Brian Simanek

Education

Ph.D., California Institute of Technology, 2012 (Advisor: B. Simon)
B.A., Williams College, 2007

Biography

Dr. Simanek joined the Baylor faculty in 2015. He grew up in Pittsburgh, PA before attending Williams College, where he met his wife Becca. As a graduate student at Caltech, he began research into the spectral theory of orthogonal polynomials, but has since branched into other areas of analysis, such as potential theory. Aside from mathematics, he enjoys outdoor adventures like swimming, biking, and camping, and following sports of all kinds.

Academic Interests and Research

Brian Simanek’s research interests include orthogonal polynomials, potential theory, and spectral theory.

Selected Publications

1. (with M. Derevyagin) On Szego's Theorem for a non-classical case, Journal of Functional Analysis 272 (2017), no. 6, 2487–2503.
2. A new approach to ratio asymptotics for orthogonal polynomials, Journal of Spectral Theory 2 (2012), no. 4, 373-395.
3. (with E. Mina-Diaz) Spectral transforms of measures and orthogonal polynomials on regions, Journal of Mathematical Analysis and Applications, 407 (2013), no. 2, 290-304.
4. (with A. Martinez-Finkelshtein and B. Simon) Poncelet’s Theorem, paraorthogonal polynomials and the numerical range of compressed multiplication operators, Advances in Mathematics 49 (2019), 992–1035.
5. (with R. Grigorchuk) Spectra of Cayley graphs of the lamplighter group and random Schrodinger operators, Transactions of the AMS 374 (2021) no. 4, 2421-2445.

Teaching Interests

Dr. Simanek’s enjoys teaching all mathematics classes and is very interested in designing advanced mathematics courses for undergraduates and graduate students.



Courses taught at Baylor

MTH 1321 - Calculus I
MTH 1322 - Calculus II
MTH 2321 - Calculus III
MTH 4312 - Cryptology
MTH 4316/5316 - Matrix Theory
MTH 4329 - Complex Variables
MTH 5345 - Functional Analysis
MTH 5350 - Complex Analysis
MTH 6V23 - Potential Theory