Cristian Rios
Positions
Associate Professor
Faculty of Science, Department of Mathematics and Statistics
Associate Head (Research)
Faculty of Science, Department of Mathematics and Statistics
Contact information
Phone number
Office: +1 (403) 220-3221
Location
Office: MS546
Preferred method of communication
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
Existence and a priori regularity of solutions. Degenerate elliptic equations.
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.
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