Publications

Convex sets can have interior hot spots

The hot spots conjecture asserts that for any convex bounded domain $\Omega$ in $\mathbb{R}^d$, the first non-trivial Neumann …
arxiv:arXiv:2412.06344
Convex sets can have interior hot spots

Predicting quantum channels over general product distributions

We investigate the problem of predicting the output behavior of unknown quantum channels. Given query access to an n-qubit channel E …
arxiv:arXiv:2409.03684

Periodicity and decidability of translational tilings by rational polygonal sets

The periodic tiling conjecture asserts that if a region Σ⊂Rd tiles Rd by translations then it admits at least one fully periodic …
arxiv:arXiv:2408.02151
Periodicity and decidability of translational tilings by rational polygonal sets

Query lower bounds for log-concave sampling

Log-concave sampling has witnessed remarkable algorithmic advances in recent years, but the corresponding problem of proving lower …
arxiv:arXiv:2304.02599
Query lower bounds for log-concave sampling

Uniform Fourier Restriction Estimate for Simple Curves of Bounded Frequency

In this paper we prove a uniform Fourier restriction estimate over the class of simple curves where the last coordinate function can be …
arxiv:arXiv:2303.11693

A new proof of the description of the convex hull of space curves with totally positive torsion

We give new proofs of the description convex hulls of space curves $\gamma : [a,b] \mapsto \mathbb{R}^{d}$ having totally positive …
arxiv:arXiv:2201.12932
A new proof of the description of the convex hull of space curves with totally positive torsion

Additive energies on discrete cubes

We prove that for $d\geq 0$ and $k\geq 2$, for any subset $A$ of a discrete cube ${0,1}^d$, the $k-$higher energy of $A$ (i.e., the …
arxiv:arXiv:2112.09352

On classical inequalities for autocorrelations and autoconvolutions

In this paper we study an autocorrelation inequality proposed by Barnard and Steinerberger. The study of these problems is motivated by …
arxiv:arXiv:2106.13873
On classical inequalities for autocorrelations and autoconvolutions

Decoupling for fractal subsets of the parabola

We consider decoupling for a fractal subset of the parabola. We reduce studying l2Lp decoupling for a fractal subset on the parabola …
arxiv:arXiv:2012.11458
Decoupling for fractal subsets of the parabola

On Sparsity in Overparametrised Shallow ReLU Networks

The analysis of neural network training beyond their linearization regime remains an outstanding open question, even in the simplest …
arxiv:2006.10225
On Sparsity in Overparametrised Shallow ReLU Networks

A geometric lemma for complex polynomial curves with applications in Fourier restriction theory

The aim of this paper is to prove a uniform Fourier restriction estimate for certain 2−dimensional surfaces in R2n. These surfaces are …
arxiv:arXiv:2003.14140
A geometric lemma for complex polynomial curves with applications in Fourier restriction theory

Role Detection in Bicycle-Sharing Networks Using Multilayer Stochastic Block Models

Urban spatial networks are complex systems with interdependent roles of neighborhoods and methods of transportation between them. In …
arxiv:arXiv:1908.09440
Role Detection in Bicycle-Sharing Networks Using Multilayer Stochastic Block Models