Erica de la Canal

I am fifth year PhD Candidate in Mathematics at The University of Texas at Austin, under the supervision of Prof. Irene M. Gamba.

Previously, I got my Licenciatura en Ciencias Matemáticas Diploma from Universidad Nacional de Mar del Plata, with the Licenciatura thesis "Direct and inverse sharp Young's inequality and its applications to Information theory", under the supervision of Prof. Irene M. Gamba and Prof. Sandra Molina. (If you know Spanish, you can read it here.)

Research interests

I am interested in analysis aspects of kinetic theory, in particular in the Boltzmann equation. I am currently working on the system of Boltzmann equations for a mixture of monatomic gases, with my advisor and Prof. Milana Pavić-Čolić..

Publications

• Erica de la Canal, Irene M. Gamba, Milana Pavić-Čolić. Propagation of L^p_β norm, 1 < p ≤ ∞ , for the system of Boltzmann Equations for monatomic gas mixtures , ArXiv: 2001.09204 (2020).
• Erica de la Canal, Irene M. Gamba, Milana Pavić-Čolić (2021). On existence, uniqueness and Banach space regularity for solutions of Boltzmann equations systems for monatomic gas mixtures. In C. Bernardin, F. Golse, P. Gonçalves, V. Ricci, & A. J. Soares (Eds.), From Particle Systems to Partial Differential Equations: International Conference, Particle Systems and PDEs VI, VII and VIII, 2017-2019. Springer.

Awards

• 2020-2021: University Graduate Continuing Fellowship at UT Austin, USA

• 2017-2018: Frank Gerth III Teaching Excellence Award at UT Austin, USA

• 2013: Premio Académico at Universidad Nacional de Mar del Plata, Argentina

Talks

• March 2020: Propagation of solutions to Boltzmann systems in Banach spaces, at the 2020 Texas Differential Equations Conference, UT Austin

• December 2019: Polynomial and Exponential weighted L^p solutions of the system of Boltzmann equations for monatomic gas mixtures, at the SIAM Conference on Analysis of Partial Differential Equations, at La Quinta Resort and Club, La Quinta, California, USA

• Fall 2019: Propagation of L^p norms for the solution of the system of Boltzmann Equations for a gas mixture, at Junior Analysis Seminar, UT Austin

• June 2019: L^p estimates for the solution of the system of Boltzmann equations for monatomic gas mixtures, at the Kinetic Theory Junior Trimester Program, at the Hausdorff Research Institute for Mathematics, Bonn, Germany

• April 2019: L^p estimates for collisional Boltzmann operator for binary interactions of monatomic gases, at the Workshop on Mathematical Modelling in Kinetic Theory of Gases, at the University of Novi Sad, Serbia

• February 2019: Generation and propagation of L^p polynomially weighted norms for gas mixtures. at the Flash Workshop on kinetics of mixtures and plasmas, at ICES, UT Austin

• Fall 2018: Convolution inequalities for the Boltzmann collision operator, at Junior Analysis Seminar, UT Austin

• Spring 2018: A use of the Fourier Transform for the Boltzmann Equation, at Junior Analysis Seminar, UT Austin

• Spring 2017: Gain of Integrability for the Boltzmann Equation, at Junior Analysis Seminar, UT Austin

Teaching

• Fall 2018: Teaching assistant for Method of Applied Mathematics, at UT Austin (M383C)

• Spring 2018: Teaching assistant for Advanced Calculus, at UT Austin (M427L)

• Spring 2017-Fall 2017: Teaching assistant for Multivariable Calculus, at UT Austin (M408M)

• Fall 2015-Fall 2016: Teaching assistant for Analysis III, at Universidad Nacional de Mar del Plata

• Spring 2013-Spring 2015: Teaching assistant for Analysis III, at Universidad Nacional de Mar del Plata