Cristian Rios

Cristian Rios

PhD

Positions

Associate Professor

Faculty of Science, Department of Mathematics and Statistics

Associate Head (Research)

Faculty of Science, Department of Mathematics and Statistics

Contact information

Email

crios@ucalgary.ca

Phone number

Office: +1 (403) 220-3221

Location

Office: MS546

Preferred method of communication

email

I'm looking for...

Learning opportunities

  • Currently accepting PhD students
  • Currently accepting MS students
  • Currently accepting undergraduate research projects

 

Background

Educational Background

Doctor of Philosophy Mathematics, University of Minnesota, 2001

M.S. Mathematics, University of Minnesota, 1998

Licenciado en Matemática Aplicada Mathematics, Universidad Nacional del Litoral, 1993

Técnico Electromecánico Electromechanics, Escuela Industrial Superior, 1988

Research

Areas of Research

Partial Differential Equations

Existence and a priori regularity of solutions. Degenerate elliptic equations.

Participation in university strategic initiatives

Brain and mental health

Child health and wellness

Energy innovations for today and tomorrow

Engineering solutions for health

Human dynamics in a changing world

Infections, inflammation and chronic diseases

New earth-space technologies

One health

Courses

Course number Course title Semester
MATH 501-601 Measure and Integration Winter 2024
MATH 518 Honours Thesis Winter 2024
MATH 516 Senior Project Winter 2024
MATH 335 Analysis I Fall 2023
MATH 367 University Calculus III Fall 2022
MATH 335 Analysis I Fall 2022
MATH 501-601 Measure and Integration Winter 2022
MATH 516 Senior Project Winter 2022
MATH 518 Honours Thesis Winter 2022
MATH 335 Analysis I Fall 2021
MATH 367 University Calculus III Fall 2021
MATH 605 Differential Equations III Winter 2021
MATH 335 Analysis I Fall 2020
MATH 331 Advanced Calculus for the Natural Sciences Winter 2019
EDE 689 Geometry in Nature, Art and Computer Graphics Winter 2019

More Information

Journal articles - peer reviewed

  • L. Korobenko, C. Rios, E. Sawyer and Ruipeng Shen, Local boundedness, maximum principles, and continuity of solutions to infinitely degenerate elliptic equations, Mem. Amer. Math. Soc. 269 (2021), No. 1311
  • Rios, Cristian, David Cruz-Uribe and José María Martell. "On the Kato problem and extensions for degenerate elliptic operators.". Analysis and PDE 11.3 (2018): 609-660. Print.
  • Rios, Cristian, Lyudmila Korobenko and Diego Maldonado. "From Sobolev Inequality to Doubling". Proceedings of the American Mathematical Society 143.9 (2015): 4017-4028. Print.
  • Rios, Cristian and Cruz-Uribe, David. "The Kato problem for operators with weighted ellipticity". Transactions of the American Mathematical Society 367.7 (2015): 4727-4756. Print.
  • Rios, Cristian and Korobenko, Lyudmila. "Hypoellipticity of certain infinitely degenerate second order operators". Journal of Mathematical Analysis and Applications 409.1 (2014): 41–55. Print.
  • Rios, Cristian, Sawyer, Eric and Wheeden, Richard. "Hypoellipticity for infinitely degenerate quasilinear equations and the Dirichlet problem". Journal d'Analise Mathematíque 119. (2013): 1-62. Print.
  • Rios, Cristian and Cruz-Uribe, David. "The solution of the Kato problem for degenerate elliptic operators with Gaussian bounds". Transactions of the American Mathematical Society 364.7 (2012): 3449–3478. Print.
  • Rios, Cristian and Sawyer, Eric. "Smoothness of radial solutions to Monge-Ampère equations". Proceedings of the American Mathematical Society 137.4 (2009): 1373-1379. Print.
  • Rios, Cristian and Cruz-Uribe, David. "Gaussian bounds for degenerate parabolic equations". Journal of Functional Analysis 255.8 (2008): 283-312. Print.
  • Rios, Cristian, Sawyer, Eric and Wheeden, Richard. "Regularity of subelliptic Monge-Ampère equations". Advances in Mathematics 217.3 (2008): 967-1026. Print.
  • Rios, Cristian, Sawyer, Eric and Wheeden, Richard. "A priori estimates for infinitely degenerate quasilinear equations". Differential Integral Equations 21.1-2 (2008): 131-200. Print.
  • Rios, Cristian. "L^p regularity of the Dirichlet problem for elliptic equations with singular drift". Publicacions Mathematíque 50.2 (2006): 475-507. Print.
  • Rios, Cristian, Sawyer, Eric and Wheeden, Richard. "A higher-dimensional partial Legendre transform, and regularity of degenerate Monge-Ampère equations". Advances in Mathematics 193.2 (2005): 373-415. Print.
  • Rios, Cristian. "The L^p Dirichlet problem and nondivergence harmonic measure". Transactions of the American Mathematical Society 355.2 (2003): 665-687. Print.

PhD thesis

  • Rios, Cristian. Sufficient conditions for the absolute continuity of the nondivergence harmonic measure 2001.