Rafael Ceja Ayala, M.S. (He/Him), PhD Candidate
Department of Mathematics
Purdue University
150 N. University Street, West Lafayette, IN 47907
Office: MATH 645
Email: rcejaaya@purdue.edu
My name is Rafael Ceja Ayala and I am a sixth year PhD candidate in the mathematics department at Purdue University. 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 currently work 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 I took some courses in Photography.
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 a bridge the gap between minorities students and their access to a higher education.
Here is a quick link to my Curriculum-Vitae (CV)!
If interested about my photography work click here!
SOME UPDATES
1. Writing my dissertation at this moment.....
2. Attended SACNAS National Diversity in STEM Conference.
3. I participated in the Future Faculty Diversity Program at Virginia Tech October 2023.
4. Featured Lathisms mathematician during hispanic heritage month 2023.
5. Recipient of the Bilsland Dissertation Fellowship for Spring 2024.
6. Invited keynote speaker for the Academic Talent Search at Sonoma State University May 2023.
7. I participated in the Pre-Doctoral Scholars program at Oregon State University March 2023.
8. I was featured in the mathematics department as the Mathematics Student Feature for the month March 2023.
Graduate Student Analysis Seminar (on hold)
This semester (Spring 2024) I am organizing the Graduate Student Analysis Seminar, where our mission is to provide a comfortable, safe, and enriching space where graduate students can talk about analysis and other related topics in mathematics. We hope this seminar provides participants with space for open discussion and greater insight into topics that can inspire a further understanding of mathematics. If you would like to give a talk do not hesitate to contact us.
Send us an email if you would like to give a talk or want to be part of our email list!
Either email Sebastian Muñoz Thon or Rafael Ceja Ayala at smunozth@purdue.edu or rcejaaya@purdue.edu
Basic Skills Workshop
I am also part of the Basic Skills Team in the department of mathematics. The workshop was founded in 2012 as a part of Purdue University's Association for Women in Mathematics by Lidia Mrad to provide workshops to Purdue graduate students providing skills outside the traditional academic setting. We cover topics such as navigating graduate school, teaching, career planning, using technology for professional purposes, etc. Students can register for the Basic Skills Workshop as a one-credit-hour seminar course during the fall and spring semesters.
Mentorship
I am part of the Alliance for Graduate Education and Professoriate (AGEP) Scholars program and through this program I have been mentoring undergraduate students who are part of the Louis Stokes Alliance for Minority Participation Program here at Purdue University.
LSAMP Purdue Program Mentor: Prinitha Senthil (Computer Science) & Kyndahl Bishop (Mathematics) (Spring 2023)
LSAMP Purdue Program Mentor: Loahni Hernandez (Fall 2022)
LSAMP Purdue Program Mentor: Jessica Soleto and Gabriel Muzio (Spring 2022)
LSAMP Purdue Program Mentor: Santiago Lopez and Oliver Bonilla (Fall 2021)
This year I am mentoring an incoming PhD student through the Association of Women in Mathematics chapter at Purdue University.
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 - 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.
In Progress: “Inverse parameter and shape problem for an isotropic scatterer
with two conductivity coefficients”. (Under Preparation-Working Title)
with two conductivity coefficients”. (Under Preparation-Working Title)
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
Bilsland Dissertation Fellow Spring 2024
Gates Millennium Fellowship 2018 - Present
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