Email: nickcook at math dot ucla dot edu
Office: Mathematical Sciences, 6147
Analysis, probability and combinatorics;
Random matrices and related fields (random graphs, additive combinatorics, geometric functional analysis); applications to mathematical physics and theoretical computer science.
Preprints(also available on arXiv)
Size biased couplings and the spectral gap for random regular graphs. (with Larry Goldstein and Tobias Johnson).
The circular law for signed random regular digraphs. Submitted.
On the singularity of adjacency matrices for random regular digraphs. Probability Theory and Related Fields, to appear.
Dense random regular digraphs: Singularity of the adjacency matrix. An earlier version of the above paper.
Discrepancy properties for random regular digraphs. Random Structures and Algorithms, to appear.
The circular law for signed random regular digraphs.
Conference on Stochastic Processes and their Applications, Oxford University, 16 July 2015.
Random regular digraphs: Singularity and discrepancy.
Conference on Stochastic Processes and their Applications, Universidad de Buenos Aires, 31 July 2014.
A geometric proof of regularity of solutions to the Monge—Ampère equation (after Cafarelli, and Guillen–Kitagawa).
Summer school on optimal transport and applications, Lake Arrowhead, UCLA, 10 Oct. 2013.
2015–2016: No teaching.
Winter 2015: Math 32BH Multivariable Calculus II (honors). Course website.
2013–2014: No teaching.
Teaching assistant for:
Spring 2015: Math 111 Theory of Numbers, Professor Chandrashekhar Khare. Course webpage
Spring 2015: Math 32A Multivariable Calculus.
Spring 2013: Math 171 Stochastic Processes, Dr. Nestor Guillen. Course webpage.
Winter 2013: Math 245B Graduate Real Analysis, Professor Terence Tao. OH Tu 11:30-12:30, Th 12:30-1:30.
Handout: Weak convergence implies strong convergence in l^1.
Winter 2002 #5 is a qualifying exam problem with 1) a fast solution, and 2) a closed graph theorem solution.
Fall 2012: Math 245A Graduate Real Analysis, Professor John Garnett. Course handout.
Solutions to selected homework problems (the exercises are from Terry Tao's measure theory text).
Summer 2012: Math 115A Linear Algebra, Dr. Blake Hunter. Course webpage.
Spring 2012: Math 171 Stochastic processes, Professor Marek Biskup.
Winter 2012: Math 170B Probability, Section 2, Professor Lincoln Chayes.
Fall 2011: Math 33A Linear Algebra, Professor Rowan Killip.
Spring 2011: Math 33A Linear Algebra, Professor Alan Laub.
Winter 2011: Math 33B Differential Equations, Professor Bruce Rothschild.
Fall 2010: Math 32A Multivariable Calculus, Dr. Mario Micheli.
Otto and Villani: on a generalization of an inequality by Talagrand, for Inequalities in PDE seminar (Spring 2013).
- Two proofs of Wigner's semicircular law, for participating analysis seminar at UCLA (Spring 2012).
- Talagrand's inequalities and applications, for participating analysis seminar (Fall 2011) and concentration of measure seminar at UCLA (Spring 2012).
Analysis qualifying exam, problem hints and solution sketches. Joint with Will Feldman, Alan Mackey and Brent Nelson.
I briefly tried tidying this up and filling in some details, but decided it's probably best that the student studying for the exam fill in the details herself. I have been told there is at least one incorrect solution, so stay alert!
- I work with the LA Math Circle at UCLA.
- I helped with math exhibits at the 2013 and 2014 Exploring Your Universe fair, an annual event at UCLA for K-12 students featuring science activities and demonstrations. Here are slides I prepared for the "Extremely large numbers" exhibit (including an illustration of the Ackermann function).