Postdoctoral Researcher

ETHZ

About me

I am a Postdoc at ETHZ with Svitlana Mayboroda, working on harmonic analysis and spectral theory.

I was born in Barcelona, where I lived most of my life. I moved to Los Angeles in 2016 to finish my Bachelor’s, and to Zurich in 2017 to do a Master’s in mathematics. In June 2023 I got my PhD from UCLA, under the supervision of Terence Tao. Between the Phd and the Postdoc, I was research intern at the ML Foundations group at Microsoft Research.

My graduate school was supported by a UCLA dissertation year fellowship, Teaching and Research Assistantships at UCLA, a “La Caixa” post-graduate fellow, and an ESOP fellow at ETHZ.

My name is pronouced [ˈʒawmə] , my pronouns are he/him.

Interests

  • Harmonic Analysis
  • Elliptic PDEs
  • Convex Analysis
  • Machine Learning

Education

  • PhD Mathematics, 2023

    UCLA

  • MSc Mathematics, 2018

    ETH Zurich

  • BSc Mathematics, 2017

    Universitat Autonoma de Barcelona

  • BSc Physics, 2017

    Universitat Autonoma de Barcelona

Talks & Travel

Travel plans and topics for talks with an astherisk* are temptative. If I’m travelling near you and want to meet, contact me!

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Upcoming Past
[Travel] Boolean Analysis in Computer Science
Oct 11, 2024 — Oct 25, 2024 Hausdorff Insitute of Mathematics, Bonn
[Travel] Arbeitsgemeinschaft: Quantum Signal Processing and Nonlinear Fourier Analysis
Oct 6, 2024 — Oct 11, 2024 MFO Oberwolfach
[Travel] Uniformity and Stability of Oscillatory Integrals
Jul 8, 2024 — Jul 12, 2022 Hausdorff Center for Mathematics, Bonn
[Travel] Barcelona Analysis Conference
Jun 3, 2024 — Barcelona
[Travel] Dual Trimester Program: Synergies between modern probability, geometric analysis and stochastic geometry
Jan 8, 2024 — Jan 31, 2022 Hausdorff Insitute of Mathematics, Bonn
[Travel] Dual Trimester Program: Synergies between modern probability, geometric analysis and stochastic geometry
Jan 8, 2024 — Jan 31, 2022 Hausdorff Insitute of Mathematics, Bonn
[Travel] NTNU
Oct 20, 2023 — Nov 3, 2022 Trondheim, NO
[Travel] Microsoft Reseach Internship
May 30, 2023 — Sep 1, 2022 Seattle, WA
[Travel] University of Rochester
May 22, 2023 — May 25, 2022 Rochester, NY
[Travel] Stanford University
Oct 17, 2022 — Oct 28, 2022 Palo Alto, California
[Travel] Nodal domains and landscape functions
Oct 2, 2022 — Oct 7, 2022 Kopp, Germany
[Talk] Decoupling, Cantor sets, and additive combinatorics
Sep 15, 2022 3:30 PM — 3:30 PM [CST] University of Minnesota PDE Seminar
[Travel] University of Minneapolis
Sep 7, 2022 — Sep 28, 2022 UMN, Minneapolis
[Travel] Harmonic analysis on manifolds summer school
Aug 1, 2022 — Aug 5, 2022 UW Madison, WI
[Travel] COLT
Jul 2, 2022 — Jul 5, 2022 London
[Travel] Fourier Analysis @200
Jun 23, 2022 — Jul 1, 2022 ICMS, Edinburgh
[Travel] Workshop on Analysis and PDEs
Jun 23, 2022 — CRM - Barcelona
[Travel] Princeton Machine Learning Theory Summer School 2022
Jun 13, 2022 — Jun 17, 2022 Princeton
[Travel] Analysis on the hypercube with applications to quantum computing
Jun 6, 2022 — Jun 10, 2022 AIM, San Jose
[Travel] CBMS Conference
May 21, 2022 — May 28, 2022 FSU, Tallahasee
[Travel] ETH Zurich
Mar 14, 2022 — Mar 19, 2022 Visiting Joao P. Ramos
[Talk] The convex hull of space curves with totally positive torsion
Mar 9, 2022 3:00 PM — 4:00 PM [EU] Bilbao Analysis and PDE
[Travel] Basque Center for Applied Mathematics
Mar 8, 2022 — Mar 14, 2022 Visiting Mateus Costa da Sousa.
[Talk] The convex hull of space curves with totally positive torsion
Mar 7, 2022 3:00 PM — 4:00 PM [EU] UAB Analysis Seminar
[Talk] Decoupling, Cantor sets, and additive combinatorics
Feb 17, 2022 3:00 PM — 4:00 PM [UK] University of Bristol's Analysis and Geometry Seminar
[Talk] Decoupling for Cantor sets on the parabola
Feb 3, 2022 12:00 PM — 1:00 PM [EU] Workshop on Harmonic analysis, Singular Integrals and PDEs (HIM, Bonn)
[Travel] Interactions between Geometric measure theory, Singular integrals, and PDE
Jan 23, 2022 — Mar 5, 2022 Haudroff Mathematical Institute, Bonn, Germany
[Talk] The sensitivity theorem
Nov 16, 2021 3:00 PM — 4:00 PM [PST] UCLA Participating Analysis Seminar
[Talk] Decoupling, Cantor sets and additive combinatorics
Oct 20, 2021 3:00 PM — 4:00 PM [UK] UK Virtual Harmonic Analysis Seminar
[Travel] Summer School on discrete analysis and complexity of quantum algorithms
Oct 11, 2021 — Oct 15, 2021 Online
[Travel] Brascamp-Lieb inequalities Summer School
Sep 26, 2021 — Oct 1, 2021 Wolffhotel, Kopp, Germany
[Talk] Uniform boundedness in operators parametrized by polynomial curves
Aug 16, 2021 3:00 PM — 4:00 PM [EST] Probability and analysis webinar
[Travel] Harmonic Analysis and Analytic Number Theory, Dual trimester program
Aug 1, 2021 — Aug 20, 2021 Haudroff Mathematical Institute, Bonn, Germany
[Travel] Harmonic Analysis and Analytic Number Theory, Dual trimester program
May 3, 2021 — Jun 26, 2021 Haudroff Mathematical Institute, Bonn, Germany
[Talk] Decoupling for Cantor Sets
Mar 12, 2021 12:00 AM — 2:00 AM [UTC] Fourier restriction online 2021
[Talk] Uniform boundedness in operators parametrized by polynomial curves
Feb 11, 2021 2:00 PM — 3:00 PM [PST] UC Davis Student-Run Analysis and PDE
[Talk] Uniform boundedness in operators parametrized by polynomial curves
Dec 7, 2020 5:00 PM — 6:00 PM [CEST] Online Analysis Research Seminar
[Talk] Uniform boundedness in operators parametrized by polynomial curves
Nov 9, 2020 3:00 PM — 4:00 PM [CEST] Seminari d'Anàlisi UB-UAB
[Talk] Decoupling and applications: from PDEs to Number Theory.
Oct 21, 2020 12:00 PM — 1:00 PM [CEST] SIMBa seminar (UB / BGSMATH)
[Talk] On Sparsity in Overparametrised Shallow ReLU Networks
Oct 19, 2020 2:00 PM — 3:00 PM [EST] NYU, MaD Group Meeting

