I am a Ph.D. candidate at the University of Wisconsin-Madison studying mathematics and plan to graduate in Spring 2026. My research interests are in nonlinear dispersive PDEs. Specifically, low regularity well-posedness and global dynamics of solutions to dispersive equations. My advisor is Mihaela Ifrim. My graduate minor is in Education, as I'm also very passionate about teaching!
I am originally from Southern California and completed my undergraduate at North Dakota State University. Outside of math I like to run, boulder, and knit.
Email: abyars@wisc.edu
Office: Van Vleck 518
Conferences:
SIAM Great Lakes Section Annual Meeting, Illinois Institute of Technology, Chicago, IL, September 2025
Advances in Dispersive Equations: Challenges and Perspectives, CIRM, Marseille, France, May 2025
Rivière-Fabes Symposium on Analysis and PDE, University of Minnesota, April 2025
Workshop on Kinetic Theory and Fluids, Madison, WI, March 2025
Seminar Talks
UC Berkeley, Analysis and PDE Seminar, October 2025
CUNY, Harmonic Analysis and PDE Seminar, October 2025
UC Davis, PDE and Applied Math Seminar, October 2025
University of Maryland, PDE-Applied Math Seminar, September 2025
Michigan State University, Analysis and PDE Seminar, September 2025
To see a full list of conferences I've attended, see Activities.
Organizations:
I was one of the organizers and founders (with Summer Al Hamdani) of GAPS! In this seminar, graduate students in Analysis and PDEs give talks about their research, a result they use in their research, or something they find interesting. The goal is to have accessible talks so that first and second years can also participate and get to know what people in the department are working on.
I co-organized GmMaW, a group which is a supportive place for gender minorities in math and seeks to grow this community through events and outreach.
I co-organized the DRP, which pairs undergraduates with a graduate mentor for a semester long reading project. I also lead a DRP project in the Spring of 2022, where we read Measure, Topology, and Fractal Geometry
Other Service:
I was a mentor for Girls math night, where I meet weekly with a high schooler to discuss topics not usually covered in school. Currently we are reading about metric spaces.
CTAPP:
I served on the Committee for TA Policies and Procedures (CTAPP), where we reviewed TAs to make sure they are doing well, address any concerns about TAs, and decide on departmental TA awards. We occasionally also met to discuss changes to TA requirements.
GPC:
I also serve on the Graduate Program Committee (GPC), where we make decisions about the graduate program such as course offerings/qualifying exams, new graduate courses being offered, minor requirements, etc.