Vlad Mărgărint

Research Interests
  • Mathematical Physics: Schramm-Loewner evolutions;
  • Rough Path Theory;
  • (Biased) Random walks on random graphs and their scaling limits;
  • Random Matrix Theory;
Background

Postdoctoral Fellow at NYU Shanghai (since September 2019)

DPhil (PhD) student in Mathematics, University of Oxford (2015-2019), under the supervision of Prof. Dmitry Belyaev and Prof. Terry Lyons.

MSc in Mathematics, ETH Zürich (between 2013-2015), under the supervision of Prof. Antti Knowles.

BSc in Mathematics, University of Bucharest (between 2010-2013), under the supervision of Prof. Victor Vuletescu.

Curriculum Vitae
Vlad in Italy

Contact:
margarint@nyu.edu, +40732046315
 Office 1133, NYU Shanghai, 1555 Century Avenue, Pudong, Shanghai.

Papers and preprints
  1. Convergence in High Probability of the Quantum Diffusion in a Random Band Matrix Model. Journal of Statistical Physics (2018) [Springer] (under the supervision of Antti Knowles).
  2. Proof of the Weak Local Law for Wigner Matrices using Resolvent Expansions [arXiv] (under the supervision of Antti Knowles).
  3. Convergence to closed-form distribution for the backward SLE at some random times and the phase transition at κ=8 [arXiv] - with Terry Lyons and Sina Nejad.
  4. An asymptotic radius of convergence for the Loewner equation and simulation of SLE traces via splitting [arXiv] - with James Foster and Terry Lyons.
  5. A new approach to SLE phase transition [arXiv] [Update PDF] - with Dmitry Belyaev and Terry Lyons.
  6. Complex Solutions to Bessel SDEs and SLEs [arXiv] - with Atul Shekhar.
  7. Continuity in κ in SLE theory using a constructive method and Rough Path Theory - with Dmitry Beliaev and Terry Lyons [arXiv] (to appear in Annales de l’Institut Henri Poincaré).
  8. Continuity of Zero-Hitting Times of Bessel Processes and Welding Homeomorphisms of SLE [arXiv] - with Dmitry Beliaev and Atul Shekhar. (to appear in ALEA- Latin American Journal of Probability and Mathematical Statistics).
  9. Quasi-Sure Stochastic Analysis through Aggregation and SLE Theory [arXiv].
Work in preparation
  1. On Aldous' Cover Time Conjecture [PDF]-with George Andriopoulos.
  2. Random Matrices and Multiple SLEs [PDF]
  3. Weak symmetries/Transversal Calculus [PDF]
Videos, slides and posters
  • Talk at the 'One World' Symposium [video]
  • Pathwise and probabilistic analysis in the context of SLE [PDF]
  • Using results on Bessel processes in the study of SLE [PDF]
  • Truncated Taylor approximation of Loewner dynamics [PDF]
  • Quantum Diffusion and Random Matrix Theory [PDF]
  • [P] Two results obtained in Random Matrix Theory [PDF]
  • Shapeletes and Compressive Sensing [PDF]
Expository Texts
  • SLE Theory for beginners [PDF]
  • Introduction to Rough Paths Theory with applications [PDF]
  • Differentiable forms, integration and the Degree Theorem (Topology and Differential Geometry) [PDF]
  • Distribute Education Project (in Romanian) [PDF]
Teaching

NYU Shanghai:

Calculus (mixed-mode) (Fall 2020), Honors Analysis I (online) (Spring 2020), Linear Algebra (online) (Spring 2020), Calculus (Fall 2019).

University of Oxford:

Tutor for: Numerical Analysis (Spring 2016); Stochastic Differential Equations (Winter 2017); Applied Probability (Winter 2017); Complex Analysis: Conformal maps and Geometry (Winter 2017); Continuous Martingales and Stochastic Calculus (Spring 2017); Statistical Mechanics (Winter 2017); Statistics and Data Analysis (Spring 2017, Spring 2018); Distribution Theory and Fourier Analysis (Winter 2018).

Teaching Assistant for: Approximations of functions (Winter 2015); Stochastic Analysis and PDEs (Spring 2016); Complex Analysis: Conformal maps and Geometry (Winter 2017).

ETH Zürich:

Methods of Mathematical Physics II (Spring 2014), Analysis I (Winter 2014), Analysis II (Spring 2013).

Links on my activity