I’m an Assistant Professor at Princeton ORFE.

I work on **deep learning**, **probability**, and **spectral asymptotics**.

Email: bhanin 'at' princeton.edu

CV (September 2020)

- In Fall 2020, I am teaching ORF 569
**Theory and Practice of Deep Learning**. Here is the [syllabus]. - In Fall 2019, I taught two sections of Math 300
**Foundations of Mathematics**(at Texas A&M). - In Fall 2018, I taught a graduate course, Math 689, called
**Deep Learning: Theory and Applications**(at Texas A&M). - In Fall 2017, I taught two sections of Math 221
**Multivariable Calculus**(at Texas A&M). - In Fall and IAP 2015, I taught Math 18.02A and 18.02B
**Multivariable Calculus**(at MIT). - In Fall 2014, I TAed Math 18.03
**Differential Equations**(at MIT). - In Winter 2013, I TAed Math 321-1
**Honors Real Analysis**(at Northwestern). - In Fall 2012, I TAed Math 310-1
**Probability Theory**(at Northwestern). - In Fall 2012, I TAed Math 300
**Foundations of Higher Mathematics**(at Northwestern). - In Winter 2011, I TAed Math 310-2
**Probability Theory**(at Northwestern). - In Winter 2011, I TAed Math 321-2
**Honors Real Analysis**(at Northwestern). - In Fall 2011, I TAed Math 321-2
**Honors Real Analysis**(at Northwestern). - In Fall 2011, I TAed Math 310-1
**Probability Theory**(at Northwestern). - In Fall 2010, I TAed Math 300
**Foundations of Higher Mathematics**(at Northwestern). - In Fall 2010, I TAed Math 310-1
**Probability Theory**(at Northwestern).

**Non-asymptotic Results for Singular Values of Gaussian Matrix Products**, with G. Paouris (2020) [arXiv]**Finite Depth and Width Corrections to the Neural Tangent Kernel**, with M. Nica, Splotlight at ICLR (2020) [arXiv]**Deep ReLU Networks Have Surprisingly Few Activation Patterns**, with D. Rolnick, NeurIPS (2019) [arXiv]**Nonlinear Approximation and (Deep) ReLU Networks**, with I. Daubechies, R. DeVore, S. Foucart, and G. Petrova. Accepted: Constructive Approximation (Special Issue on Deep Networks in Approximation Theory, 2019) [arXiv]**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, ICML 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. Communications in Mathematical Physics (in press, 2019) [arXiv]**How to Start Training: The Effect of Initialization and Architecture**, with D. Rolnick. NIPS 2018 [arXiv]**Which Neural Net Architectures Give Rise to Vanishing and Exploding Gradients?**. 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). Mathematics 2019, 7(10), 992 (Special Issue on Computational Mathematics, Algorithms, and Data Processing) [arXiv]**The Lemniscate Tree of a Random Polynomial**, with M. Epstein and E. Lundberg (2018). Annales Institute Henri Poincare (B). [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. Communication in Mathematical Physics (in press, 2020). [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.