 456 Representation Theory and Math 293 Undergraduate Research Topics in Representation Theory. 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 Alexander Diaz-Lopez, Erik Insko and Mohammed Omar, which proves in the affirmative the Peak Polynomial Positivity Conjecture of Billey, Burdzy and Sagan posed in 2013. This article appeared in the Journal of Combinatorial Theory Series A, and was accepted as an extended abstract and oral presentation, by Professor Harris, at the Formal Power Series and Algebraic Combinatorics conference in London, England in July 2017.

Professor Harris was awarded six grants this year, two of which supported the research of 7 Williams students. One such grant is through the National Science Foundation (award DMS-1620202) and the second is a grant through the Center for Undergraduate Research in Mathematics. Professor Harris presented 16 lectures, of which three were conference plenary/keynote addresses, one was a Distinguished Women in Math Lecture, and two talks were international invitations to present her research in Buenos Aires, Argentina and Toronto, Canada. In addition, Professor Harris attended eight conferences and was invited to two working workshops one at the American Institute for Mathematics in San Jose, California and the second at the Banff International Research Station in Banff, Alberta Canada.

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 founded 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 [email protected] and Hispanics in different areas of the Mathematical Sciences. The American Mathematical Society used the information contained in their website and created a new poster featuring the 2016 mathematicians which has been distributed to high schools and colleges nationwide.

Professor Brianna Heggeseth transitioned from maternity leave to her research sabbatical to continue her methodology research in the area of longitudinal data analysis and establish new applied collaborations.

During her leave, she met colleagues at the Dartmouth Department of Epidemiology and Biostatistics and was added as a statistical consultant on a grant application. Additionally, she submitted a grant application to NIEHS/NIH to develop statistical methods for chemical mixtures with a set of interdisciplinary collaborators from the west coast.

In her methodology work, she finished a comparison of statistical methods for detecting the relationship between environmental exposures and non-linear childhood growth patterns and she submitted a manuscript for review. She presented this work at the ENAR Biometrics 2017 conference and the Joint Statistical Meetings 2017. Additionally, her work on centered longitudinal data was accepted for publication in the Annals of Applied Statistics. She continued work on developing a new correlation model for centered longitudinal data. Additionally, she is preparing a new project to utilize tree-based methods to determine important factors that explain variation in growth patterns that she will work on with a summer student and then her thesis student.

With collaborators in Berkeley, CA, she started a new applied project studying the impact of phthalates on childhood growth and applied statistical techniques from the area of functional data analysis. At Williams, 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.

She looks forward to returning to the rewarding work of teaching in the fall and working with her thesis student during the year.

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.

Professor Johnson appeared in NESN’s Kid’s Clubhouse, discussing his joint work with Prof. Frank Morgan and *Davide Carozza ‘09* on the science of base running.

Professor Bernhard Klingenberg conducted various consulting projects on and off campus, one of them leading to a paper in the journal Gynecologic Oncology on patient’s acceptance of various side effects in treating ovarian cancer. Prof. Klingenberg also expanded and improved his website *ArtofStats.com *which now allows public access to over 20 web-apps for all sorts of basic statistical analysis in the cloud. In May, he presented these to a broader audience at the 2017 United States Conference on Teaching Statistics conference at Penn State University. Prof. Klingenberg also continued to serve as an associate editor for the journal Statistical Modelling.

In July 2016, Professor Susan Loepp took over from Frank Morgan as chair of Math/Stat. In addition to her chair duties, she enjoyed teaching and her research in commutative algebra. In spring 2017, she taught “Protecting Information” for the last time with Bill Wootters who is retiring from Williams. Loepp especially enjoyed meeting regularly with Cory Colbert and Haydee Lindo about their research in commutative algebra. Colbert and Lindo are both Gaius Charles Bolin Fellows in mathematics at Williams. Lindo and Loepp co-advised the senior honors thesis of *Nina Pande ’17* and Loepp advised the senior honors thesis of *Sarah Fleming ’18*.

In summer 2015, Loepp advised the Commutative Algebra research group as part of the department’s SMALL program. The group included the three Williams students *Sarah Fleming ’18*, *Peter McDonald ’16*, and *Nina Pande ’17*. Two papers that include original results from SMALL 2015 have recently been accepted for publication, and both papers will appear in the *Journal of Commutative Algebra.*

In January, Loepp attended the Joint Mathematics Meetings in Atlanta where she gave a talk on the undergraduate research she has been advising for the last 20 years. She is also 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, the Mathematical Association of America and the Association for Women in Mathematics.

