About Me

Recent/Upcoming events


January 4-7, 2023: I presented my research in the ILAS Special Session on Matrices and Operators, and Christina Durón presented our outreach at the SIGMAA MCST Special Session on Math Circle Activities as a Gateway into Math at JMM 2023 in Boston, MA.


January 25, 2023: My paper with Tom Trogdon, "Growth factors of random butterfly matrices and the stability of removing pivoting" (preprint version), has been accepted for publication and will appear in the SIAM Journal on Matrix Analysis and Applications


February 15, 2023: I will present my research in the Mathematical Physics and Probability Seminar at the University of Arizona.


February 26-March 3, 2023: I will present my research in the Butterfly factorizations: Algorithms, applications and theory minisymposium in the SIAM Conference on Computational Science and Engineering (CSE23) in Amsterdam, The Netherlands. I received a SIAM Early Career Travel Grant to support this presentation.


Previous events

Short bio: I am the Richard Pierce Postdoctoral Fellow in the Department of Mathematics at the University of Arizona, mentored by Nick Ercolani. My primary research is in random matrix theory, with an emphasis on applications to problems in numerical analysis, machine learning, data science, statistical modeling, random graphs and number theory. I also am involved in educational research and outreach relating to equal access issues in STEM. I completed my PhD in mathematics from the University of California, Irvine in 2021, under the advisement of Mike Cranston and Tom Trogdon (University of Washington). My dissertation, entitled "Numerical, spectral, and group properties of random butterfly matrices", can be found here.

I completed my AB in mathematics from the University of Chicago in 2006. I then worked for 9 years in the "real world", first as a research analyst with the Social and Economic Sciences Research Center with Washington State University and then as a data analyst/BI engineer with the Office of Research Information Services at the University of Washington. I started my PhD program one month after the birth of my first son (not pictured).

Outside of math, I enjoy running, watching movies, doing trivia, and spending as much time as possible with my family (me+wife+two sons+two dogs). My most recent hobby involves relocating scorpions found in my backyard using a blacklight, although I much prefer not finding scorpions in my backyard using a blacklight.

Pronouns: he/him/his

Contact: johnpeca@math.arizona.edu

Office: Math 710

Address: Department of Mathematics
University of Arizona
617 N Santa Rita Ave
Tucson, AZ 85721