Mathematics Research

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.

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 graduating from UC Davis, I went on to obtain a Ph.D. in Economics from Harvard in 1983. I taught for six years as an assistant professor at UC Irvine before moving to Dickinson College in Pennsylvania, where I still teach. Being at a liberal arts college has allowed me to stretch beyond my formal area of expertise. I have done that extensively, working in areas as far-flung as sports psychology, political geography, communications theory, public health, economics pedagogy, as well as a bit of economics. 

Recent emeritus Blake Temple is keeping busy reporting on new results.

After graduating with my Ph.D. in Applied Mathematics in 2020, I started working full-time as a Systems Engineer at NASA's Jet Propulsion Laboratory (JPL) in Pasadena, CA. I had previously interned at JPL during my undergraduate and graduate years, making the transition to a permanent position relatively smooth. As a mathematician in the engineering department at JPL, I tackled a variety of modeling tasks related to both project planning and operations.

I retired in 2015 and bear a title of Professor Emeritus for more than 7 years. It is a common belief that after many years of hard work, emeriti enjoy their well deserved rest, not burdened by any formal duties. It may be true in general, but not in my case. I have an impression that never in my life I worked as hard as now. During my retirement I have never stopped teaching.

Craig was my first graduate student. He has had an extremely productive and distinguished career. Over the decades since I first met Craig we have shared many adventures together. It is hard to believe that he is retiring.

I retired on July 1, 2019 and immediately started a long trip: seven countries in seven months. (I had needed to stay in Davis since 2012.) I visited the Simons Center (Stony Brook, NY), the Institute for Theoretical Physics (Sao Paulo, Brazil), IHES (Bures-sur-Yvette, France), Skolkovo (Moscow, Russia), MPIM (Bonn, Germany), a conference in Luxembourg, Hebrew University (Jerusalem, Israel), Weizmann Institute (Rehovot, Israel), and University of Warwick (UK).