I am an assistant professor of mathematics at Georgia Tech. My work is in probability theory, especially random matrices and the geometry of high-dimensional random functions.

From fall 2022 to spring 2024, I was a postdoctoral fellow at Harvard University's Center of Mathematical Sciences and Applications, under the supervision of Prof. Horng-Tzer Yau. Before that, 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 Georgia Tech Stochastics Seminar.

My email is bmckenna3 (at) gatech.edu. Here is my CV.

Research

• Injective norm of real and complex random tensors I: From spin glasses to geometric entanglement, with Stephane Dartois, 2024.
• 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. Annals of Applied Probability, vol. 34, no. 1B, pp. 1623-1662, 2024. arXiv link.
• 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. Communications on Pure and Applied Mathematics, vol. 77, no. 2, pp. 1302-1352, 2024. arXiv link.
• Complexity of bipartite spherical spin glasses. Annales de l'Institut Henri Poincaré, vol. 60, no. 1, pp. 636-657, 2024. arXiv link.
• Large deviations for extreme eigenvalues of deformed Wigner random matrices. Electronic Journal of Probability, vol. 26, paper no. 34, 2021. arXiv link.

Talks

• Lehigh University-University of Minnesota Joint Probability Seminar, (November 2024).
• Duke Probability Seminar, (November 2024).
• Random Tensors and Related Topics, Institut Henri Poincaré, (October 2024).
• Berkeley Probability Seminar, April 2024.
• Stanford Probability Seminar, April 2024.
• CRM-ISM Montreal Probability Seminar, March 2024.
• Georgia Tech Stochastics Seminar, March 2024.
• 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 2024, I am teaching Probability Theory (Math 3235), an undergraduate course, at Georgia Tech. 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 fifth and sixth papers above. The first lecture is here and the second lecture is here.