I am a member of the Department of Applied Mathematics at the School of Engineering at Santa Clara University.
Previous academic positions include the University of Valencia, the University of Edinburgh (UK), Lund University (Sweden), the University of California Los Angeles, the University of Georgia, Temple University, and California Polytechnic State University.
Research interests
- My research interests focus on Harmonic Analysis and its applications to the study of Partial Differential Equations (PDEs) and Numerical Analysis.
- In Harmonic Analysis, I work on Singular Integration, T1 Theory, Time-Frequency Analysis, Wavelet Theory, and compact Calderón-Zygmund operators.
- In the field of PDEs, I study dispersive and elliptic equations, the Schrodinger and Wave maximal operators, the Cauchy Integral operator and the Double Layer Potential operator.
- In Numerical Analysis, I develop algorithms for the rapid evaluation of dense matrices associated with compact operators.
Courses
Recently I have been lecturing the courses Differential Equations Amth106, Probability and Statistics Amth 108, Risk Analysis Amth 112, and Numerical Methods Amth 118.
Publications
- Villarroya P., New local T1 Theorems on non-homogeneous spaces. Publ. Mat. 68, 445–506, (2024)
- Villarroya P., A global Tb Theorem for boundedness and compactness of Calderon-Zygmund operators, J. Math. Anal. Appl., 480, 1, (2019)
- Olsen J.F., Villarroya P., Endpoint estimates for compact Calderon-Zygmund operators. Revista Matematica Iberoamericana, Vol. 33, No. 4, 1285-1308, (2017)
- Villarroya P., A characterization of compactness for singular integrals. Journal de Mathematiques Pures et Appliquees, 104, 3, 485-532, (2015)
- Benyi A., Demeter C., Nahmod A., Thiele C., Torres R., Villarroya P., Modulation invariant bilinear T(1) theorem. J. Anal. Math., 109, 279-352, (2009)