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

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!

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

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. Melanie 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, Melanie 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.

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

Math Department and AWM Essay Contests

January 13, 2022

For the sixth 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 six 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, 2022. View detailed information including contest rules, tips on choosing an interviewee, and lists of past winners. Last year two local students won prizes at the national level! (Click/tap to view a larger image of poster.)

composite image of class of 2025 Byrne Scholars, left to right: Ahrav Jain, Garrett H. Cheng, Carter Kruse; second row, left to right: Harrison Stropkay, Logan Dailey, Allison Zhuang, Andrew Xu; third row, left to right: Niccolo Campolo, Tunmay Gerg, Katie Cox

Introducing the Class of ’25 Byrne Scholars

January 12, 2022

The Math Department warmly welcomes the Class of 2025 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: Ahrav Jain, Garrett H. Cheng, and Carter Kruse. Second row, left to right: Harrison Stropkay, Logan Dailey, Allison Zhuang, and Andrew Xu. Third row, left to right: Niccolo Campolo, Tunmay Gerg, and Katie Cox. (Not pictured: Clark Paolini.)

photo of Dan Rockmore in front of a blackboard

Professor Rockmore writes on proofs in The New York Review of Books

January 03, 2022

In the January 13, 2022 issue of The New York Review of Books [may require subscription], Professor Dan Rockmore gives a delightfully erudite review of Philip Ording’s 99 Variations on a Proof. Ording’s book was inspired by Raymond Queneau’s Exercises in Style (1947) and is wide in scope and style — deep, historical, amusing, and playful — as is Professor Rockmore’s review. “Mathematics is writing,” says Rockmore. A proof is “as close to the written transmission of one person’s pure thought as any writing can be. But even in mathematical writing, it’s not just what you say but how you say it — better known as style.” Rockmore, Professor of Mathematics and director of the Neukom Institute, is co-editor of the recently published book Law as Data: Computation, Text, & the Future of Legal Analysis.

photo of Dartmouth Formula Racing competing in the Autocross Event at 2018 Formula Hybrid

Independent research with Dartmouth Formula Racing at Thayer

January 02, 2022

With support from the generous Byrne gift, Byrne Scholar and Thayer School of Engineering student Ben Martin ’22 pursued an independent research project this past summer designing a testing setup to experimentally determine the braking characteristics of the Dartmouth Formula Racing team’s current generation of brake system. DFR designs and builds hybrid race cars to compete in the Formula Hybrid annual competition in New Hampshire; Dartmouth’s team has been competing in automotive engineering design competitions since 1995, and has competed in Formula Hybrid since its inauguration in 2006. “I planned out experiments to determine kinetic and static coefficients of friction between the pads and rotors at various temperatures, thermal response of the brake system at different levels of energy dissipation, and long term wear characteristics,” says Ben, who is Brakes Team Lead and Manufacturing Team Lead at DFR. DFR photo by Kathryn Lapierre.

composite photo of Richard Haburcak, Matt Jones,Sam Tripp, Grant Molnar, Juanita Duque-Rosero, Jonathan Lindbloom, Yanbing Gu, Kathy Lin, Matthew Ellison, and Ben Adenbaum

Directed Reading Program continues in Winter and Spring 2022!

December 07, 2021

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 2022 DRP is December 24. Clockwise from top left: program organizer Richard Haburcak along with DRP graduate mentors Matt Jones, Sam Tripp, Grant Molnar, Juanita Duque-Rosero, Jonathan Lindbloom, Yanbing Gu, Kathy Lin, Matthew Ellison, and Ben Adenbaum.

photo of Joe Gyorda ’22 with Dartmouth Triathlon Team members

Modeling athletic performance using mathematical data science

December 06, 2021

Byrne Scholar and Mathematical Data Science major Joe Gyorda ’22, second from left, interned this summer at HALE Sports, which seeks to optimize the health and performance of athletes through analyzing somatic and biometric data. “The first team was building a computer vision model in which athletes could receive real-time feedback on various exercises (e.g., squat, pushup) to correct their form. Machine learning and body pose estimation models were implemented to analyze body position/angles and identify correct/incorrect form,” says Joe, himself a triathlete. In his second team Joe worked with longitudinal somatic survey data collected from college athletes, with the goal being to implement clustering algorithms to track athlete variables over time and using predictive models to determine which variables (e.g., energy, mood) are impacted by changes in another (e.g., sleep). “I am very grateful for the generosity of the Byrne Fund for supporting me and my work!”

