Vlad Mărgărint
Research Interests
- Mathematical Physics: Schramm-Loewner evolutions, Field Theory;
- Rough Path Theory;
- (Biased) Random walks on random graphs and their scaling limits;
- Random Matrix Theory;
Background
Assistant Professor Faculty Fellow of Mathematics at NYU Shanghai (Spring 2021)
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
Contact:
margarint@nyu.edu, +40732046315
Office 1133, NYU Shanghai, 1555 Century Avenue, Pudong, Shanghai.
Papers and preprints
- 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).
- Proof of the Weak Local Law for Wigner Matrices using Resolvent Expansions [arXiv] (under the supervision of Antti Knowles).
- 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.
- An asymptotic radius of convergence for the Loewner equation and simulation of SLE traces via splitting [arXiv] - with James Foster and Terry Lyons.
- A new approach to SLE phase transition [arXiv] [Update PDF] - with Dmitry Belyaev and Terry Lyons.
- Complex Solutions to Bessel SDEs and SLEs [arXiv] - with Atul Shekhar.
- 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).
- 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).
- Quasi-Sure Stochastic Analysis through Aggregation and SLE Theory [arXiv].
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
Teaching
NYU Shanghai:
Lector for Mathematics for Economics II (Spring 2021) (mixed-mode) for NYU New York 'Go Local' students, Instructor for 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).