I am a postdoctoral fellow at Harvard University's Center of Mathematical Sciences and Applications, under the supervision of Prof. Horng-Tzer Yau. My work is in probability theory, especially random matrices and the geometry of high-dimensional random functions.

Previously, I spent spring 2022 on a Fulbright-Austrian Marshall Plan Foundation grant doing research at the Institute of Science and Technology Austria (ISTA), under the supervision of Prof. László Erdős. In fall 2021, I was a postdoctoral fellow in mathematics at MSRI (now SLMath).

I received a Ph.D. in mathematics in 2021 from the Courant Institute, New York University, and an A.B. in mathematics in 2016 from The University of Chicago. My Ph.D. thesis, advised by Prof. Gérard Ben Arous and Prof. Paul Bourgade, is here.

I co-organize the CMSA Probability Seminar with Kevin Yang.

My email is bmckenna (at) fas.harvard.edu. Here is my CV.

Research

• Universality for the global spectrum of random inner-product kernel matrices in the polynomial regime, with Sofiia Dubova, Yue M. Lu, and Horng-Tzer Yau, 2023.
• Large deviations for the largest eigenvalue of generalized sample covariance matrices, with Jonathan Husson, 2023.
• Extremal statistics of quadratic forms of GOE/GUE eigenvectors, with László Erdős, 2022. To appear in Annals of Applied Probability.
• Exponential growth of random determinants beyond invariance, with Gérard Ben Arous and Paul Bourgade. Probability and Mathematical Physics, vol. 3, no. 4, pp. 731-789, 2022. arXiv link.
• Landscape complexity beyond invariance and the elastic manifold, with Gérard Ben Arous and Paul Bourgade, 2021. To appear in Communications on Pure and Applied Mathematics.
• Complexity of bipartite spherical spin glasses, 2021. To appear in Annales de l'Institut Henri Poincaré.
• Large deviations for extreme eigenvalues of deformed Wigner random matrices. Electronic Journal of Probability, vol. 26, paper no. 34, 2021. arXiv link.

Talks

• Séminaire de Probabilités, Institut de Mathématiques de Toulouse, June 2023.
• Séminaire Images Optimisation et Probabilités, Institut de Mathématiques de Bordeaux, June 2023.
• High Dimensional Statistics and Random Matrices, Porquerolles, June 2023.
• MIT Probability Seminar, May 2023 (notes for blackboard talk).
• Northwestern University Probability Seminar, April 2023.
• University of Chicago Probability and Statistical Physics Seminar, April 2023.
• Bielefeld-Melbourne Random Matrix Seminar, December 2022.
• Cornell Probability Seminar, November 2022 (notes for blackboard talk).
• Texas A&M Mathematical Physics and Harmonic Analysis Seminar, November 2022.
• CUNY Probability Seminar, October 2022 (notes for blackboard talk).
• Workshop on Spin Glasses, Les Diablerets, September 2022 (slides, video).
• QMATH 15, UC Davis, September 2022 (notes for blackboard talk).
• Youth in High-Dimensions, ICTP (Trieste), June 2022 (video).
• KTH Random Matrix Theory Seminar, February 2022.
• Vienna Probability Seminar, January 2022.
• Harvard Probabilitas Seminar, October 2021.
• University of Basel Seminar in Probability Theory and Statistics, September 2021.
• One World Probability Seminar, June 2021 (video).
• MIT Probability Seminar, March 2021.
• Northeast Probability Seminar, November 2020 (video).
• Northwestern University Probability Seminar, January 2020.
• Northeast Probability Seminar, November 2019.
• Saint-Flour Probability Summer School, July 2019.
• Cornell Probability Summer School, June 2019.

Teaching

In fall 2023, I am teaching Introduction to Calculus (Math 1a), an undergraduate course, at Harvard. Enrolled students can access the Canvas page here.

On the graduate side, in fall 2021 I gave two 90-minute videotaped guest lectures in Gérard Ben Arous's graduate course Random Matrices and Random Landscapes at UC Berkeley, mostly talking about the fourth and fifth papers above. The first lecture is here and the second lecture is here.