Daniel Krashen to give C. Dwight Lahr Lecture

November 09, 2021

Daniel Krashen, Presidential Professor of Mathematics at the University of Pennsylvania, will give a public lecture titled Professional empathy at 3:15 p.m. on Tuesday November 16 in Kemeny 008. Dr. Krashen’s research is in algebra and arithmetic geometry, specifically the study of division algebras, quadratic forms, and linear algebraic groups. These areas have connections to a wide range of fields, including physics and cryptography. He has been awarded multiple NSF grants, including a CAREER award and the prestigious Presidential Early Career (PECASE) award. He is a fellow of the American Mathematical Society. Dr. Krashen has been active in promoting outreach and diversity in mathematics at a range of levels, from middle school through early career professors, including in his work on the editorial boards of the Notices of the American Mathematical Society and the American Mathematical Monthly.

image from Dimitris Giannakis' paper 'Bridging Data Science and Dynamical Systems Theory', featured in the October 2020 issue of Notices of the American Mathematical Society

Professor Giannakis’ research highlighted in the Concord Monitor

November 03, 2021

Professor Dimitris Giannakis, whose research connects ideas from data science, machine learning, and dynamical systems theory, was recently quoted in an article in the Concord Monitor [may require subscription], speaking on the development of mathematical frameworks to improve understanding of complex systems such as the earth’s climate dynamics. “We are combining this existing body of theoretical knowledge from abstract math with data science ... to identify phenomena in nature and generate questions that are relevant at the abstract mathematical level as well as the world,” he says. “It brings in a lot of different fields of mathematics in one arena.” This image is from his paper Bridging Data Science and Dynamical Systems Theory (co-authored with Tyrus Berry and John Harlim), which was featured in the October 2020 issue of Notices of the American Mathematical Society. “I think mathematics is very beautiful as a language; beautiful in its own right, without reference to anything else,” says Professor Giannakis, who is a member of the Jack Byrne Academic Cluster in Mathematics and Decision Science.

Byrne Scholar Archita Harathi ’22 inducted into Phi Beta Kappa

November 02, 2021

Congratulations to Byrne Scholar Archita Harathi ’22, one of 22 students recently inducted into Phi Beta Kappa in this year’s fall ceremony at Dartmouth. Archita, who is majoring in Math and Economics and minoring in Computer Science, has been supported by Byrne funds in several endeavors: a summer ’21 investment banking internship at Goldman Sachs in the structured finance group; a virtual winter ’21 management consulting internship focusing on technology, media, and telecom industries at Altman Solon; and, during her freshman summer, research abroad at the British Antarctic Survey in Cambridge. Archita also received the Town Scientific Prize for her achievement in mathematics in 2020. When not busy with academics, Archita finds time to study Indian classical music and competed in this year’s Dartmouth Idol with the help and guidance of Walt Cunningham at the Hop.

Professor Fu receives Dean of the Faculty Award for Outstanding Mentoring and Advising

October 21, 2021

Professor Feng Fu is among thirteen members of the Faculty of Arts and Sciences who have been recognized for exceptional achievement in scholarship, teaching, and mentoring for 2021. We congratulate Professor Fu on his many successes, as well as those of his students and mentees! “I am very fortunate to have the opportunity of working with our group of talented students at all levels,” says Professor Fu. “I am particularly passionate about working with both undergraduate and graduate students, and always do my best to help them to succeed in their later careers (academia and industry) after training in my lab.” The Fu Lab invites creative and self-motivated scientists (postdocs, graduate students, and undergraduates) to join the research group.

composite photo of Shikhin Sethi ’19, Matt Radosevich ’20, and Jacob Swenberg ’21

2022 Byrne Prize in Mathematics: accepting applications

October 18, 2021

We are now accepting applications for the 2022 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 Shikhin Sethi ’19, Matt Radosevich ’20, and Jacob Swenberg ’21.

composite photo of 2021 Dartmouth AWM exec board: Kayla Hamann ’22, Paola Karapataki ’22, Lizzie Hernández-Videa ’22, Jenny Song ’23, and Sonal Butala ’22.

Join math organizations on campus!

