Department News and Happenings | Mathematics at Dartmouth

Mathematics is an amazing and beautiful intellectual creation, one of the human race’s deepest endeavors. The world around us, and the future world we are creating, is woven through with mathematics — from the symmetry groups of Navajo weavings, to the airflow around a flapping bird’s wing, to the security of global computer networks.

Learn more about our vibrant department, explore our daily events calendar for the most current department events, and please come visit us in Kemeny Hall.

Recent happenings in and around the Math Department

Math alumna continues collaboration with Professor Wallace

January 28, 2023

Frederika Rentzeperis ’20, now an MD/PhD student at the Icahn School of Medicine at Mount Sinai, has continued collaborating with Professor Dorothy Wallace on two recently published articles in Mathematical Biosciences and Applied Mathematical Modelling. Rentzeperis did her senior honors thesis work under the guidance of Professor Wallace, and in 2020 participated in Dartmouth’s Mathematical Oncology DSP at the Moffitt Cancer Center in Tampa, Florida. Professor Wallace led the program, which offered students opportunities to learn how to combine math, biology, evolutionary principles, and computer modeling while exploring oncology research. “One of our papers from 2022 has coauthors from the Moffitt collaboration/DSP and I still work remotely with some of the people there,” Rentzeperis says. She also did undergraduate research at Dartmouth, conducting in silico trials related to prostate cancer growth and also laboratory research to investigate glioblastoma metastasis and proliferation. After receiving her degree in Mathematics and Biology, she became a researcher in the NIH Postbac IRTA program before starting at Icahn.

Eliza Crocker ’23 sailing roster portrait

Byrne Scholar Eliza Crocker ’23 inducted into Phi Beta Kappa

January 14, 2023

Congratulations to Byrne Scholar Eliza Crocker ’23, one of 24 students who were inducted into Dartmouth’s chapter of Phi Beta Kappa in November. Crocker is pursuing a major in Computer Science as well as a minor in Mathematics. With support from Byrne funds, she spent winter term ’21 conducting a research assistantship under the guidance of Professor John Voight, learning about data collection and analysis techniques to make observations regarding the Galois groups of various Belyi maps; this led to her writing two papers and presenting her research findings to faculty and other undergraduates. During winter ’21 she also participated in our department’s Directed Reading Program with graduate mentor Alex Wilson, and gave her final DRP presentation on the topic of representation theory. Crocker is a member of Dartmouth varsity sailing, and last fall she helped the team win the 2022 Victorian Urn Trophy for the NEISA Fall Women's Championship!

from left: Michael Gonzalez ’23 and Mario Tomba ’25

At the 2023 Joint Mathematics Meetings in Boston

January 10, 2023

Michael Gonzalez ’23 and Mario Tomba ’25 presented their poster Encoding trees with chromatic polynomials at JMM in Boston in early January. With co-author Andrew Koulogeorge ’24, they did research in algebraic combinatorics under the guidance of faculty mentor Rosa Orellana. “The poster session was an excellent opportunity to summarize our research findings and practice explaining them to others,” says Gonzalez, left, who is considering applying to PhD programs in Math or Computer Science. “It was fun interacting with other student researchers from all over the country and learning about their diverse mathematical backgrounds and interests. It was also cool to see so many other passionate students talking about their work — it puts into perspective the massive range of mathematical research going on today.” Tomba, right, was supported by the Kaminsky Award from UGAR and is studying pure mathematics with a growing interest in algebraic combinatorics and representation theory.

poster for Essay Contest 'Biographies of Contemporary Women in Mathematics'

Math Department and AWM Essay Contests

January 04, 2023

For the eighth year in a row our department is pleased to sponsor the Essay Contest Biographies of Contemporary Women in Mathematics, modeled on the national AWM Essay Contest and open to all middle and high school students in the Upper Valley and to all Dartmouth undergraduates. We are very excited to share this program with our community and hope to receive some outstanding essays. In the past seven years we have had many students receive recognition or win prizes in the national AWM Essay Contest! You may submit your essay to both contests; the deadline is February 1, 2023. View detailed information including contest rules, tips on choosing an interviewee, and lists of past winners. Last year local student Haley Song received First Place, middle school level, in the AWM national contest for her essay on Carolyn Gordon, Dartmouth Professor of Mathematics, Emerita. (Click/tap to view a larger image of poster.)

composite photo of 2022 senior honors theses students, from left: Archita Harathi ’22, Zachary Couvillion ’22, and Ivy Junqing Yan ’22

Faculty-mentored research opportunities for undergraduates

January 03, 2023

Interested in working with a Math Department faculty member on independent research? View research opportunities available in various fields, including: arithmetic geometry; knot theory and applications to general relativity; enumerative combinatorics; network science; combinatorics, algebra and graph theory; and explicit methods in number theory. Additionally the Fu Lab always welcomes talented and motivated scientists at all stages (including undergraduates!) to join the lab, which seeks to understand a broad variety of evolutionary dynamics using mathematical modeling and computational approaches. Many undergraduate projects can lead to senior thesis for honors or high honors. We again congratulate our graduating seniors who submitted and presented honors theses in 2022: Archita Harathi ’22 (advisor Feng Fu), Zachary Couvillion ’22 (advisor John Voight), and Ivy Junqing Yan ’22 (advisor Anne Gelb).

Byrne Scholar Paul Shin ’24 receives prize for achievement in Mathematics

December 21, 2022

Congratulations to Byrne Scholar Paul Shin ’24, who has received Dartmouth’s Francis L. Town Scientific Prize for his achievement in Mathematics! Shin has a broad range of academic interests, ranging from pure and applied mathematics to physics and climate science. Last spring he studied numerical semigroups in Barcelona, and last fall at Dartmouth’s Phi Beta Kappa meeting he received an award bestowed on sophomores “who have the highest academic rank at the conclusion of five terms of enrollment at Dartmouth, completed not later than June of the second calendar year following matriculation.” He plans to continue studying mathematics in graduate school, and is currently particularly interested in learning more about topics related to the foundations of mathematics.

