Marius Beceanu's Website
HackerRank
Placed 6th in the 2022 ServiceNow Code to Win competition organized on the HackerRank platform.
Top 0.5% out of 450,000 competitors, among over 5 million site members. Top 100 in Weekly Contests 373 and 375. Top 200 in Biweekly Contests 110 and 122 and in Weekly Contest 363.
9/30/2023: Finally upgraded to the premium version. LeetCode is useful and I wanted to give something back (not to mention the perks). However, I waited for more than a year, to amass enough points for a LeetCode "free" T-shirt. I felt that gathering the points with a paid subscription would be doing it on "easy mode": not worth it. The T-shirt is on its way now (update: it has arrived), hence no reason not to subscribe.
At that time I was ranked roughly 35,000th in the general rankings. Thus, LeetCode may have sent out over 30,000 T-shirts!
Publication list
This is a list of my publications, last updated January 11th, 2024:
Spectral multipliers III: endpoint bounds, intertwining operators, and twisted Hardy spaces (in collaboration with M. Goldberg), arXiv:2308.12829
Spectral multipliers II: elliptic and parabolic operators and Bochner-Riesz means (in collaboration with M. Goldberg), preprint, arXiv:2308.09606
A semilinear Schrödinger equation with random potential (in collaboration with A. Soffer), preprint, arXiv:1903.03451
Large global solutions for nonlinear Schrödinger equations III, energy-supercritical cases (in collaboration with Q. Deng, A. Soffer, Y. Wu), preprint, arXiv:1901.07709
Large initial data global well-posedness for a supercritical wave equation (in collaboration with A. Soffer), preprint, arXiv:1602.08163
The Schrödinger equation with potential in random motion (in collaboration with A. Soffer), preprint, arXiv:1111.4584, accepted by Letters in Mathematical Physics
Spectral multipliers and wave propagation for Hamiltonians with a scalar potential (in collaboration with M. Goldberg), Journal of Functional Analysis (2024), Vol. 286, Issue 6, 110300, doi:10.1016/j.jfa.2023.110300
A positivity criterion for the wave equation and global existence of large solutions (in collaboration with A. Soffer), Int. Math. Res. Notices 20 (2023), pp. 17911-17952, doi:10.1093/imrn/rnad127
Strichartz estimates for the Klein--Gordon equation in R^{3+1} (in collaboration with G. Chen), Pure Appl. Anal. 4(4): 767-809 (2022), doi:10.2140/paa.2022.4.767
Large global solutions for nonlinear Schrödinger equations II, mass-supercritical, energy-subcritical cases (in collaboration with Q. Deng, A. Soffer, Y. Wu), Communications in Mathematical Physics (2021) Vol. 382, pp. 173-237
Large global solutions for nonlinear Schrödinger equations I, mass-subcritical cases (in collaboration with Q. Deng, A. Soffer, Y. Wu), Advances in Mathematics (2021), Vol. 391, 107973, doi:10.1016/j.aim.2021.107973
Approximate analytical solutions to the heat and Stokes equations on the half-line obtained by Fokas’ transform (in collaboration with M. Lachaab), Journal of Applied Mathematics and Physics (2021), Vol. 9, No. 4
Structure formulas for wave operators (in collaboration with W. Schlag), American Journal of Mathematics (2020) 142, No. 3, pp. 751-807
Structure formulas for wave operators under a small scaling-invariant condition (in collaboration with W. Schlag) J. Spectr. Theory 9 (2019), pp. 967-990
Large outgoing solutions to supercritical wave equations (in collaboration with A. Soffer), Int. Math. Res. Notices 20 (2018), pp. 6201-6253, doi:10.1093/imrn/rnx050
Decay estimates for the wave equation in two dimensions, Journal of Differential Equations (2016), Vol. 260, Issue 6, pp. 5378 -- 5420
Dispersive estimates in R^3 with threshold eigenstates and resonances, Analysis & PDE 9-4 (2016), pp. 813--858
A centre-stable manifold for the energy-critical wave equation in R^3 in the symmetric setting, Journal of Hyperbolic Differential Equations (2014), Vol. 11, No. 3, pp. 437--476.
