Blanca Radillo Murguía

Blanca Radillo Murguía’s research focuses on harmonic analysis, Fourier analysis, and probability theory, with particular interest in the boundedness of maximal operators. Working under the supervision of Dr. Paul Hagelstein, she is pursuing her Ph.D. in Mathematics, expected in May 2026. Her work employs methods such as covering lemmas, Fourier analytic techniques, interpolation theorems, and probabilistic arguments. A central aspect of her research is the study of Kakeya sets in specific directional contexts, where she aims to demonstrate that the associated directional maximal operator is unbounded in L^p spaces.

Her current project has advanced the theory of harmonic analysis by revisiting an open problem related to the differentiation of integrals in the plane and suggesting new paths for extending this problem to higher dimensions. Blanca’s broader goal is not only to resolve individual questions but also to develop frameworks that capture fundamental aspects of these mathematical challenges. She has presented her work at conferences across the globe, including in the United States, Spain, Ukraine, Australia, and Latin America, and was invited to speak at the Brazos Analysis Seminar hosted by her university.

Blanca’s growing reputation in the field is reflected in her invitations to upcoming conferences, including the Analysis Seminar at Georgia Tech, the AMS Fall 2025 Central Sectional Meeting in St. Louis, and the AMS Spring 2026 Central Sectional Meeting in Fargo. Beyond presenting, she has attended workshops and conferences in countries such as Germany, Mexico, Spain, and the United Kingdom, many of which were supported by the Graduate School and NSF grants. These experiences have broadened her perspective, strengthened her research, and connected her with the international mathematical community.

What Faculty Say

Blanca’s research lies in a difficult area of harmonic analysis related to the weak type bounds of geometric maximal operators. Very few mathematicians work in this area .... Ordinarily I would not have given Blanca a thesis topic in this area, but she came to Baylor with a strong background in analysis from the University of Colima, Mexico, where she studied with Ricardo Saenz (a Princeton Ph. D. student of E. M. Stein, mentor of two Fields medalists himself.) Her thesis research has led to two papers that have already been accepted for publication...The paper in the Duke Mathematical Journal is especially noteworthy. This journal is widely considered in the top five-six mathematical journals worldwide. Few even tenured professors in mathematics have a publication in a journal of this quality. - Dr. Paul Hagelstein, Math faculty