Publications and Preprints

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 …
Sitan Chen, Jaume de Dios, Jun-Ting Hsieh, Hsin-Yuan Huang, Jane Lange, Jerry Li
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 …
Jaume de Dios, José Madrid, Jan Grebík,, Rachel Greenfeld
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 …
Sinho Chewi, Jaume de Dios Pont, Jerry Li, Chen Lu, Shyam Narayanan
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 …
Jaume de Dios, Helge Jørgen Samuelsen
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 …
Jaume de Dios, Paata Ivanisvili, José Madrid
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 …
Jaume de Dios, Rachel Greenfeld, Paata Ivanisvili, José Madrid
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 …
Jaume de Dios, José Madrid
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 …
Alan Chang, Jaume de Dios, Rachel Greenfeld, Asgar Jamneshan, Zane Kun Li, José Madrid
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 …
Joan Bruna, Jaume de Dios
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 …
Jaume de Dios
arxiv:arXiv:2003.14140
A geometric lemma for complex polynomial curves with applications in Fourier restriction theory
See all publications

Teaching

Current and past classes.

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Current Classes Past Classes

UCLA Math 33B: Differential equations - Spring 2021

First-order, linear differential equations; second-order, linear differential equations with constant coefficients; power series solutions; linear systems. TA for Sections 1C, 1D. (Taught by Chengxi Wang). Link to the CCLE site.
UCLA Math 33B: Differential equations - Spring 2021

UCLA Math 32A: Calculus of Several Variables - Winter 2021

The course 32A treats topics related to differential calculus in several variables, including curves in the plane, curves and surfaces in space, various coordinate systems, partial differentiation, tangent planes to surfaces, and directional derivatives. The course culminates with the solution of optimization problems by the method of Lagrange multipliers. TA for Sections 1A, 1B. (Taught by Suzuki Fumiaki). Link to the CCLE site.
UCLA Math 32A: Calculus of Several Variables - Winter 2021

UCLA Math 32B: Calculus of Several Variables - Winter 2021

The course 32B treats topics related to integration in several variables, culminating in the theorems of Green, Gauss and Stokes. Each of these theorems asserts that an integral over some domain is equal to an integral over the boundary of the domain. In the case of Green’s theorem the domain is an area in the plane, in the case of Gauss’s theorem the domain is a volume in three-dimensional space, and in the case of Stokes' theorem the domain is a surface in three-dimensional space. These theorems are generalizations of the fundamental theorem of calculus, which corresponds to the case where the domain is an interval on the real line. The theorems play an important role in electrostatics, fluid mechanics, and other areas in engineering and physics where conservative vector fields play a role. TA for Sections 1A, 1B. (Taught by March Boedihardjo). Link to the CCLE site.
UCLA Math 32B: Calculus of Several Variables - Winter 2021

UCLA Math 32A: Calculus of Several Variables - Fall 2020

The course 32A treats topics related to differential calculus in several variables, including curves in the plane, curves and surfaces in space, various coordinate systems, partial differentiation, tangent planes to surfaces, and directional derivatives. The course culminates with the solution of optimization problems by the method of Lagrange multipliers. TA for Sections 1C, 1D. (Taught by Peter Spaas). Link to the CCLE site.
UCLA Math 32A: Calculus of Several Variables - Fall 2020

UCLA Math 131A: Analysis - Fall 2020

Math 131AB is the core undergraduate course sequence in mathematical analysis. The aim of the course is to cover the basics of calculus, rigorously. TA for Section 2A. (Taught by James Cameron). Link to the CCLE site.
UCLA Math 131A: Analysis - Fall 2020

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