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What’s happening in Math

Welcome to Dartmouth Mathematics

Graduate Students

Congratulations to our recent PhDs!

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 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

Alumni News

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

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!

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

Department News

Directed Reading Program 22S final presentations

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 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
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Recent Publications

Sequential Image Recovery from Noisy and Under-Sampled Fourier Data

Yao Xiao, Jan Glaubitz, Anne Gelb, Guohui Song

Journal of Scientific Computing

A bipartite graph-based expected networks approach identifies DDR genes not associated with TMB yet predictive of immune checkpoint blockade response

William H. Weir, Peter J. Mucha, William Y. Kim

Cell Reports Medicine

Unramified Brauer groups of conic bundle threefolds in characteristic two

Asher Auel, Alessandro Bigazzi, Christian Böhning, Hans-Christian Graf von Bothmer

American Journal of Mathematics

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