Professor Elizalde selected for Ivy+ Fellowship

December 07, 2022

Professor and Department Chair Sergi Elizalde is one of five Dartmouth faculty leaders selected for the inaugural class of Ivy+ Faculty Advancement Network Leadership Fellows. The network includes 12 national research universities that collaborate to advance diversity, equity, inclusion, and belonging in the American professoriate. The leadership fellows were nominated by their deans and selected based on their commitment to inclusive and equitable leadership. “The Ivy+ Faculty Advancement Network provides a great resource for learning a lot of the skills necessary for being a department chair,” Elizalde says. “The fellowship consists of a series of workshops throughout the year that focus on topics like equity-minded leadership, advancing faculty diversity, and best practices for recruiting and assigning committee work.” Elizalde and the other Dartmouth 2022–2023 Ivy+ fellows join 40 department chairs, deans, and other senior administrators from Columbia, Cornell, Duke, the Massachusetts Institute of Technology, Princeton, Stanford, the University of Chicago, the University of Pennsylvania, and Yale.

Athina Avrantini ’23 receives Byrne Prize in Mathematics

November 23, 2022

We are pleased to announce that the John J. Byrne Jr. Prize in Mathematics has been awarded to Athina Avrantini ’23! This prize was established in 2019 and is awarded to the top Dartmouth graduating mathematics major interested in continuing mathematics at the graduate level. Avrantini, who is majoring in math and minoring in computer science, has participated in Dartmouth’s Summer Hybrid Undergraduate Research (SHUR) 2021 and our department’s Directed Reading Program, and is also involved with the Dartmouth chapter of the Association for Women in Mathematics. “I am currently working with Professor Asher Auel on a senior thesis investigating cyclic error-correcting codes,” she says. “I am now in the process of applying to PhD programs, and I am immensely grateful for the Byrne Prize and the support I have received from the math department in the pursuit of this goal.” View more about Avrantini and past Byrne Prize recipients to hear more about their time at Dartmouth and future plans.

Graduate Student Lizzie Buchanan receives Bogart Teaching Award

November 17, 2022

Congratulations to fifth-year PhD student Lizzie Buchanan, the recipient of this year’s Kenneth P. Bogart Teaching Award for dedication to and excellence in advancing the educational mission of the department! Buchanan, who this month received her Certificate in Mathematical Pedagogy, has taught Math 3 and Math 8, and will be teaching Math 22 in Spring ’23. Her research interests are in topology, specifically knot theory. In addition to teaching, she is also a mentor in the Winter Term 2023 Directed Reading Program, and for the past two years has supported our PhD students in her role as our department's Graduate Program Committee Liaison. “I am a huge fan of tactile and visual aids, and I try to incorporate them as much as possible,” Buchanan says. “For example, I bring in bowls, vases, and shoes to help visualize volumes of revolution or surfaces like paraboloids. I intentionally use common items instead of specially made math aids, because then my students can mentally attach a new unfamiliar object to a familiar one, making the new one easier to ‘hold’. Throwing around a travel pillow to talk about saddle points can be fun and silly, and makes the concept less intimidating.”

From left: graduate students Alex Wilson, Dylan Green, Juanita Duque-Rosero, Alina Glaubitz, Matthew Ellison, Ben Adenbaum, Brian Mintz, and Richard Haburcak.

Directed Reading Program continues in Winter 2023!

November 16, 2022

Our Directed Reading Program pairs undergraduate students with graduate mentors to undertake independent reading projects covering advanced topics in mathematics that are generally not taught at the undergraduate level. We look forward to learning interesting mathematics with you! View a list of possible projects and graduate mentors; if you are very interested in a particular topic that is not on the list, there may be a graduate mentor who would be happy to read through that topic with you. The deadline to apply for the Winter 2023 DRP is December 9. From left: graduate student mentors Alex Wilson, Dylan Green, Juanita Duque-Rosero, Alina Glaubitz, Matthew Ellison; program organizers Ben Adenbaum and Brian Mintz; and organizer and mentor Richard Haburcak. The department gives special thanks to Richard, Ben, and Brian as co-organizers of this year’s program.

poster for Lahr lecture by Bianca Viray, with photo and abstract

Bianca Viray to give C. Dwight Lahr Lecture

November 08, 2022

Bianca Viray, Professor of Mathematics at the University of Washington, will give a lecture titled The Interplay of Geometry and Arithmetic at 6 p.m. on Tuesday November 15 in Haldeman 041. “A trailblazer in her research field, Bianca Viray believes that mathematics is for everyone and works tirelessly to achieve a vision of inclusivity and diversity,” states the recent Simons Foundation article Mathematician Bianca Viray Invites Everyone to the Table. In addition to having received an early-career NSF CAREER award, Viray was named a 2020 Simons Fellow in Mathematics and has also received a 2022-2023 Birman Fellowship from the American Mathematical Society. Our department’s C. Dwight Lahr Lecture series is named in memory and honor of Dwight Lahr’s contributions to the Department of Mathematics and to Dartmouth, and in recognition of his commitment to inclusivity and diversity. (Click/tap to view a larger image of poster with abstract.)

