University at Albany, SUNY

Marius Beceanu's Website

Contact Information

I am an Assistant Professor in the SUNY Albany Mathematics and Statistics Department.

Email: my first initial followed by my last name at albany dot edu

Office: Earth Science 136B.

Office hours: to be announced.

NEAM 2017

The Second Northeast Analysis Meeting (NEAM 2017) will take place at SUNY Albany from the 13th to the 15th of October, 2017: website

Publications

This is a list of my publications, last updated 6/26/17:

  1. Structure formulas for wave operators under a small scaling-invariant condition (in collaboration with W. Schlag), preprint, submitted, arXiv:1701.03015.
  2. Structure formulas for wave operators (in collaboration with W. Schlag), preprint, submitted, arXiv:1612.07304.
  3. A positivity criterion for the wave equation and global existence of large solutions (in collaboration with A. Soffer), preprint, submitted, arXiv:1605.07713.
  4. Large initial data global well-posedness for a supercritical wave equation (in collaboration with A. Soffer), preprint, arXiv:1602.08163.
  5. The Schrödinger equation with potential in random motion (in collaboration with A. Soffer), preprint, arXiv:1111.4584, accepted by Letters in Mathematical Physics.
  6. Large outgoing solutions to supercritical wave equations (in collaboration with A. Soffer), Int. Math. Res. Notices (2017) rnx050, doi:10.1093/imrn/rnx050.
  7. Decay estimates for the wave equation in two dimensions, Journal of Differential Equations (2016), Vol. 260, Issue 6, pp. 5378–5420.
  8. Dispersive estimates in ℝ3 with threshold eigenstates and resonances, Analysis & PDE 9-4 (2016), pp. 813–858.
  9. A centre-stable manifold for the energy-critical wave equation in ℝ3 in the symmetric setting, Journal of Hyperbolic Differential Equations (2014), Vol. 11, No. 3, pp. 437–476.
  10. Strichartz estimates and maximal operators for the wave equation in ℝ3 (in collaboration with M. Goldberg), Journal of Functional Analysis (2014) 266, Issue 3, pp. 1476–1510.
  11. Structure of wave operators for a scaling-critical class of potentials, American Journal of Mathematics (2014) 136, No. 2, pp. 255–308.
  12. Potentiels variables et équations dispersives, Séminaire Laurent Schwartz –- EDP et applications (2012-2013), Exp. No. 19, 11 pp..
  13. 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.
  14. 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.
  15. 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.
  16. New estimates for a time-dependent Schrödinger equation, Duke Mathematical Journal (2011), Vol. 159, No. 3, pp. 417–477.
  17. A centre-stable manifold for the focussing cubic NLS in ℝ1+3, Communications in Mathematical Physics (2008), Vol. 280, Issue 1, pp. 145–205.
  18. 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

Teaching

Currently I teach at SUNY Albany. In Fall 2017 I'll be teaching a course on Mathematics in the Physical Sciences and a course on PDEs. The course websites are on Blackboard.

I have previously taught at Caltech, the University of Chicago, Rutgers, and UC Berkeley.

I have also been a College Fellow at the University of Chicago, mentored by Professors Murthy and Kissin, and served as an Assistant Instructor at Princeton for Drs. Mitchener and Stalker.

Courses I have taught include the standard Calculus sequence, Vector Calculus, an Introduction to Mathematical Reasoning course, Discrete Probability, Mathematics in the Physical Sciences, Real Analysis, ODE, and PDE courses.

Earlier work

My Ph.D. thesis, written under the advice 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 Iaşi, 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 Takoo-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

Caragiale

These are some short stories by a classical Romanian
writer, I. L. Caragiale, in my translation.
You can find the originals here and here. Both stories
are out of copyright.

Căldură mare (Strong Heat) rtf
Bubico rtf
D-l Goe (Mr. Goe) rtf

Last modified: June 27th, 2017.
Old website: link