# Professors awarded nsf fellowships

Elizabeth Field

*Alicia Lamarche*

Two professors in the Department of Mathematics each have been awarded a Mathematical Sciences Postdoctoral Research Fellowship from the National Science Foundation. The fellowship is for three years and is given to support future leaders in mathematics and statistics by helping them participate in postdoctoral research that will enhance their development.

Congratulations to both on receiving these awards!

#### Elizabeth Field

Elizabeth Field serves as assistant professor (lecturer). "I'm delighted to have received this award, and I'm very excited to be able to continue as a postdoc at the University of Utah and to pursue research projects which will be supported by this fellowship," said Field. "The Math Department has a fabulous group of undergraduate, graduate, postdoctoral, and faculty researchers in my area, and I'm thrilled to be able to continue to work with them."

Field's research intersects three related fields of mathematics: geometry, topology, and algebra. Geometry and topology both study the "shape" of an object, with geometry focusing on rigid features such as distance, and topology concerned with more fluid notions, such as dimension. The algebraic side of what Field studies provides a formal way of describing how geometric and topological objects interact with various other spaces.

Her research takes inspiration from what is known about finite-type surfaces and 3-manifolds, with the goal of extending results to the setting of infinite-type surfaces, as well as to more general algebraic settings. In general, geometry, topology, and algebra have many applications to areas such as neural mapping, data analysis, and cryptography; however, Field's research is theoretical in nature and doesn't focus on these applications.

Field is grateful for the support and encouragement of the faculty in her research area, especially to Distinguished Professor Mladen Bestvina, who will serve as her official NSF sponsoring scientist, and assistant professor Priyam Patel, who has inspired many of the goals of Field's research.

She received a Ph.D. from the University of Illinois at Urbana-Champaign in 2020 and began teaching at the U in July 2020.

#### Alicia Lamarche

Alicia Lamarche is an assistant professor (lecturer) in the department. “I am incredibly grateful and excited for this opportunity that will allow me to focus on my research goals,” said Lamarche. “I want to thank all of the wonderful mentors, collaborators, and peers that I’ve had the privilege of working with (and learning from) thus far in my mathematical career.”

Her research interests lie somewhere in the intersection of algebraic geometry and number theory. In particular, Lamarche is interested in using techniques from algebraic geometry to answer questions that are traditionally number-theoretic in nature, such as determining if/when a collection of equations has a solution given certain constraints—and examining the geometry of these solutions.

She received a Ph.D. in mathematics under the supervision of Dr. Matthew Ballard from the University of South Carolina in May 2020 and began her postdoc position at the U in July 2020.