Neukom Institute abstract illustration of people generating ideas

Neukom Institute opportunities for postdocs, graduate students, and undergraduates

October 30, 2022

The Neukom Institute for Computational Science is currently accepting applications for Class of 2023 Neukom Fellows, an interdisciplinary postdoctoral program at Dartmouth that may provide another means of working with or being mentored by faculty in our department. The Neukom Fellows program brings to campus early-career interdisciplinary postdoctoral researchers whose work has a computational theme. View the list of current Neukom fellows to see research interests and mentorships. Applications must be received by November 15, 2022. Dartmouth’s Neukom Institute also provides support for undergraduates working on computational projects by way of the Neukom Scholars Program for undergraduates and also Neukom Travel Grants, which support both undergraduate and graduate student research.

photo of Ina Petkova working on knot theory in her office, writing on a blackboard

Professor Petkova’s NSF CAREER award featured in Dartmouth News

October 25, 2022

Congratulations to Professor Ina Petkova, one of six Dartmouth recipients of the National Science Foundation’s Faculty Early Career Development Program (CAREER) awards in 2022, as recently featured in Dartmouth News. “The CAREER grant is the NSF’s most prestigious award in support of early-career faculty. These awards are very difficult to obtain, particularly in pure mathematics,” says department chair Sergi Elizalde. Petkova studies the mathematics of knots, and with funding support from the CAREER grant, she will advance what are called cut-and-paste techniques of studying knots and links. As Principal Investigator, Petkova intends to further develop an invariant from bordered Floer homology for contact 3-manifolds with convex boundary, and use this invariant to address open questions in contact topology, an area with applications in physics, including classical mechanics, thermodynamics, and control theory. She also plans to extend bordered Floer homology and tangle Floer homology to integral coefficients and understand and develop the connections between knot Floer homology and quantum algebra. Photo by Katie Lenhart

photo of Dartmouth Mathematical Society meeting, Fall 2022

Join math organizations on campus!

October 12, 2022

The Dartmouth College Mathematical Society hosted its first gathering of the academic year on Thursday September 22, meeting for an hour of pizza and problem solving. This year the president is Andrew Koulogeorge ’24 and faculty advisors are Professor Vladimir Chernov and Professor Rosa Orellana. The purpose of the society is to create a community where students can interact and explore interesting mathematical topics in a setting outside of the classroom environment. The goal is to encourage, foster interest in, and enrich the understanding of mathematics; students can discuss news and share experiences in courses, study abroad programs, and research internships. Other math organizations on campus include the Dartmouth SIAM chapter (faculty advisors: Scott Pauls and Feng Fu) and the Dartmouth AWM student chapter (faculty advisors: Carolyn Gordon and Rosa Orellana).

Professor Rockmore on the appeal of infinity

October 04, 2022

“Why are we so intrigued by the infinite? Maybe it’s because of the tension between our finite lives and the seemingly unbounded range of our imagination,” writes Professor Dan Rockmore in his review of Netflix’s new documentary, A Trip to Infinity, in The New Yorker Annals of Inquiry. Rockmore is familiar with the fine balance needed when communicating mathematical concepts using film as a medium, having co-produced the 2002 NSF-funded educational documentary The Math Life, which featured lively interviews with a diverse group of mathematicians. “Math documentaries always pose a challenge to filmmakers because mathematics does not exist in the realm of images but in the realm of ideas,” says Rockmore, referencing his earlier Annals of Inquiry essay The Myth and Magic of Generating New Ideas.

abstract image of a portion of the earth superimposed with mathematical representations

2023 Byrne Prize in Mathematics: accepting applications through November 1

September 29, 2022

We are now accepting applications for the 2023 Byrne Prize in Mathematics. If you are graduating this year and planning to go to graduate school in math or a related field, please consider applying! The prize, established in 2019, is a $35,000 fellowship that recognizes the top Dartmouth graduating mathematics major interested in continuing mathematics at the graduate level. View the application requirements along with info about our past recipients Zachary Couvillion ’22, Jacob Swenberg ’21, Matt Radosevich ’20, and Shikhin Sethi ’19. All materials should be received by November 1st, 2022.

poster for Prosser lecture by Mark Levi, with photo and abstract

Mark Levi of Penn State to give Reese T. Prosser Memorial Lecture

September 28, 2022

Mark Levi, Professor and Head of Mathematics Department, Pennsylvania State University, will give a lecture titled A Physical Approach to Mathematics at 6 p.m. on Wednesday, October 12 in 041 Haldeman. Levi is the author of the books Why Cats Land on Their Feet: And 76 Other Physical Paradoxes and Puzzles and The Mathematical Mechanic: Using Physical Reasoning to Solve Problems. “Levi turns math and physics upside down, revealing how physics can simplify proofs and lead to quicker solutions and new theorems, and how physical solutions can illustrate why results are true in ways lengthy mathematical calculations never can,” states the Princeton University Press. “[Levi's work] will appeal to anyone interested in the little-known connections between mathematics and physics and how both endeavors relate to the world around us.” (Click/tap to view a larger image of poster with abstract.)

photo of Tongtong Li with second place prize for her poster presentation

The mathematics of sea ice dynamics

September 23, 2022

Congratulations to postdoctoral fellow Tongtong Li on receiving second place for her poster presentation at UMass Lowell's 2022 High Performance Computing Day! Li’s poster Improving Numerical Accuracy for the Viscous-plastic Formulation of Sea Ice presented research she is conducting with Professors Anne Gelb and Yoonsang Lee. Li’s recent SIAM News blog describes their research in some detail. The related research has also been formed into a manuscript available on arXiv and submitted. Li, along with Principal Investigators Gelb and Lee, is part of a team that received a high-profile multidisciplinary university research initiative (MURI) award from the Office of Naval Research in 2020. Their MURI project Integrated Foundations of Sensing, Modeling, and Data Assimilation for Sea Ice Prediction seeks to improve environmental variables prediction by combining disparate environmental data into a common computational toolkit, which will enhance information currently extracted from existing environmental data and physical knowledge.

composite photo, from left: Zachary Winkeler PhD ’22 and Zachary Garvey PhD ’22

Congratulations to our newest PhD graduates!

