### About Me

I am an assistant professor in the Math & Statistics Department at the University of Guelph working in the area of probability, stochastic processes, and their applications to machine learning. I am also affiliated with the CARE-AI institute and the Vector Institute.

Before Guelph, I was an NSERC postdoctoral fellow at the University of Toronto, with Jeremy Quastel as my supervisor. My old website, http://www.math.toronto.edu/mnica/ has some links to my previous projects.

Before my postdoc at U of T, I was a PhD student at the Courant Institute of Mathematical Sciences in New York under the advisement of Gérard Ben Arous.

Email: nicam@uoguelph.ca

### Education

#### University of Toronto

*2017 – 2020*

Post-Doctoral Fellowship

#### New York University

*2011 – 2017*

PhD

#### University of Waterloo

2007 – 2011

BMath

### Research

Finite Depth & Width Corrections to the Neural Tangent Kernel

*(With Boris Hanan)*

We prove the precise scaling, at finite depth and width, for the mean and variance of the neural tangent kernel (NTK) in a randomly initialized ReLU network. *ICLR Spotlight*.

. . . . .

Uniform Convergence to the Airy Line Ensemble

*(With Duncan Dauvergne & Bálint Virág)*

We prove a general theorem for uniform convergence to the Airy line ensemble that applies to many different last passage percolation settings

. . . . .

Solution of the Kolmogorov Equation for TASEP

*(With Jeremy Quastel & Daniel Remenik)*

We provide a direct and elementary proof that the transition probability formulas for TASEP solve the Kolmogorov backward equation. *Published in Annals of Probability.*

### Theory of Deep Learning Notes/Videos

Notes on Infinite Depth-and-Width Limits

Notes on Feature Regression and Wide Neural Networks

## Expository Math Notes/Videos

Notes on Fibonacci Numbers using Generating Functions and Infinite Sums