2024

During the 2023-2024 academic year, my second year as chair, I focused on getting the new degree requirements approved and on adapting the Group to the new budgetary challenges that the University is facing. 

A tensor is a multi-way array of numbers. An order-1 tensor is just a vector $u \in \mathbb{R}^n$. An order-2 tensor is a matrix $M \in \mathbb{R}^{n_1 \times n_2}$. An order-3 tensor is a 3-way array $T \in \mathbb{R}^{n_1 \times n_2 \times n_3}$, and so on.

Melissa Sherman-Bennett does research in algebraic combinatorics, focusing recently on cluster algebras, total positivity, and connections to particle physics. She received her Ph.D. in 2021 from UC Berkeley, under Lauren Williams. Before coming to Davis, she was a President’s Postdoctoral Fellow at UCLA and NSF Postdoctoral Fellow at Michigan and MIT.

Abi Gopal joined the Department of Mathematics in July 2024 as an assistant professor. Prior to this, he was a Gibbs assistant professor of mathematics at Yale University.

Abi's research is in the field of numerical analysis. He is particularly interested in numerical methods for integral equations, analysis-based algorithms, and numerical linear algebra. His work is primarily motivated by applications in wave propagation and quantum chemistry.

Informally, a mechanical linkage is a system of rigid links (rods or bars) connected by ideal joints and moving in the plane or in the space. This definition suffices for engineering purposes, and one can find it in some form in many engineering books. However, from the mathematical viewpoint, this is not a satisfactory definition.

After earning her B.S. in Mathematics in 1966,  Joan Marie Peters Ogden was a GS-7 mathematician in the Ships' Engineering section in the U.S. Navy in 1966 and 1967. While there, she helped NASA with mathematic modeling for naval ships, modeling ships motions to drive the hydraulics necesary for keeping the communication dish steady, to keep the dishes trained correctly during the Apollo Program.

I spent 10 wonderful years at Davis, completing both my B.S. and Ph.D. in the Department. During my final year of grad school, I interned as a Pathways intern at NASA’s Ames Research Center, and after completing my Ph.D. in 2021, joined NASA as a full time research scientist. 

Melissa Zhang is a low-dimensional topologist who likes to use algebraic, combinatorial, and categorical methods to solve problems. Her favorite topological objects are knots and surfaces smoothly embedded in 3- and 4-dimensional spaces.

She received her Ph.D. from Boston College under the supervision of Eli Grigsby and David Treumann. She was previously a postdoc at the University of Georgia, SLMath/MSRI, and UC Davis (and is now a super-postdoc, as she never left).

We are welcoming 11 new graduate students to the Mathematics Ph.D. program this year, and we have 75 Ph.D. students in total in the program. Last year, 11 of our students completed their Ph.D.’s and have continued their journeys in careers in academia and industry.

This also is the start of my second year as vice chair of graduate affairs. Over the last year, I have tried to approach challenges with empathy and a problem solving mentality. Here are some of the initiatives and challenges from the past year.