September 20, 2022

We are proud to celebrate the accomplishments of Zachary Winkeler and Zachary Garvey, who both received their doctoral degrees this summer! Winkeler, currently Visiting Assistant Professor at Smith College, earned his PhD under the guidance of faculty advisor Ina Petkova. His research is in topology, specifically knot theory and, more specifically, knot homology theories. Garvey studied index theory and noncommutative geometry and completed his thesis under the guidance of faculty advisor Erik van Erp. He is currently Lecturer in Mathematics at University of Colorado Boulder. You may view recent PhD theses abstracts as well as our list of recent PhD students, which goes back a number of years and shows the first jobs and current positions of our PhD alumni. Congratulations to both!

photo of Eugene Demidenko receiving 'Outstanding Book in Statistics' book award for 'Advanced Statistics with Applications in R' at the Joint Statistical Meetings in August 2022

Professor Demidenko receives award for Advanced Statistics with Applications in R

September 14, 2022

Professor Eugene Demidenko has received an award from the American Statistical Association’s Technometrics Journal for his recent book Advanced Statistics with Applications in R. Professor Demidenko received the award in August at the Joint Statistical Meetings in Washington, D.C., where his book was named “Outstanding Book in Statistics”. The book is the product of forty years of experience teaching probability and statistics and their applications for solving real-life problems. The book, on display in the second floor of Kemeny Hall, is a primary text in Math 40 and Math 70, the latter being the culminating course of our Mathematical Data Science major. The course is generally taught every spring and prepares students for a career in data analysis and statistical problem solutions. Congratulations to Professor Demidenko on this award!

composite image of class of 2026 Byrne Scholars, left to right: Alek Mekhanik and Klara Drees-Gross; second row, left to right: Henry Moore, Samuel Ryan, John Wang, and Ari Nathanson; third row, left to right: Matthew Marks, Travis Owusu, and Kabir Moghe

Introducing the Class of ’26 Byrne Scholars

September 12, 2022

The Math Department warmly welcomes the Class of 2026 Byrne Scholars! The Jack Byrne Scholars Program in Math and Society allows students to study with faculty committed to using mathematics to build solutions to today’s complex problems; to present research findings at conferences; to conduct independent research at Dartmouth; and to participate in research exchanges domestically and abroad. Each Byrne Scholar receives an enrichment grant from the generous Byrne Gift and joins a community of Byrne Scholars who provide mentorship both in and out of the classroom. Left to right: Alek Mekhanik and Klara Drees-Gross. Second row, left to right: Henry Moore, Samuel Ryan, John Wang, and Ari Nathanson. Third row, left to right: Matthew Marks, Travis Owusu, and Kabir Moghe.

composite image, from left: LGP-30 typwriter console and Sister Mary Kenneth Keller teaching R. Buckminster Fuller about computer programming

Even before BASIC...

August 23, 2022

What does a photo of Sister Mary Kenneth Keller teaching R. Buckminster Fuller about computer programming tell us about Dartmouth’s early computing history? Prior to being the first person in the U.S. to earn a PhD in Computer Science, Mary Kenneth Keller, a Catholic religious sister, participated in an NSF-funded summer program led by Mathematics Professor Tom Kurtz to introduce high school teachers to computing, using the College’s first computer, an LGP-30 (console on left) in 1961. She went on to receive her doctorate in Computer Science from the University of Wisconsin–Madison in June 1965 and became a widely known and respected pioneer in computing education. A recent pre-print about Mary Kenneth Keller notes it was her first experience in computer education: “It looked to me as if the computer would be the most revolutionary tool for doing math that I could get.” Just a few years later, Dartmouth reached the conclusion that “learning to use a high-speed computer should be an essential part of liberal education,” resulting in the creation of BASIC in 1964 under the leadership of Professors Kurtz and John Kemeny. Photo credit, right: Clarke University Archives

mathematical figure of two drumheads of different shapes having the same vibration frequencies

Professors Gordon and Webb featured in Scientific American

August 12, 2022

A recent article in Scientific American features the work of Professors Carolyn Gordon and David Webb in the field of spectral geometry, which provides information about geometric shapes based on their vibration frequencies. In 1992, Gordon, Webb, and Scott Wolpert, currently an emeritus professor at the University of Maryland, published a groundbreaking paper, One cannot hear the shape of a drum, in which they provided examples of differently shaped heads of drums that produce the same sound. The Scientific American article, Mathematicians Are Trying to ‘Hear’ Shapes—And Reach Higher Dimensions, goes on to describe more recent work in the field. Gordon and Webb present spectral geometry more generally in a 1996 article in American Scientist where they make an analogy between spectral geometry and spectroscopy which can be used to identify elements in distant stars by looking at the spectrum of the light they produce. The figure here, from their 1996 article, depicts two drumheads of different shapes having the same vibration frequencies.

composite image of 2022 incoming graduate students, clockwise from upper left: Luke Askew, Lily McBeath, Atticus McWhorter, Jessica Rattray, Mark Lovett, Jamie Schmidt, Caroline Hammond, Lucy Knight, and (center) Beth Anne Castellano

Welcoming our incoming PhD students

July 31, 2022

We are pleased to extend a warm welcome to nine new graduate students in our department! Clockwise from upper left: Luke Askew (Colorado State University), Lily McBeath (University of California, Los Angeles and Irvine), Atticus McWhorter (Bowdoin College), Jessica Rattray (Vassar College), Mark Lovett (University of Pennsylvania), Jamie Schmidt (Michigan State University), Caroline Hammond (University of Delaware), Lucy Knight (University of Durham, England), and (center) Beth Anne Castellano (Lafayette College). We look forward to working with them in the fall.

composite photo of 2022 local Math Essay Contest winners, clockwise from upper left: Beatrix Bornholdt-Collins, Haley Song, Sora Shirai, and Bonnie Blake

Congratulations to our 2022 Math Essay Contest winners!

