geometry and topology

The last time UC Davis saw me was when graduated in the summer of 2018 with a Ph.D. in Mathematics. My dissertation was in low-dimensional topology under Abby Thompson, focusing on Heegaard splittings of knot complements in the 3-sphere (with additional mentorship of Javier Arsuaga in the application of knot theory to molecular biology, particularly the folding of chromosomes in yeast). Only a few months prior to that, I had accepted an offer to join the faculty at University of the Pacific (UOP) in Stockton, CA, as a tenure-track assistant professor of applied mathematics.

Sneha Chaubey is visiting the Department of Mathematics in the Fall quarter of 2025 as a Visiting Associate Professor. She is an Associate Professor of Mathematics at IIIT-Delhi, India. Her research interests lie in number theory and its interactions with geometry and dynamics. She is especially interested in analytic number theory, the distribution of sequences and their spacing statistics, using level spacing statistics and correlation measures, zeros of L-functions, and exponential sums. 

Maria received her Ph.D. in 2012 from Palacky University in the Czech Republic, but most of her study time she spent at Princeton University, where she worked under the supervision of David Gabai. Afterwards, she was an instructor at Caltech and in 2016 she joined UC Davis, first as a KAP and then continued as a lecturer. She is primarily interested in Geometry and Topology. She had collaborated with Joel Hass on imaging problems. After a break for sabbatical and maternal leaves, she is excited to be back in the department and teaching again.

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.

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.

Jared Krandel is a new KAP who will be starting at UC Davis in January 2025. He graduated from Stony Brook University in Spring 2024 and is spending this Fall as a postdoc at SLMath in Berkeley. Most of his work so far has been in an area of geometric measure theory called quantitative rectifiability. He studies geometric properties of rectifiable curves and surfaces through things like analyst's traveling salesman problems, characterizations of uniform rectifiability, parameterizability problems, and more. 

Yoon Jae "Nick" Nho is a Krener Assistant Professor, mentored by Professor Roger Casals. His research is in symplectic geometry and topology, and he is interested in geometric structures that are related to physics. He received his Ph.D. from the University of Cambridge in August 2024, under the supervision of Professor Ailsa Keating. 

He is from South Korea, and his hobbies include reading books, watching films, and listening to music.

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.