UC Davis has had a long history of fostering research for all it's members and students. It's always important to revisit and adjust programs over time, and now a greater focus is being directed once again at undergraduate opportunities.
Wein and Iyer's NSF CAREER awards. Krener recognized with Quazza Medal. Shkoller and Fraas speak at ICMP 2024. Jacob et al win 2024 Frontiers of Science Award. Vazquez elected AAAS Fellow. De Loera, Schilling, and Thomas recognized for teaching and leadership. Xu wins INFORMS award. Casals awarded MCA Prize. Shkoller to lead COMPASS team.
Imagine a boulder in a stream. As the water hits the boulder, it splits around the object. Once it’s passed around, the two flowing streams crash together, creating turbulent conditions that, if visible, would manifest as chaotic whorls and vortexes. This isn’t just true of water. It’s true of all fluids, including air.
The mathematical equations underlying fluid motion — known as the Navier-Stokes equations — are among the most notoriously challenging partial differential equations because in principle they encode complex behaviors similar to the one you just imagined.
Your DNA contains the genetic blueprint necessary to not just build your body but to build the proteins and molecules that ensure your body’s functionality. DNA encodes RNA, RNA encodes proteins and voila, your body functions.
But the biological reality of this process is much more complex. The shapes, twists and entanglements of your DNA and RNA— their topology — influence their functionality and your health. Damage to DNA, like radiation exposure leading to double-strand breaks, can cause mutations that develop into diseases like cancer.
The equations and theorems were sand scribbles written in the beach by Anne Schilling’s father, a physicist who worked at the European Organization for Nuclear Research (CERN). As her father wrote, Schilling absorbed as much of the information as possible before the Atlantic Ocean’s waves washed the mathematics away, the seafoam acting like an eraser on a blackboard.
On a Sunday morning in September 2023, UC Davis mathematician Roger Casals Gutiérrez was entranced by something he saw in his kitchen.
As sunlight filtered through the kitchen window, it cast its rays in a beautiful pattern on the wall. Comprised of lines, curves and points of varying illumination, the projected pattern appeared both circular and triangular, a hodgepodge of intersecting, nebulous shapes with various spots of brightness.
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.