Strichartz estimates and maximal operators for the wave equation in R^3 (in collaboration with M. Goldberg), Journal of Functional Analysis (2014) 266, Issue 3, pp. 147--1510.
Structure of wave operators for a scaling-critical class of potentials, American Journal of Mathematics (2014) 136, No. 2, pp. 255--308
Potentiels variables et équations dispersives, Séminaire Laurent Schwartz --- EDP et applications (2012-2013), Exp. No. 19, 11 pp.
The Schrödinger equation with potential in rough motion (in collaboration with A. Soffer), Communications in Partial Differential Equations (2012), Vol. 37, Issue 6, pp. 969--1000
Dispersive estimates for the Schrödinger equation with scaling-critical potential (in collaboration with M. Goldberg), Communications in Mathematical Physics (2012), Vol. 314, Issue 2, pp. 471--481
A critical centre-stable manifold for Schrödinger's equation in three dimensions, Communications on Pure and Applied Mathematics (2012), Vol. 65, Issue 4, pp. 431--507
New estimates for a time-dependent Schrödinger equation, Duke Mathematical Journal (2011), Vol. 159, No. 3, pp. 417--477
A centre-stable manifold for the focussing cubic NLS in R^{1+3}, Communications in Mathematical Physics (2008), Vol. 280, Issue 1, pp. 145--205
Local exact controllability of the diffusion equation in one dimension, Abstract and Applied Analysis (2003), Vol. 2003, No. 14, pp. 793--811
Papers on ArXiv (most up-to-date listing): link
A conference proceedings volume for which I am listed as an editor:
Nonlinear Dispersive Waves and Fluids, edited by S. Zheng, M. Beceanu, J. Bona, Geng Chen, T. V. Phan, Contemporary Mathematics, Volume 725, AMS Book Series 2019.
Earlier work
My Ph.D. thesis, written under the supervision of Professor Wilhelm Schlag:
PDF file
Also see the 2008--2012 publications on the list above.
The following is a paper submitted to SICON in 2005. It is the generalization of my UAIC undergraduate thesis to arbitrarily many dimensions. Posted here is a revised version from 2007 that takes into account the referees' remarks:
PDF file
My Princeton undergraduate thesis, supervised by Professors Sergiu Klainerman and Igor Rodnianski:
PDF file
My undergraduate thesis at UAIC Iași, supervised by Professor Viorel Barbu:
English Romanian
Also see the 2003 publication on the list above.
My two junior-year projects at Princeton:
The first was done within the Junior Seminar, run by Professor Ramin Takloo-Bighash and Steve J. Miller.
It investigates some elementary properties of the period of the continued fraction of sqrt n.
PDF file
The second was done under the supervision of Professor Peter Sarnak.
It provides a computational confirmation of the Taniyama--Shimura conjecture, for non-integer primes in Z[i] of norm up to 45,000.
PDF file
The alphabet
By homotopy classes:
ADOPQR B CEFGHIJKLMNSTUVWXYZ
By homeomorphisms:
AR B CGIJLMNSUVWZ DO EFTY HK P Q X
Translations from Caragiale
Below are some short stories by a classical Romanian writer, I. L. Caragiale, in my translation.
You can find the original works here. All of Caragiale's work is out of copyright.
Căldură mare (Strong Heat) Original work here
D-l Goe (Mr. Goe) Original work here
Lanțul slăbiciunilor (The Weaknesses' Chain) Original work here
Pictures
It is customary for a website to include pictures. They can be found here.
YouTube channel
My YouTube channel contains videos I recorded for an Ordinary Differential Equations class. The production values are not great, but the content is fine.
Quotes
"An illustration will make my meaning clearer:—here are three fingers—a little finger, a second finger, and a middle finger."
Plato, The Republic
"Je suis un grand poète. Mes poésies, je ne les écris pas : elles consistent en actions et en sentiments."
Vautrin