In 1980, Johnnie Lee released his hit country song “looking for love in all the wrong places.” That year I began my graduate studies at UCLA and shortly thereafter I was looking for (and finding) randomness in all the "wrong places." This talk will illustrate various mathematical places where, surprisingly, beautiful connections to, and applications of, randomness (probability) can be found. These connections, not so apparent on the surface, lie at the interface of spectral theory and the geometry and analysis of the Laplacian and closely related nonlocal operators. Nonlocal operators arise when the Brownian motion, which “goes” with the Laplacian, is replaced by other Lévy processes. They have been studied extensively in recent years by probabilsts and analysts in areas of pure and applied mathematics.
BIO: If at first you don’t succeed, try again, and again, and again and again, … Bañuelos was born in a farming community in the state of Zacatecas, Mexico. As a child he did not attend school until he moved to the US, two months short of his 16th birthday. You may read about his journey to mathematics in his biographical profile, part of the “SACNAS Biography Project,” found at http://bio.sacnas.org/biography/Biography.asp?mem=186&type=2
Bañuelos received the Ph.D. from UCLA in 1984. He was a Bantrell Research Fellow at Caltech (1984-1986), an NSF Postdoctoral Fellow at the University of Illinois (1986-1987) and a recipient of the the NSF Presidential Young Investigator Award in 1987. He moved to Purdue in 1987 as Assistant Professor and was promoted to Full Professor in 1992. He was head of the department from 2007 to 2011. He is a Fellow of the Institute of Mathematical Statistics, a Fellow of the American Mathematical Society, and a 2018 inaugural Fellow of the Association for Women in Mathematics. In 2004. He received the Blackwell-Tapia Prize in Mathematics at a conference held at IPAM.
His research is at the interface of probability, harmonic analysis, partial differential equations and spectral theory. He has authored or co-authored over 100 research articles, one book, and several lecture notes in probability and analysis. He has lectured widely on these topics worldwide. He has served on many editorial boards and scientific committees, including the United States National Committee for Mathematics, MSRI’s Scientific Advisory Council, and IPAM’s Board of Trustees.
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