July 21, 2022

Congratulations to the middle and high school winners of our local essay contest Biographies Of Contemporary Women In Mathematics, modeled on the national AWM Essay Contest and open to all middle and high school students in the Upper Valley. The local 2022 winning essays are from students (clockwise from upper left) Beatrix Bornholdt-Collins, Haley Song, Sora Shirai, and Bonnie Blake. In addition to the local prize, Haley received First Place, middle school level, in the AWM national contest! Haley’s and Bonnie’s essays both feature Carolyn Gordon, Dartmouth Professor of Mathematics, Emerita, and Research Professor of Mathematics. Professor Gordon, who is adamant about providing welcoming environments in which girls and women can pursue mathematics with confidence, served as president of the Association for Women in Mathematics from 2003–2005 and subsequently established an AWM chapter at Dartmouth, which she continues to advise. You may read all the 2022 winning essays here, along with those from prior years.

image of Jared Duker Lichtman AB, AM ’18 from a Numberphile YouTube video

Jared Duker Lichtman explains his recent proof for Numberphile

July 07, 2022

In a wonderful and popular new Numberphile video, Jared Duker Lichtman AB, AM ’18 expounds and further discusses his recent proof of the Erdős primitive set conjecture. Lichtman talks in some depth about primes and primitive sets, describing his fascination with uncovering hidden mathematical beauty and structure within an ostensibly very chaotic class of sets. When he heard about this particular Erdős conjecture during his undergraduate years at Dartmouth, Lichtman states that he “absolutely fell in love with the problem, because it’s saying that these primes are very special in a precise way... I just found this such a beautiful statement.” In a second, follow-up Numberphile video, Lichtman provides additional context for primitive sets in general and mentions some examples of related open problems. He dedicates his proof of the Erdős primitive set conjecture to his undergraduate advisor, Professor Carl Pomerance, with whom he has written several joint papers.

Congratulations to Ina Petkova on her promotion!

July 03, 2022

Please join us in congratulating Ina Petkova, who has been promoted to Associate Professor with tenure! Professor Petkova works in low-dimensional topology, with focus on Heegaard Floer homology and its various generalizations. Earlier this year she received the National Science Foundation’s Faculty Early Career Development Program (CAREER) award, described as its “most prestigious award in support of early-career faculty who have the potential to serve as academic role models in research and education and to lead advances in the mission of their organizations.” Her five-year grant will provide funding for her project, Bordered Floer homology and applications, as well as for mentoring and outreach. This summer Professor Petkova is co-leading Dartmouth SHUR 2022, partially funded by the NSF, which has invited Dartmouth undergraduates to participate in research exploring computational approaches to Legendrian Knots.

photo of recent Mathematics PhDs and advisors, from left: Professor Feng Fu, Yao Xiao PhD ’22, Professor Anne Gelb, Matt Jones PhD ’22, James Ronan PhD ’21, Sam Tripp PhD ’22, and Laura Petto PhD ’21

Congratulations to our recent PhDs!

June 29, 2022

We are honored to celebrate the achievements of our graduate students who recently earned their doctoral degrees and participated in this year’s June Investiture ceremony! From left: Professor Feng Fu, Yao Xiao PhD ’22 (advisor Anne Gelb), Professor Anne Gelb, Matt Jones PhD ’22 (advisors Feng Fu and Scott Pauls), James Ronan PhD ’21 (advisor Anne Gelb), Sam Tripp PhD ’22 (advisor Ina Petkova), and Laura Petto PhD ’21 (advisor M. Cheney). James Ronan and Laura Petto both received their PhDs in June 2021 during a time of COVID restrictions, and were able to celebrate their achievements by walking in Investiture this year. You may view recent PhD theses abstracts as well as our list of recent PhD students, which goes back a number of years and shows the first jobs and current positions of our PhD alumni. Congratulations to all!

photo of Jared Duker Lichtman AB, AM ’18 at University of Oxford Mathematical Institute

Former Byrne Scholar Jared Duker Lichtman proves decades-old Erdős conjecture

June 08, 2022

In February Jared Duker Lichtman AB, AM ’18, currently a Clarendon Scholar at the University of Oxford Mathematical Institute, released A proof of the Erdős primitive set conjecture, resolving a longstanding conjecture which states that the Erdős sum of the set of prime numbers is the largest of any set of primitive numbers (sets in which no number divides any other). Lichtman began working on the primitive set conjecture with his advisor, Professor Carl Pomerance, while an undergraduate at Dartmouth. Their work led to several joint papers, including The Erdős conjecture for primitive sets and A generalization of primitive sets and a conjecture of Erdős. Quanta Magazine describes his resolution of the conjecture in some detail. You may read Lichtman’s own explanation of his fascination with this topic and watch a short video in an article by the Oxford Mathematical Institute. Noted number theorist András Sárközy, who co-authored many papers with Paul Erdös, said proof of the conjecture “seemed beyond reach”; other number theorists were of similar opinion. Please join us in congratulating our alumnus on this major achievement!

composite image, clockwise from upper left: Varun Malladi ’23, Michael Gonzalez ’23, Ivy Junqing Yan ’22, fourth year PhD student Richard Haburcak, and Calvin George ’24

Directed Reading Program 22S final presentations

June 07, 2022

To conclude a wonderful spring term of learning mathematics in our Directed Reading Program, four undergraduates gave final presentations on June 1. Topics included sheaf cohomology, the probabilistic method, Bayesian modeling and computation, and integer-point enumeration in polyhedra. Our program pairs undergraduate students with graduate mentors to undertake independent reading projects covering advanced topics in mathematics that are generally not taught at the undergraduate level, fostering a supportive environment for students seeking to further their interest in mathematics. Thank you to everyone who made this possible, especially all of our graduate mentors! Clockwise from top left: Varun Malladi ’23, Michael Gonzalez ’23, Ivy Junqing Yan ’22, program organizer Richard Haburcak, and Calvin George ’24. DRP will resume in Winter Term 2023!

