Welcome!

I am a fifth year PhD Candidate in Mathematics at The University of Texas at Austin. I am interested in Partial Differential Equations, Calculus of Variations, and Geometric Analysis. I am currently working on regularity theory for transmission problems, and nonlocal parabolic equations. It is my honor to be coadvised by Prof. Luis Caffarelli and Prof. Pablo Raúl Stinga.

CV

Email: maria.soriac [at] math.utexas.edu
Office: PMA 10.146

Education

  • 2011-2015: Bachelor's Degree in Mathematics, Universitat Autònoma de Barcelona
    Thesis: About the Euler Equations: The Particle-Trajectory Method for Existence and Uniqueness of Solutions (pdf)
    Advisor: Prof. Joan Mateu
  • 2015-2016: Master's Degree in Mathematics, Universidad Autónoma de Madrid
    Thesis: The De Giorgi Conjecture and the Allen-Cahn equation (pdf)
    Advisor: Dr. Alberto Enciso.

Publications and Preprints

  • Regularity for C1,α interface transmission problems, L. A. Caffarelli, M. Soria-Carro, and P. R. Stinga, Arch. Ration. Mech. Anal. (2021)
  • El teorema de Müntz-Szász sobre la aproximación de funciones continuas, D. Eceizabarrena, A. Mas-Mas, F. Mengual-Bretón y M. Soria-Carro, TEMat , Vol. 1 (2017), págs. 31-44.

Awards and Grants

Teaching

  • Spring 2021: Teaching assistant for Complex Analysis (M381D)
  • Spring 2020: Teaching assistant for Intro to Real Analysis (M361K)
  • Fall 2019: Teaching assistant for Methods of Applied Mathematics I (M383C)
  • Spring 2019: Teaching assistant for Complex Analysis (M381D)
  • Fall 2018: Teaching assistant for Differential Equations and Linear Algebra (M427J)

Talks

    Conference Talks

  • September 2019: Regularity for C1,α Interface Transmission Problems. Joint work with L. A. Caffarelli and P. R. Stinga. Invited plenary talk at the Midwest Geometry Conference 2019, Iowa State University
  • June 2019: C1,α Regularity for a Transmission Problem Via an Approximation Technique. Joint work with L. A. Caffarelli and P. R. Stinga. Short talk at the Barcelona Analysis Conference, Universitat de Barcelona
  • October 2018: A stability argument for transmission problems and C1,α regularity. Joint work with L. A. Caffarelli and P. R. Stinga. Invited talk on the special session: Recent Trends on Local, Nonlocal and Fractional Partial Differential Equations at AMS Fall Central Sectional Meeting, University of Michigan in Ann Arbor

    Seminar Talks

  • July 2021: Regularity for C1,α Interface Transmission Problems, Learning Seminar on Analysis of PDEs , Centre for Mathematics of the University of Coimbra
  • Fall 2020: Lipschitz free boundaries are C1,α, Junior Analysis Seminar, University of Texas at Austin
  • Fall 2019: The Pohozaev Identity: Classical and Fractional Versions, Junior Analysis Seminar, University of Texas at Austin
  • Spring 2018: The Mean Value Theorem for elliptic operators in divergence form, Junior Analysis Seminar, University of Texas at Austin
  • Fall 2018: On the existence of a weak solution to the Monge-Ampère equation, Junior Analysis Seminar, University of Texas at Austin
  • Spring 2017: Exponential integrability of BMO functions, Junior Analysis Seminar, University of Texas at Austin

Other

I am happy to be an organizer of the Directed Reading Program and the Distinguished Women in Math Lecture Series. Both programs are offered at The Univeristy of Texas at Austin, and they are run by Graduate Students. I am also a member of the Graduate Student Committee in the Math Department.