Professor Steven Miller received a three year individual NSF grant to continue his investigations in number theory and probability, 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 over 10 papers and gave almost 40 talks, including conferences in Canada, France and India. 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 Probability, and to giving presentations to the public at the Boston Museum of Science. With Ralph Morrison he ran math puzzle night and continued our streak of over 1% campus participation on the Putnam exam. He was the thesis advisor to *David Burt ’17* (Information Theory), *Becky Durst ‘17* (Benford’s law), *Aaditya Sharma ‘17* (Random Matrix Theory), *Anand Hemmady ‘17* (L-functions), the second reader on four more, and also expanded his involvement in using online resources in teaching; all his course lectures are available online through YouTube, as are many of his talks. Additionally, with colleagues in LACOL he beta tested shared courses across liberal arts colleges, with 3 Swarthmore and 2 Amherst students taking his spring Problem Solving class. In addition to giving many math talks at Williamstown Elementary, 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.

Professor Frank Morgan spent his first year of retirement as mathematical traveler and Editor-in-Chief of the *Notices of the American Mathematical Society*, the largest publication in higher mathematics. He gave 35 talks on four continents. Meanwhile he is continuing work on optimal shapes, some with his 30^{th} group of SMALL undergraduate research students this summer.

Professor Ralph Morrison completed his first year at Williams College. He continued his research on tropical geometry and algebraic geometry with a number of collaborators, both in the U.S. and abroad. He taught three sections of Multivariable Calculus in the fall, and introduced a new 300-level post-core class on Computational Algebraic Geometry in the spring. Along with Steven Miller, he ran the department’s weekly Math Puzzle Night, led the Williams team to a Green Chicken victory over Middlebury, and continued the streak of at least 1% of campus participating on the Putnam exam.

Professor Allison Pacelli continued her work with Albany elementary school teachers and principals this year. She is part of a New York State Math & Science Partnership Grant aimed at increasing the mathematical knowledge and pedagogical effectiveness of K-5 teachers. She continued her teaching and research in algebraic number theory. The Williams College Math Camp, which she founded in 2013, is now in its fifth year.

In summer 2016, Professor Cesar Silva was SMALL director and had a research group of six students; they completed two papers, one of which has already been accepted for publication. He also taught in the Summer Science Program. In fall 2016, Silva taught Math 350 (Real Analysis) and Math 374, a topology tutorial. In spring 2017, he was on sabbatical and continued his research in ergodic theory. Silva visited colleagues at the University of Rouen, France, in March-April and at the University of Brest, France, in May-June. In the academic year 16-17, he had two thesis students, *Alex Kastner’17* and *Matt Quinn ‘17*. Together with his colleague Steve Miller, Silva wrote and were awarded a new National Science Foundation grant to support the SMALL summer research program.

Silva was a member of an AMS committee and participated in an NSF panel. He was also Associate Editor for the *Notices* of the American Mathematical, and was on the Editorial Board of Pro Mathematica, Peru. He completed a volume as editor, jointly with Auslander (Maryland) and Johnson (Swarthmore) published by the American Math Society in 2016.

Professor Mihai Stoiciu taught “Foundations in Quantitative Skills” and “Numerical Problem Solving” (tutorial) during the Fall Semester and “Measure Theory and Probability” during the Spring Semester of the Academic Year 2016–2017. He also supervised the undergraduate theses of *Nikolaus Howe ‘17* and *Andy Yao ‘17*. During the year, Stoiciu continued his research on spectral properties of random and deterministic operators. His paper “Orthogonal Polynomials on the Unit Circle, CMV Matrices, and the Distribution of Their Eigenvalues” was published in the journal “Memoria – Seminario de Operadores y Fisica-Matematica, IIMAS-UNAM”.

Stoiciu was invited to present his research at the Summer Analysis Workshop, hosted by Oberlin College and at the conference “NEAM – 1st Northeastern Analysis Meeting”, hosted by SUNY Brockport. At Williams College Stoiciu gave a faculty seminar in April 2017 on his recent research in spectral theory. 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.

Professor Laurie Tupper finished her first year at Williams College. She has continued her research in spatial, temporal, and high-dimensional data, with particular emphasis on defining distance and similarity between such observations. She taught three sections of Elementary Statistics and Data Analysis, and in the spring developed and taught a new course on Time Series Analysis.

Professor Daniel Turek successfully completed his first year at Williams. In the Fall, he created and taught a course on Bayesian Statistics which covered analytical theory in the first half of the semester, and use of modern statistical software in the second half. This provided students with a mix of theory and practical ability for modern large-scale data analysis.

Turek co-edited a book on reproducible scientific research, titled The Practice of Reproducible Research: Case Studies and Lessons from the Data-Intensive Sciences, which was published in 2017. As part of the book launch, he was invited to give a talk (“Features and Trends of the Reproducibility Case Studies”), presented at the Berkeley Institute of Data Science, at the University of California, Berkeley.

Turek also received a sub-award of an NSF grant to continue development of the NIMBLE statistical software package for R. This package provides an algorithmic platform for advanced computational tools and analysis workflows for graphical statistical models.