I am a Professor in the Math Department at the University of Washington, Seattle.

I can be reached via [first 8 letters of last name]@uw.edu

My main field of research is Analysis. I like questions combining PDEs, Spectral Theory, Harmonic Analysis

and all sorts of applications. CV

List of open problems

Winter 2024: Math 180 (A Walk in the Garden of Mathematics)

Spring 2024: Math 563A (Graduate Graph Theory)

- (with Tony Zeng) A curious dynamical system in the plane arxiv
- Universal lower bounds for Dirichlet eigenvalues, arxiv
- (with Jeck Lim) On differences of two harmonic numbers, arxiv
- (with Bandeira and Mixon) A lower bound for the Balan-Jiang matrix problem, arxiv
- Randomly Pivoted Partial Cholesky: Random How? arxiv
- On a problem involving unit fractions arxiv
- A note on approximate Hadamard matrices arxiv,
*Designs, Code and Cryptography*, accepted. - (with Thomas) Conformally rigid graphs, arxiv
- Bad Science Matrices arxiv
- Sums of square roots that are close to an integer arxiv,
*J. Number Theory*, accepted. - Nonlinear recursions on the reals and a problem of Graham, arxiv
- (with Raghav Venkatraman), Dirichlet eigenfunctions with nonzero mean value, arxiv
- (with Mariana Smit Vega Garcia) An Almgren monotonicity formula for discrete harmonic functions, arxiv
- Random Growth via Gradient Flow Aggregation, arxiv
- (with Ovall, Quan, Reid) On localization of eigenfunctions of the magnetic Laplacian, arxiv
- (with Bilyk, Mastrianni), Single radius spherical cap discrepancy via gegenbadly approximable numbers arxiv,
*Advances in Mathematics*, accepted. - (with Bilyk, Chang, Heinävaara, Matzke) A random line intersects S^2 in two probabilistically independent locations, arxiv
- (with Ottolini) Greedy Matching in Optimal Transport with concave cost, arxiv
- (with Babecki and Thomas) Spectrahedral Geometry of Graph Sparsifiers, arxiv
- (with Faulhuber) Maximal polarization for periodic configurations on the real line, arxiv,
*IMRN*, accepted. - (with Ottolini) Concentration of Hitting Times in Erdos-Renyi graphs, arxiv,
*Journal of Graph Theory*, accepted. - (with Devriendt and Ottolini) Graph curvature via resistance distance, arxiv,
*Discrete Applied Mathematics*, accepted. - Local sign changes of polynomials, arxiv,
*Journal d'Analyse Mathematique*, accepted. - (with Shubham Gupta) Rearrangement Inequalities on the Lattice Graph, arxiv,
*Bull. London Math. Soc.*, accepted. - (with Andrea Ottolini) Guessing cards with complete feedback, arxiv,
*Adv. Appl. Math.*, accepted. - Quadratic Crofton and sets that see themselves as little as possible, arxiv,
*Monatshefte Math.*, accepted. - (with Hoskins and Quan) Magnetic Schrodinger operators and landscape functions, arxiv,
*Comm. PDE*, accepted. - An Inequality Characterizing Convex Domains, arxiv
- Discrete Rearrangements and the Polya-Szegő Inequality on Graphs, arxiv,
*Studia Mathematica*, accepted. - (with Burdzy, Hoskins) From pinned billiard balls to partial differential equations, arxiv
- Some Remarks on the Erdős Distinct Subset Sums Problem, arxiv,
*Int. J. Number Theory*, accepted. - An elementary proof of a lower bound for the inverse of the star discrepancy, arxiv,
*J. Complexity*, accepted. - On Combinatorial Properties of Greedy Wasserstein Minimization, arxiv,
*J. Math. Anal. Appl.*, accepted. - Approximate Solutions of Linear Systems at a Universal Rate, arxiv,
*SIAM J. Matrix Analysis and Applications*, accepted. - An Agmon estimate for Schrodinger operators on Graphs, arxiv,
*Lett. Math. Phys.*, accepted. - (with Rekha Thomas) Random Walks, Equidistribution and Graphical Designs arxiv
- The first eigenvector of a distance matrix is nearly constant arxiv,
*Discrete Math.*, accepted. - (with Alaifari, Bartolucci, Wellershoff) On the connection between uniqueness from samples and stability in Gabor
phase retrieval arxiv,
*Sampling Theory, Signal Processing, and Data Analysis*, accepted. - (with Bamdad Hosseini) Intrinsic Sparsity of Kantorovich Solutions arxiv,
*Comptes Rendus Mathematique*, accepted. - Sums of Distances on Graphs and Embeddings into Euclidean Space arxiv,
*Mathematika*, accepted. - Curvature on Graphs via Equilibrium Measures arxiv,
*J. Graph Theory*, accepted. - The Boundary of a Graph and its Isoperimetric Inequality arxiv,
*J. Discrete Applied Mathematics*, accepted. - (with Hau-tieng Wu) Fundamental component enhancement via adaptive nonlinear activation functions, arxiv,
*App. Comp. Harm. Anal.*, accepted. - Quantum Entanglement and the Growth of Laplacian Eigenfunctions arxiv,
*Comm. PDE*, accepted.

Growth of Laplacian Eigenfunctions (2022)

Five Short Stories about Optimal Transport (2022)

Nonlinear Fourier series (2021)

Random Walks on the Sphere and Linear Systems of Equations (2021)

Parabolic Techniques for Elliptic PDEs in Mathematical Physics (2021)

Exact Sparse Recovery via Refined Least Squares (2021)

Mean-Value Inequalities for Harmonic Functions (2021)

A PDE describing Roots of Polynomials under Differentiation (2021)

Optimal Coffee Shops, Numerical Integration and Kantorovich-Rubinstein Duality (2021)

The Hot Spots Conjecture on Graphs (2020)

Solving Linear Systems of Equations via Random Kaczmarz/Stochastic Gradient Descent (2020)

Nodal Sets of Eigenfunctions: Progress via Optimal Transport (2020)

Designs on Graphs (2020)

Dimension Reduction via t-SNE: Theory and Challenges (2020)

New Interactions between Analysis and Number Theory (2017)