University of Calgary
Cristian Rios
- Associate Professor
- Associate Head- Research
- Applied Mathematics
- Mathematics
Research Interests
Currently Teaching
| W2024 - MATH 501 - Measure and Integration | ||||||||||
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| W2024 - MATH 516 - Senior Project | ||||||||||
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| W2024 - MATH 518 - Honours Thesis | ||||||||||
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| W2024 - MATH 601 - Measure and Integration | ||||||||||
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| F2024 - MATH 335 - Analysis I | ||||||||||
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| W2025 - MATH 516 - Senior Project | ||||||||||
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| W2025 - MATH 518 - Honours Thesis | ||||||||||
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| W2025 - MATH 605 - Differential Equations III | ||||||||||
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Conference Organizer
Statement of Graduate Supervision
I am currently seeking graduate students. My specialty is in Analysis and Partial Differential Equations and their Applications. See my research interests and publications for more details. To apply for admission, please see the program requirements for Master or Ph.D., application procedures and the application form. Successful applicants who wish to work with me should have a strong foundation in basic mathematics and mathematical rigour. A background in real analysis, differential equations, and basic algebra is desirable.
Publications
Journal Articles - Peer Reviewed
- Rios, Cristian, Korobenko, L, Sawyer, E and Shen, R. "Local boundedness, maximum principles, and continuity of solutions to infinitely degenerate equations.". Memoirs of the American Mathematical Society 269.1311 (2021): 130. Print.
- 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.
Ph.D. Thesis
- Rios, Cristian. Sufficient conditions for the absolute continuity of the nondivergence harmonic measure 2001.
Degrees
- PhD
University of Minnesota, 2001 - MMath
University of Minnesota, 1998
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