I’m an assistant professor of mathematics at Texas A&M.

I do research in **probability**, **spectral asymptotics,** and
**deep learning**. I am currently on leave as a Visiting Scientist at Facebook AI Research NYC.

Office: BLOC 620B

Email: bhanin 'at' math.tamu.edu

CV (March 2019)

**Deep Learning: Theory and Applications**(Math 689 Fall 2018) [Course Website]

**Interface Asymptotics of Wigner-Weyl Distributions for the Harmonic Oscillator**, with S. Zelditch (2019) [arXiv]**Complexity of Linear Regions in Deep Networks**, with D. Rolnick (2019) [arXiv]**Interface Asymptotics of Eigenspace Wigner distributions for the Harmonic Oscillator**, with S. Zelditch (2019) [arXiv]**Products of Many Large Random Matrices and Gradients in Deep Neural Networks**, with M. Nica (2018) [arXiv]**How to Start Training: The Effect of Initialization and Architecture**, Accepted to NIPS 2018 [arXiv]**Which Neural Net Architectures Give Rise to Vanishing and Exploding Gradients?**, Accepted to NIPS 2018 [arXiv]**Approximating Continuous Functions by ReLU Nets of Minimal Width**, with M. Sellke (2017) [arXiv]**Universal Function Approximation by Deep Neural Nets with Bounded Width and ReLU Activations**(2017) [arXiv]**The Lemniscate Tree of a Random Polynomial**, with M. Epstein and E. Lundberg (2018) [arXiv]**Level Spacings and Nodal Sets at Infinity for Radial Perturbations of the Harmonic Oscillator**, with T. Beck. International Math Research Notices (in press, 2018) [arXiv]**Local Universality for Zeros and Critical Points of Monochromatic Random Waves**, with Y. Canzani (2017) [arXiv]**Nodal Sets of Functions with Finite Vanishing Order**, with T. Beck and S. Becker-Khan. Calculus of Variations and PDE (in press, 2018) [arXiv]**Scaling of Harmonic Oscillator Eigenfunctions and Their Nodal Sets Around the Caustic**, with S. Zelditch and P. Zhou. Communications in Mathematical Physics. Vol. 350, no. 3, pp. 1147--1183, 2017. [arXiv]**C^∞ Scaling Asymptotics for the Spectral Function of the Laplacian**, with Y. Canzani. The Journal of Geometric Analysis. DOI 10.1007/s12220-017-9812-5. [arXiv]**Pairing of Zeros and Critical Points for Random Polynomials**. Annales de l'Institut Henri Poincare (B) Probabilites et Statistiques. Volume 53, Number 3 (2017), 1498-1511. [arXiv]**Scaling Limit for the Kernel of the Spectral Projector and Remainder Estimates in the Pointwise Weyl Law**, with Y. Canzani. Analysis and PDE, Vol. 8 (2015), No. 7, pp. 1707-1731. [arXiv]**High Frequency Eigenfunction Immersions and Supremum Norms of Random Waves**, with Y. Canzani. Electronic Research Announcements. MS 22, no. 0, January 2015, pp. 76 - 86. [arXiv]**Pairing of Zeros and Critical Points for Random Meromorphic Functions on Riemann Surfaces**. Mathematics Research Letters, Vol. 22 (2015), No. 1, pp. 111-140. [arXiv]**Nodal Sets of Random Eigenfunctions for the Isotropic Harmonic Oscillator**, with S. Zelditch and P. Zhou. International Mathematics Research Notices, Vol. 2015, No. 13, pp. 4813 - 4839. [arXiv]**Correlations and Pairing Between Zeros and Critical Points of Gaussian Random Polynomials**. International Math Research Notices (2015), Vol. (2), pp. 381-421. [arXiv]**An Intriguing Property of the Center of Mass for Points on Quadradtic Curves and Surfaces**, Mathematics Maganize, v. 80, No. 5, pp. 353-362, 2007.