Francisco Villarroya Alvarez

Francisco Villarroya Alvarez is an Assistant Professor in the Department of Applied Mathematics at Santa Clara University's School of Engineering. He holds a Ph.D. in Mathematics from the University of Valencia, Spain, and has held academic positions at prestigious institutions including the University of Edinburgh, Lund University, and the University of California Los Angeles.

Research Interests

His research spans three main areas:

• Harmonic Analysis: Singular Integration, T1 Theory, Time-Frequency Analysis, Wavelet Theory, and compact Calderón-Zygmund operators.
• Partial Differential Equations: Dispersive and elliptic equations, Schrodinger and Wave maximal operators, Cauchy Integral operators, and Double Layer Potential operators.
• Numerical Analysis: Development of algorithms for rapid evaluation of dense matrices associated with compact operators.

His work bridges theoretical mathematics with practical applications in signal processing and computational methods.