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What’s happening in Math

Image courtesy of Bjoern Muetzel.

Welcome to Dartmouth Mathematics

Faculty and Graduate Student Research

Research by four department authors published in PNAS

Second-year PhD student David Freeman, Professor Dimitris Giannakis, third-year PhD student Brian Mintz, and Professor Joanna Slawinska are authors of the paper Data assimilation in operator algebras, recently published in PNAS. The paper grew out of a collaboration with Slawinska and Abbas Ourmazd (University of Wisconsin–Milwaukee) on using techniques from ergodic theory and quantum mechanics to perform sequential data assimilation of partially observed dynamical systems, with applications in climate dynamics. In 2021 work by Giannakis, Freeman, and Mintz as part of graduate independent reading course furthered the research: “During that course and in the subsequent months, we developed a formulation that views data assimilation as information processing through a quantum channel associated with algebras of observables of the dynamical system,” says Giannakis. “Classical (Bayesian) and ‘quantum’ data assimilation correspond to abelian and non-abelian choices of that algebra, respectively, which we believe provides an interesting unified viewpoint that offers opportunities for new algorithms for forecasting dynamical systems.”

clockwise from top left: David Freeman, Dimitris Giannakis, Joanna Slawinska, and Brian Mintz

Graduate Students

Interning at Los Alamos National Laboratory

Second-year applied mathematics PhD student Jonathan Lindbloom traveled to New Mexico last summer for an internship at Los Alamos National Laboratory, where he worked with the Theoretical Division's T-1 group (Physics and Chemistry of Materials) on the project Surrogate Modeling for High Explosives Diameter Effect Calculations. Lindbloom’s research interests include learning about computational methods for solving Bayesian inverse problems and quantifying uncertainty. He has been a graduate student mentor in our department’s Directed Reading Program, guiding undergraduates in the topics Nonlinear Dynamics, Chaos, And Ergodicity and Bayesian Modeling And Computation. This photo, taken in fall 2021, shows Lindbloom in the White Mountains on his way to hike Mount Carrigain, one of New Hampshire’s 48 four-thousand footers.

Jonathan Lindbloom in the New Hampshire White Mountains

Department News

Math Department’s Directed Reading Program featured in Dartmouth News

Hearty congratulations to all the organizers, mentors, and undergraduates who have participated in our department’s successful Directed Reading Program! A recent Dartmouth News story describes how graduate student Richard Haburcak founded the program in 2021 with the idea of it being inclusive from the start: “The DRP strives to increase diversity in mathematics and foster a supportive environment for students to explore mathematics,” says Haburcak. “We want to give students the chance to see math the way that mathematicians see math, to see the human side of math, and to be able to learn about topics that you usually don't have the chance to study until much later.” At the recent 23W poster session in March, Sofia Goncalves ’25 presented her work Mathematics in Magic: Looking into the Magic of Universal Cycles. Sofia’s mentor was fifth-year graduate student Alex Wilson, whose research focuses on algebraic combinatorics, specifically combinatorial representation theory. Photo by Lizzie Buchanan

graduate student Alex Wilson and Sofia Goncalves ’25
More news

Recent Publications

On Harmonic Hilbert Spaces on Compact Abelian Groups

Suddhasattwa Das, Dimitrios Giannakis

The Journal of Fourier Analysis and Applications

Graph-theoretic algorithms for Kolmogorov operators: approximating solutions and their gradients in elliptic and parabolic problems on manifolds

Andrew D. Davis, Dimitrios Giannakis

Calcolo: a Quarterly on Numerical Analysis and Theory of Computation

Howe duality of the symmetric group and a multiset partition algebra

Rosa Orellana, Mike Zabrocki

Communications in Algebra

More publications

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