Rafael Ceja Ayala, Ph.D.

School of Mathematical and Statistical Sciences

Arizona State University

Email: rcejaaya@asu.edu

Office: Charles Wexler Hall, WXLR 533, Tempe, AZ 85287

My CliftonStrengths: Deliberative, Adaptability, Strategic, Responsibility & Achiever

My name is Rafael Ceja Ayala and I am a Presidential Postdoctoral Fellow at Arizona State University and will be working under the supervision of my mentor Dr. Malena Español. I will be teaching MAT 265 (Calculus for Engineers I) in Fall 2024. I graduated from the mathematics department at Purdue University with a PhD in Applied Mathematics. I am originally from Mexico but at the age of 14, my family and I moved to a small town in Northern California called Ukiah. I am proud to say that I am a product of hardworking immigrants.

At Purdue, I worked under the supervision of Dr. Isaac Harris. Before my journey at Purdue, I graduated from California State University, Sacramento where I studied Mathematics, Latin-American Literature and took some Photography courses.

I have always been passionate about the work that is yet to be done for minoritized students and students of color in mathematics. Through my research and teaching, I hope to make an impact in the mathematics community and also bridge the gap between minorities students and their access to higher education.

Here is a quick link to my Curriculum-Vitae (CV)!

If interested in my photography work click here!

For my poetry, please click on writing!

SOME UPDATES

-I will be attending the Arizona Postdoctoral Research Conference and presenting a poster on my research.

-Invited to give a talk to the seminar on modeling and computation at the University of Arizona at the beginning of October.

-I will be attending the Math Modern Workshop this year at the end of October.

-I will be attending SACNAS 2025 and I am co-organizing a mini-session titled Diverse Perspectives: Interdisciplinary Research in Applied Mathematics.

-Attended ICERM-Empowering a Diverse Computational Mathematics Research Community in July-August 2024.

-Invited to speak at the graduate student panel at Career Paths in the Mathematical Sciences.

-Recipient of the Bilsland Dissertation Fellowship for Spring 2024.

-I participated in the Future Faculty Diversity Program at Virginia Tech October 2023.

-Featured Lathisms mathematician during hispanic heritage month 2023.

-Invited keynote speaker for the Academic Talent Search at Sonoma State University May 2023.

Education

B.A. in Mathematics, California State University, Sacramento, 2018

M.S. in Applied Mathematics, Purdue University, 2022

PhD in Applied Mathematics, Purdue University, 2018 -2024

Presidential Postdoctoral Fellow, Arizona State University, 2024-present

Research

My research interests are in Inverse Problems for Partial Differential Equations. I work with problems related to transmission eigenvalues and reconstructions of small and extended regions using different areas of Functional Analysis and Scattering Theory. These problems arise in many physical applications such as nondestructive testing and detecting defects in complex structures.

Accepted in Analysis and Mathematical Physics: R. Ceja Ayala, I. Harris, and A. Kleefeld "Inverse parameter and shape problem for an isotropic scatterer with two conductivity coefficients". Analysis and Mathematical Physics, 14 No. 90 (2024) (arXiv:2402.07880)

Submitted: A. Alvarado, R. Ceja Ayala, E. Knutsen, and J. Turner ”Investigation of the Collatz Function in the Gaussian and Eisenstein Integers.”

Accepted in Inverse Problems and Imaging: R. Ceja Ayala, I. Harris, and A. Kleefeld ''Direct sampling method via Landweber iteration for an absorbing scatterer with a conductive boundary''. Inverse Problems and Imaging DOI:10.3934/ipi.2023051 (arXiv:2305.15310)

Accepted in Applicable Analysis Journal: R. Ceja Ayala, I. Harris, A. Kleefeld, and N. Pallikarakis ''Analysis of the transmission eigenvalue problem with two conductivity parameters''. Applicable Analysis, DOI: 10.1080/00036811.2023.2181167 (2023) (arXiv:2209.07247)

Research Interests: Direct and Inverse Scattering, Transmission Eigenvalue Problems, Inverse and Inverse Problems for PDEs and Numerical Methods.

The figure is a reconstruction using an interpolating polynomial of degree M = 4 of a peanut region by the Landweber direct sampling method. Images left to right: reconstruction using equidistant points, singular values, and Gaussian quadrature points.

Honors

Presidential Postdoctoral Fellow 2024-present

Bilsland Dissertation Fellow Spring 2024

Gates Millennium Fellowship 2018 - 2024

Purdue Doctoral Fellowship 2018 - 2022

Gates Millennium Scholarship 2014 - 2018

McNair Scholars Program (2016 Cohort)

The California State University Louis Stokes Alliance for Minority Participation (page 45) (CSU-LSAMP) 2014-2018