October 17, 2021

Math orgs on campus include Dartmouth SIAM (faculty advisors: Scott Pauls and Feng Fu), Dartmouth Math Society (faculty advisors: Vladimir Chernov and Rosa Orellana), and the Dartmouth AWM student chapter (faculty advisors: Carolyn Gordon and Rosa Orellana). This term the Dartmouth AWM exec board would like to share news of the AWM’s 50th anniversary We Speak: Inspiring Women in Math Speaker Series, featuring talks by women who have made a positive difference in the mathematics community. Clockwise from upper left: Current members of the Dartmouth AWM exec board Kayla Hamann ’22, Paola Karapataki ’22, Lizzie Hernández-Videa ’22, Jenny Song ’23, and Sonal Butala ’22.

Welcome Assistant Professor Ethan Levien

October 11, 2021

The department welcomes Assistant Professor Ethan Levien, whose research interests include stochastic processes, mathematical biology, and applied statistics. Professor Levien, who will be starting his own research group in our department, obtained his PhD in Mathematics from the University of Utah, where he studied the stochastic dynamics of chemical reaction networks. He went on to spend three years as a postdoctoral fellow in applied mathematics at Harvard University and Brandies University. His current research focuses on the role of randomness in biology, especially single-cell physiology and evolution. “Using mathematics, I try to answer questions such as: How do cells regulate their size? Why do certain traits appear to evolve separately in distinct organisms? What causes physiological differences in genetically identical cells?”

film poster for Adventures of a Mathematician

Film screening of Adventures of a Mathematician, 5 p.m. on Friday October 15

October 10, 2021

Join us at 5 p.m. on Friday, October 15 in Kemeny 008 for a screening of the movie Adventures of a Mathematician. Released in theaters last week, the film is a thought-provoking account of Jewish-Polish immigrant and mathematician Stan Ulam, who flees to the US in the 1930s. There, Stan helps build the first computer and create the hydrogen bomb. View more information, including the trailer! There will be an introduction and Q&A with the film director Thor Klein and the science advisor George Dyson at 5pm, followed by the screening. RSVP is encouraged to help us with planning. Sponsored by the Jack Byrne Scholars Program.

Byrne Scholar develops software for ESL tutoring startup

October 09, 2021

Supported by the Byrne gift, Byrne Scholar Anne Bailey ’22 interned at language-learning startup Cambly, whose web and mobile apps facilitate learning English as a second language by connecting students with tutors around the world. During her time at Cambly, Anne developed a system using the AWS Lambda service and learned much about developing scalable software along the way — something not necessarily easy to learn in the classroom. “Overall, this internship taught me a lot about full-stack software engineering, and I had a great time,” Anne says. “As a computer science major and linguistics minor, working as a software engineer intern at a language-learning company was a great intersection of my interests.”

poster for Prosser lecture by Christopher Moore, with photo and abstract

Christopher Moore to give Reese T. Prosser Memorial Lecture

September 30, 2021

Cristopher Moore, Professor at the Santa Fe Institute, will give a lecture titled Easy, Hard, and Impossible: The Limits of Computation at 6 p.m. on Wednesday, October 6 in 008 Kemeny Hall. From the abstract: “Every day we ask computers to solve problems for us — to find the fastest route across town, fold a protein into the right shape, or prove an unsolved mathematical question. In each case the space of possible solutions is vast. Why is it that for some problems, we can quickly zoom in on the solution, while for others it’s like looking for a needle in a haystack? What is it about the structure of a problem that makes it easy, or hard, or even impossible to solve?” (Click/tap to view a larger image.)

composite photo of Peter Mucha and Dimitris Giannakis

Professors Mucha and Giannakis join the Jack Byrne Academic Cluster

September 27, 2021

Professors Peter Mucha and Dimitris Giannakis are the newest members of the Jack Byrne Academic Cluster in Mathematics and Decision Science, as reported in a recent Dartmouth News story. Part of the Academic Cluster Initiative, the Byrne cluster focuses on applying mathematical thinking to some of society’s major challenges in health care, transportation, and manufacturing. Peter Mucha, Jack Byrne Distinguished Professor in Mathematics, notes that “the Byrne Cluster was particularly appealing to me because its goals are so well aligned with the activities of my research group, both developing new mathematical tools for analyzing data and working with others to use those tools in different applications.” Dimitris Giannakis, Jack Byrne Professor in Mathematics, looks forward to working across disciplines: “One of my primary research areas is climate dynamics, and I am excited about the opportunities that the Byrne Cluster will provide for innovative work in this area, in both its physical and societal dimensions.”

