Dr. Maria Cristina Pereyra
PhD., Yale University, 1993.
Harmonic Analysis.
Dr. Maria Cristina Pereyra
Professor Maria Cristina Pereyra
Chair (2019-2023)
Department of Mathematics and
Statistics
1 University of New Mexico
MSC01 1115
Albuquerque, NM 87131
Office: SMLC 394
Phone: (505) 277-4613
Fax: (505) 277-5505
E-Mail: crisp AT math DOT unm DOT edu
Biographical Sketch, Wikipedia, French Wikipedia
RESEARCH
My area of research is
Harmonic Analysis,
with particular interest in dyadic harmonic analysis and weighted theory. I have also worked on Hardy spaces defined on product spaces of homogeneous type.
A few years ago I played with
wavelets.
- Publications , Google Scholar Profile
- Books
- Invited Speaker
- Conferences organized recently
- Potential Theory Workshop: Intersections in Harmonic Analysis, Partial Differential Equations and Probability. Sep 28-Oct 06, 2023 - Centro de Investigaciones Matematicas (CIMAT), Guanajuato, Mexico.
- Special Session on Harmonic Analysis and Applications. October 23-24, 2021 - Virtual (originally scheduled at Albuquerque, NM).
- ICM 2018 Satellite Conference in Harmonic Analysis. July 24-29, 2018 - Porto Alegre, Rio Grande do Sul, Brazil.
ICM=International Congress of Mathematicians. Held every 4 years, Field Medals are awarded in the ICM.
- 15th New Mexico Analysis Seminar. February 19-21, 2016 - Albuquerque, NM.
- 14th New Mexico Analysis Seminar. March 26-28, 2015 - Las Cruces, NM.
- Special Session on Weighted Norm Inequalities and Applications. April 5-6, 2014 - Albuquerque, NM. AMS Southwestern Regional Meeting.
- An Afternoon in Honor to Cora Sadosky . April 4th, 2014 - Albuquerque, NM.
- 13th New Mexico Analysis Seminar. April 3-4, 2014 - Albuquerque, NM.
- My Students
To work with me in harmonic analysis you need to have
a background in analysis, including: Introduction to Analysis I and II (Math 510-511),
Complex Analysis (Math 561-562), Analysis III and IV (Math 563-565, covering the basics of Measure Theory, Functional Analysis, Distribution Theory and Fourier Analysis in R^n)
The courses on Fourier analysis and Wavelets (Math 472/572) and
Harmonic Analysis (formerly Math 565) will provide the foundations for this area
of research, this is just the begining... Perhaps the information posted in
Math 565 -
Harmonic Analysis (Spring 2008)
, and in
Math 572/472 -
Fourier Analysis and Wavelets (Spring 2024)
, can help you as a guide on what is expected and
what are good reference books, as well as lecture notes.
An analyst should have a broader background, the connections to differential
equations, geometry and probability, are very important,
and worth exploring. I would start
making sure you have the basics: ODES/PDES (Math 512-513),
(Topology/Differentiable manifolds) Math 535-536, Math 541 (Probability).
Keep an eye open for special topics courses (e.g. Number Theory and Analysis,
Pseudo-differential operators, Non-linear dispersive equations, Martingales,
Quasi-conformal mappings, Global analysis, Operator theory, etc, etc, etc).
Keep an eye open for colloquia and seminars, as my advisor Peter Jones
told me when I was a student, attending seminars is like going to the opera,
you might not understand a word of say, German, but you get the feeling...
PROFESSIONAL SERVICE
- Mathematics and Statistics Department Chair from Fall 2020 to Summer 2023.
- Mathematics and Statistics Department Interim Chair from Fall 2019 to Summer 2020.
- Member Pure and Applied Undergraduate Texts Editorial Committee (Feb 2020 through Jan 2024, renewed for a second term Feb 2024 through Jan 2028).
- Elected Member at Large of the American Mathematical Society (AMS) Council (Feb 2019 through Jan 2022).
- I have been a regular NSF panelist for a variety of panels.
TEACHING
- Courses for Spring Semester 2025
- Office Hours
- TBA
- On zoom: TBA
- By appointment.
- I was the PI for a large NSF grant
Mentoring throught Critical Transition Points (MCTP)
for four years: 2008-2012.
The funded activities include Summer Programs,
Undergraduate Research Projects and Graduate Traineeships.
I am CoPI of an even larger grant (PI is Professor Nitsche)
MCTP
for five years: 2012-2017. The funded activities involve
Summer Programs,
Undergraduate Research Projects, Graduate Traineeships, Postdoctoral Fellows,
a strong education component targeting K12 teachers and outreach to schools
promoting interaction between university and high school students.
- I was Department's Graduate Chair from Fall 2016 to Spring 2017 and from Fall 2006 to Summer 2009. I was in charge of overseeing
all our Teaching and Research Assistants, and other graduate students.
During my tenure we instituted the
Academic Warm-up
as part of the In-service Week.
NEW MEXICO MATH CONTEST
- From 1999-2005 and againg 2024-2025 I am co-director of the
New
Mexico Math Contest exams. For the AY 2023-24 Profs. James Degnan and Stephen Lau were in charge. FOr AY 2022-23 Professor Degnan and Lecturer Michael Heitzman were in charge. FOr the AY 2021-22 Porf. James Degnan and Postdoc Gleb Zelezov were in charge. For the AY 2020-21 Prof. Zeb Chaudhry and Postdoc Gleb Zhelezov were in charge. For the For the AY 2018-20 Profs. Honiang Huang and Zeb Chaudhry were in charge. For the AY 2017-2018, Profs. Janet Vassilev and Hongnian Huang were in charge. For the AY 2016-17, Profs. Janet Vassilev and Daniel Appelo were in charge.
From 2008-2016 Profs. Janeth and Dimiter Vassilev were
in charge of the Contest, they received the contest torch from
Prof. Michael Nakamaye and Cathy Briand who were in charge from 2005-2008.
Before my time Prof. L.-S. Hahn was the heart and soul of the Contest for many years, Prof. Hahn was awarded the "Citation for Public Service" by the "American Mathematical Society" in 1998 because of his work with the New Mexico Mathematics Contest. This distinguished citation is presented annually for notable contributions to the mathematics profession through public service.
CONFERENCES ORGANIZED