Celebrating Senior Honors Theses in the Class of 2022

June 06, 2022

Congratulations to our graduating seniors who submitted and presented honors theses this year! Archita Harathi ’22 (Cliques Can Click! Evolutionary Dynamics on Two-Clique and Clique-Like Graphs with Resource Heterogeneity, advisor Feng Fu) and Zachary Couvillion ’22 (On Specializations of Belyi Maps and Inverse Galois Theory, advisor John Voight) were both awarded high honors, and Ivy Junqing Yan ’22 (Pre-processing Methods for Change Detection on Under-sampled and Noisy Fourier Data, advisor Anne Gelb) was awarded with honors. Archita received the Hazleton Mirkil Prize for Best Senior Thesis Presentation. Our Honors Program page has PDF versions of their theses as well as those from prior years. Interested in doing independent work in mathematics? View the section on The Honors Program in Mathematics in the Dartmouth ORC.

from left: Michael Gonzalez ’23, Mario Tomba Morillo ’25, and Andrew Koulogeorge ’24

Professor Orellana guides undergraduate research in algebraic combinatorics

June 03, 2022

Under the guidance of faculty mentor Rosa Orellana, undergraduates Michael Gonzalez ’23, Mario Tomba Morillo ’25, and Andrew Koulogeorge ’24 did research in algebraic combinatorics and presented their poster Encoding graphs with chromatic polynomials at this year’s Wetterhahn Science Symposium on May 25. Michael (left), a Math major and Computer Science minor, is an E.E. Just Fellow for the 2021-2022 academic year. He is especially interested in discrete mathematics, and is also interested in math/CS education. Mario (center) and Andrew (right) were both supported by funds from UGAR; Mario’s intended field of study is pure mathematics and Andrew is pursuing a degree in mathematics and computer science. Professor Orellana’s own research is in algebraic combinatorics with a focus on combinatorial representation theory and symmetric functions.

Math Camp 2022: Exploring Mathematics

May 23, 2022

Sharpen your problem solving skills and find out what college math is like! This year we are hosting Math Camp in-person, offering two summer enrichment sessions for local high school students in July and August. Topics covered will be outside of the usual high school syllabus and students can interact with mathematicians in a fun, non-graded environment, where an exploratory approach will be emphasized. Each program will cover different mathematical topics and students are invited to attend one or both 5-day sessions. This year’s sessions are How to win games with math and Solving puzzles with the mathematics of chance. There is no charge for this program. View more info and registration link. (Click/tap to view a larger image.)

2022 Thayer Prize Exam winners

May 17, 2022

The Math Department is pleased to announce impressive results in this year’s Thayer Prize Exam, an annual first-year Dartmouth mathematics competition organized by our department. Congratulations to first place winner Matthew Coleman ’25 and second place winner Jessica Jiang ’25! In his previous studies, Matthew won Mathematics Award for Outstanding Student and was named a Commonwealth Honors Scholar. Jessica was first violinist of the Wisconsin Youth Symphony Orchestra’s Youth Orchestra, and is currently a first violinist in the DSO. She intends to study applied mathematics and music. You may view the list of winners from the last 12 years along with a brief history of the prizes, which were established in 1869 to “to constitute a perpetual prize fund for superior proficiency in the higher branches of Mathematics.” The exam consists of Mathematics Olympiad style problems, and originality and creativity are heavily weighed.

composite image of Dan Rockmore and Allen Riddell

Can a machine learn to write compelling product reviews?

May 13, 2022

Could you tell if an online review describing the palate-pleasing notes of grapefruit and tangerine in your off-dry Riesling was written by a human, or by an algorithm? Professor Dan Rockmore is part of a team that developed software to produce original expert wine reviews and syntheses of beer reviews using existing datasets and product metadata. Both approaches use transformer-based deep learning neural net architecture. Started by former Neukom Institute fellow Allen Riddell, right, and developed under Rockmore’s guidance by Keith Carlson, Guarini ’21 and postdoctoral research fellow at Tuck, the project became a cross-campus collaboration resulting in a paper in the International Journal of Research in Marketing. Practical applications include tools to assist consumers and professional reviewers, although the paper acknowledges and explores the inherent ethical implications involved. Read more in Dartmouth News and Scientific American, and listen to a short fun segment on BBC Tech Tent (@18:35).

photo of Matt Jones outdoors on a fall hike at Holt's Ledge

Matt Jones accepts position at Yale Human Nature Lab

May 09, 2022

Graduating PhD student Matt Jones, here enjoying a local fall hike at Holt’s Ledge, has accepted a postdoctoral research position at the Human Nature Lab at Yale’s Institute for Network Science. Part of a collaboration between the lab and the Sunwater Institute, a think tank whose mission is to strengthen the foundations of democracy through interdisciplinary science, technology, and open dialogue, the position has two research directions: group decision-making with a focus on the US Congress, and an evolutionary perspective on human rights and liberties. Matt and other members of Dartmouth’s Fu Lab co-authored the recently published paper Polarization, abstention, and the median voter theorem. Along with his scholarly research, Matt also received the Math Department's Kenneth P. Bogart Teaching Award in 2021 for his dedication to and excellence in advancing the educational mission of the department. Congratulations to Matt on his accomplishments! Photo by Yoonsang Lee

photo of Elizabeth Cascio and Maria Castro ’23

Contributing to economic immigration research with math and social sciences

May 07, 2022

Byrne Scholar Maria Castro ’23, right, took on research last winter seeking to explore the ways in which the 1965 Immigration Act changed the scope of legal immigration into the US. Working with Economics professor Elizabeth Cascio, she compared countries that were impacted far more by the Act to countries largely unaffected by the new legislation. They found that after the Act, the share of unauthorized immigration grew in countries whose restrictions had expanded. “We tried to control for factors like civil wars, natural disasters, and economic disparities as we ran regressions to explore the relationship between unauthorized immigration and countries most affected by the Hart-Celler Act,” says Maria. “My research with Professor Cascio sought to contribute to economic immigration research, which remains largely unexplored.” Maria is an Economics major and LALACS minor interested in exploring research related to labor and public economics.