portion of image representing advisor and advisee connections between Fields Medalists, with nodes color-coded by lingo-ethnic identity

Herbert Chang ’18 and Professor Fu publish study on mathematical elitism

September 20, 2021

The Fields Medal is awarded to only a few young mathematicians every four years and was, in part, intended to recognize underrepresented mathematicians. In their analysis Elitism in mathematics and inequality, published in Humanities and Social Sciences Communications and referenced in Scientific American, former Byrne Scholar Ho-Chun Herbert Chang ’18 and Professor Feng Fu explore how 60 Fields Medal recipients relate to each other and to the broader community of mathematicians. They find that while the medal has helped to promote some previously underrepresented groups, a “Western bias” is still evident, along with an under-representation of minority groups. In particular, the study found that 44 out of 60 Fields medalists come from a highly interconnected group of mathematicians. Image by Shirley Wu.

Research by Alina Glaubitz featured in SIAM News

September 09, 2021

In July SIAM News highlighted research by second-year graduate student Alina Glaubitz (joint with Professor Feng Fu) and her work on the oscillatory dynamics of social distancing. In her presentation, delivered virtually at the 2021 SIAM Annual Meeting, Alina described how she and Professor Fu incorporated an evolutionary game theory model into the epidemiological process, revealing the presence of a feedback loop between infections and social distancing. This feedback loop, an “oscillatory tragedy of the commons,” can lead to multiple waves of infection in emerging novel zoonotic diseases, such as COVID-19, which are caused by respiratory viruses and are highly contagious through proximity transmissions.

composite photo of Carl Pomerance and the fictional character Sheldon Cooper

Professor Pomerance asks ‘Is 73 the best number?’

September 08, 2021

Professor Carl Pomerance was an invited speaker to a recent conference of the Northeastern Section of the MAA. His talk, ‘Is 73 the best number?’, was connected to his paper Proof of the Sheldon Conjecture (co-authored with Chris Spicer), which proved a mathematical concept inspired by an episode in the CBS series The Big Bang Theory. As stated in his talk’s abstract, “According to Sheldon Cooper, the often annoying lead character in the TV sitcom The Big Bang Theory, 73 is the best number. And he's eager to tell you why. But is it really? In joint work with Chris Spicer (Morningside College in Iowa), we show Sheldon just may be right.” Sheldon photo credit: Michael Yarish/©2019 Warner Bros. Entertainment Inc.

composite photo of Jonathan Meng ’18 and Feng Fu

Joint paper by Jonathan Meng ’18 and Professor Fu published in Royal Society Open Science

September 05, 2021

Jonathan Meng ’18 and Professor Feng Fu have recently published the paper Understanding gambling behaviour and risk attitudes using cryptocurrency-based casino blockchain data in Royal Society Open Science. The research was funded by the Neukom Scholars Program and Neukom-Vechain RFP. Their joint work was based on Jonathan’s mathematics senior honors thesis, Understanding Gambling Behavior and Risk Attitudes Using Massive Online Casino Data, for which Professor Fu served as advisor.

image from Craig Sutton's article 'Spectral geometry in the presence of symmetry', featured in the June/July 2021 issue of Notices of the American Mathematical Society

Professor Sutton’s research featured in Notices of the AMS

August 12, 2021

The article Spectral geometry in the presence of symmetry by Professor Craig Sutton was featured in the June/July issue of Notices of the American Mathematical Society. This image from the paper represents a cubical tiling of hyperbolic three-space $\Bbb{H}^3$, one of the eight Thurston geometries. Professor Sutton, whose research interests in differential geometry include Riemannian geometry, spectral geometry, and homogeneous spaces, is currently the House Professor of the School House community and is director of Dartmouths’s E.E. Just Program. Image courtesy of Steve Trettel.

composite image of 2021 incoming graduate students, clockwise from upper left: Jiayi Chen, Haochen Wu, Casey Dowdle, Anna Vasenina, Peter Nielsen, Yanbing Gu, and Jonathan Lindbloom