Vlad Mărgărint

Research Interests

Mathematical Physics: Stochastic and Complex Analysis; Schramm-Loewner evolutions and Rough Paths Theory. Random Matrix Theory.

Background

Postdoctoral Fellow at NYU Shanghai (since 2019)-[currently in Europe for some undetermined time].

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
 Office 1133, NYU Shanghai, 1555 Century Avenue, Pudong, Shanghai.


Papers, preprints and work in preparation
  • 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 - with Dmitry Beliaev and Atul Shekhar [arXiv].
  • 9. Quasi-Sure Stochastic Analysis through Aggregation and SLE Theory [arXiv]
Posters and Slides
  • 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:

Honors Analysis I (Spring 2020), Linear Algebra (Spring 2020), Calculus I (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).