Professor Sutton receives Dartmouth Social Justice Award

April 22, 2022

Congratulations to Professor Craig Sutton, one of five 2022 Social Justice Award recipients recognized for “outstanding contributions to social justice, peace, civil rights, education, public health, and environmental justice.” The recipients will be presented with their awards on May 23 in a ceremony featuring a speech by Martin Luther King III, whose father delivered a lecture at Dartmouth Hall 60 years earlier. Professor Sutton is director of the E.E. Just Program, which aims to increase the number of students from underrepresented groups who choose to pursue degrees and careers in STEM disciplines. Since 2015, he has also been house professor of School House, one of six house communities designed to increase intellectual and civic engagement as well as cross-cultural exchange. His research interests in differential geometry include Riemannian geometry, spectral geometry, and homogeneous spaces. Please join us in congratulating Professor Sutton on receiving this award! Read more in Dartmouth News.

from left: Matt Jones, Lizzie Buchanan, Alex Wilson

Celebrating Graduate Student Appreciation Week

April 15, 2022

The Department recently hosted a special High Tea in honor of the 31 students in our PhD program. We would like to give our heartfelt thanks to all the graduate students in our program as we celebrate their achievements in scholarship, research, teaching and service! Graduate Student Appreciation Week was started in 1993 by the National Association of Graduate and Professional Students as a way to support and appreciate graduate and professional students. Specifically, the week seeks to emphasize the contributions, impact, and value of graduate and professional students on campuses throughout the United States. From left: Matt Jones (research interests: networks, evolutionary dynamics, game theory, social systems), Lizzie Buchanan (research interests: topology, specifically knot theory), and Alex Wilson (research interests: algebraic combinatorics).

Math Department to host Sonia Kovalevsky Day, Saturday May 21, 2022

April 07, 2022

Sonia Kovalevsky Day is a fun-filled day of mathematics with hands-on workshops and talks for middle and high school female students and their teachers, both women and men. Originally started and funded by the Association for Women in Mathematics, the purpose of the day is to encourage young women to continue their study of mathematics and to assist the teachers of female mathematics students. The Dartmouth Math department hosts this event annually with the goal of inspiring young students to pursue degrees in the mathematical sciences and to honor female mathematicians such as Sonia Kovalevsky, who paved the way with her groundbreaking work and was a strong proponent of higher education for women. We are delighted to hold this fun and inspiring event in person once again!

Math alumna’s paper added to Discrete Mathematics Editor’s Choice list

March 28, 2022

Congratulations to Melanie Fraser PhD ’19, Assistant Professor of Mathematics at Southern New Hampshire University, whose paper Lewis Carroll and the Red Hot Potato: A graph theoretic approach to a linear algebraic identity is featured on the 2022 Editor's Choice list in Discrete Mathematics! In 1866, Charles Dodgson, better known as Lewis Carroll, published an algorithm for computing the determinant of a matrix. Fraser created a new proof of the Lewis Carroll Identity and its equivalence to a graph-theoretic approach called the Forest Identity. The paper is will be freely accessible for the rest of the year, and replication code for the algorithm, coded in Mathematica, is publicly available. While earning her PhD in Mathematics under the supervision of Professor Peter Doyle, Fraser received Dartmouth’s 2019 Graduate Teaching Award. She also gave a talk about the research leading up to her paper at the “AMS Special Session on Advances by Early Career Women in Discrete Mathematics” at JMM 2019.

photo of Feng Fu, Matthew Jones, and Antonio Sirianni

Team at Fu Lab develops contemporary model on voter choice

March 25, 2022

Graduate student Matt Jones, center, is lead author on the paper Polarization, abstention, and the median voter theorem, recently published in Humanities and Social Sciences Communications. With co-authors Feng Fu and Antonio Sirianni, Jones developed a mathematical model in response to apparent limitations in the median voter theorem, long considered the default model of voter behavior and candidate choice. Taking into consideration three contemporary factors — the influence of ideologically motivated third-party candidates, varied reasons for voter abstention, and increasing political polarization — the new model suggests voters may be drawn further to either side of a one-dimensional political spectrum, with the existence of extreme third-party candidates potentially causing a distributional tipping point with a feedback effect. “The minimal number of realistic assumptions necessary to obtain this result makes it all the more compelling and concerning,” state the authors, who propose continued reassessment of existing rational choice voting models. Read more in Dartmouth News.

Professor Pomerance reflects on the life of Richard K. Guy

March 21, 2022

In a touching memorial tribute appearing this month in Notices of the AMS, Professor Carl Pomerance and co-author Andrew Granville write on the remarkable life of mathematician Richard K. Guy, who passed away in 2020 at the age of 103. The article is a fascinating human interest story as well as an exploration into Guy’s mathematical research interests of combinatorial game theory, number theory, and geometry. For Guy, who initially considered himself an enthusiastic amateur mathematician, an encounter with Paul Erdős in 1960 was transformative: “He ended up writing four papers with Erdős, even solving an Erdős problem and developing his voracious appetite for unsolved problems.” For many years Guy ran a Research Problems column in the American Mathematical Monthly, and his books Unsolved Problems in Number Theory and The Book of Numbers (joint with John Conway) continue to inspire and delight both experienced and aspiring mathematicians.

Studying mammalian energy metabolism with Stockholm research lab

March 11, 2022

Byrne Scholar Jacob Fyda ’22 spent two terms last year doing remote research at Stockholm’s Wenner-Gren Institute for Molecular Biosciences, investigating cellular energy metabolisms related to the genetics of thermogenesis of eutherian mammals. Working with PhD student Michael Gaudry in Dr. Martin Jastroch’s Integrative Physiology of Mammalian Energy Metabolism research group, Jacob expanded on previous work he had done in-person at the institute in Summer 2019. “Our findings helped provide additional insight into the evolution of brown adipose tissue and associated genes, with the eventual goal of applying this functional and molecular knowledge to enhance treatment of metabolic diseases, including obesity and diabetes,” says Jacob. “I am incredibly grateful for the generosity of Jack and Dorothy Byrne which allowed me to develop this relationship with the lab.” Jacob’s work in Dr. Jastroch’s group has led to his co-authorship on two papers, the second of which was published in PNAS in January 2022.

The 2022 Thayer Prize Exam

March 05, 2022

Attention first-year students! The Thayer Prize Exam, a contest organized by our department each year, will take place this year on Saturday, April 30 from 10am – 1pm, with location TBD. The Mathematics Department Prize fund for this exam is up to $1000, to be distributed among the exam winners. The exam consists of Mathematics Olympiad style problems, and originality and creativity are heavily weighed. You may view some recent exams for practice, along with a brief history of the prizes and the list of winners from the last 11 years. Please contact Prize Committee Chair Professor Vladimir Chernov at least 10 days in advance if you would like to take the exam but cannot take it on April 30; the alternate date is Sunday May 1.

composite image, left to right: fourth year PhD student Richard Haburcak, Athina Avrantini ’23, and Jenny Song ’23

Directed Reading Program 22W final presentations

March 04, 2022

To conclude a wonderful term of learning mathematics in our Directed Reading Program, students will give final presentations on March 7. Topics include elliptic curves, chaos, the probabilistic method, game theory, knot theory, and fractional calculus. Presentations will be about 20 minutes each with short breaks between talks. Our program pairs undergraduate students with graduate mentors to undertake independent reading projects covering advanced topics in mathematics that are generally not taught at the undergraduate level, fostering a supportive environment for students seeking to further their interest in mathematics. Thank you to everyone who made this possible, especially all of our graduate students who volunteered to mentor this term! From left: fourth year PhD student Richard Haburcak, organizer of the program, along with presenters Athina Avrantini ’23 and Jenny Song ’23. Other undergraduates presenting include Love Tsai ’23, Andrew White ’22, Katie Woolfolk ’23, Jessica Liu ’23, and Gayeong Song ’22.

Research by Neukom Fellow Olivia Chu published in PNAS special feature

February 16, 2022

Neukom Fellow Olivia Chu is co-author of the paper The microdynamics of spatial polarization: A model and an application to survey data from Ukraine, recently published in December’s special feature in PNAS. Chu is a Neukom Postdoctoral Fellow whose research focuses on the dynamics of human behavior and in particular, the effects that heterogeneous population structures have on these dynamics. Mentored by Professor Feng Fu, her research has applications to the evolution of cooperation, social integration, and polarization. In the paper, she and co-authors use a modified version of the adaptive voter model combined with survey data to show how social learning from other individuals in discussion networks can explain growing local consensus, while at the same time exacerbating spatial differences in attitudes. Chu recently presented her work in a virtual seminar at Santa Fe Institute's CounterBalance series on cyberhate, misinformation, social polarization, and other applied aspects of belief dynamics.

poster for MATH 100 / COSC 149.9 / COSC 49.02 (Topics in Probability)

Math 100 in Spring ’22: The Many Faces of Random Walk

February 11, 2022

This spring’s Topics in Probability course (MATH 100 / COSC 149.9 / COSC 49.02) will be “The Many Faces of Random Walk”, taught by Professor Peter Winkler. The class will meet in the 10 hour, MWF 10:10-11:15. Random walk is simple and ubiquitous, both a fascinating topic in its own right and a powerful tool in mathematics and computer science. Course topics will include: reversible Markov chains; electrical networks; Markov chain Monte Carlo; mixing time and approximation algorithms, Rayleigh’s “random flight” theorem; martingales and stock exchange betting; and games and other applications. Prerequisites: mathematical background of a senior mathematics major or a beginning graduate student in mathematics or theoretical computer science, including a course in probability (e.g., MATH 20 or MATH 60). If in doubt, please contact Professor Winkler. (Click/tap to view a larger image of poster.)

Professor Petkova wins prestigious NSF CAREER Award

February 01, 2022

Professor Ina Petkova is a recipient of the National Science Foundation’s Faculty Early Career Development Program (CAREER) award, described as its “most prestigious award in support of early-career faculty who have the potential to serve as academic role models in research and education and to lead advances in the mission of their organizations.” The grant will provide funding over the next five years for her project, Bordered Floer homology and applications, and for mentoring and outreach. As Principal Investigator, Professor Petkova will seek to develop and apply cut-and-paste mathematical tools in low-dimensional topology. She intends to further develop an invariant from bordered Floer homology for contact 3-manifolds with convex boundary, and use this invariant to address open questions in contact topology, an area with applications in physics, including classical mechanics, thermodynamics, and control theory. She also plans to extend bordered Floer homology and tangle Floer homology to integral coefficients and understand and develop the connections between knot Floer homology and quantum algebra.

Zachary Couvillion ’22 receives Byrne Prize

January 23, 2022

Congratulations to Zachary Couvillion ’22, the recipient of the 2022 John J. Byrne Jr. Prize in Mathematics! This prize was established in 2019 and is awarded to the top Dartmouth graduating mathematics major interested in continuing mathematics at the graduate level. “I would say that the algebra track at Dartmouth made a particularly strong impact on my future research interests,“ says Zach. “I studied specializations of Belyi maps with Professor Voight, and some aspects of the project are evolving toward a senior thesis. I hope to begin a PhD program in math in the Fall of 2022 and explore more topics in algebra and number theory. I have received excellent mentorship and support from the math department at Dartmouth, and I am excited to continue this journey in mathematics.”

photo of Peter Winkler in the Math Department

A recent evening of ‘math dinner theatre’ hosted by Professor Winkler

January 14, 2022

Since 2019 Professor Peter Winkler has hosted a series of discussions on “Probability and Intuition” over dinner in New York City. The series, started by MoMath, often focuses on mathematical questions with surprising answers. Professor Dan Rockmore describes one of the gatherings in a recent article in The New Yorker. “You don’t need to be a researcher or math teacher to appreciate the beauty of mathematics, any more than you need to be a composer or performer to enjoy music,” says Winkler. Puzzles are his particular specialty. “Puzzles are my outreach device. I like to use puzzles to teach, to get people excited, and to challenge them to think.” One recent guest reported struggling with a certain puzzle: “On average, how many cards does it take to get to a jack in a shuffled deck of fifty-two cards?” (A good exercise for our readers!) You can register to receive a new puzzle every week from Professor Winkler at mindbenders.momath.org.