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;
  • Interactions with Machine Learning and Data Science;
Travel : University of Chicago (November 2022), IAS Princeton and University of Pennsylvania (February 2023), University of Arizona -Seminar on Stochastic Processes Annual Conference of the IMS (March 2023), University of Utah (March 2023), The 24th Midrasha Mathematicae: Random Schrödinger Operators and Random Matrices, Israel Institute for Advanced Studies (May 2023), Jeju Island South Korea (workshop, June 2023), Paris (June 2023), 10th Congress of Romanian Mathematicians and First Balkan Mathematics Congress (Romania, July 2023).
Past travel : Kyoto University, Japan (2022), Indian Statistical Institute, New Delhi, India (2022), National University of Singapore (2022), University of Luxembourg (2020), Max Planck Institute Leipzig and TU Berlin (2020)
Background

Tenure-Track Assistant Professor at the University of North Carolina at Charlotte (2023-)

Visiting Assistant Professor (via Burnett Meyer Fellowship) at the University of Colorado at Boulder (2022-2023)

Postdoctoral Fellow at NYU Shanghai (2019-2022)

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 -(last update 2021)

Contact:
vmargari@uncc.edu, +40732046315
 Office 350E, Fretwell Building, University of North Carolina Charlotte, USA.

Papers and preprints (for some manuscripts last update on journals in 2022)
  1. [New!-June 2023] A Gaussian free field approach to the natural parametrisation of SLE4[arXiv]-with L. Schoug (to appear in Electronic Communications in Probability)
  2. [New-Jan. 2023] Rate of Convergence in Multiple SLE using Random Matrix Theory [arXiv]-with A. Campbell and K. Luh
  3. [New-Dec. 2022, 39 pages] Deterministic Loewner Theory: Drivers, hitting times, and weldings in Loewner’s equation [arXiv]-with T. Mesikepp (to appear in the Journal of the London Mathematical Society)
  4. [New] On Loewner chains driven by semimartingales and complex Bessel-type SDEs [arXiv]-with A. Shekhar and Y. Yuan
  5. [New] Local Central Limit Theorem for Two-Body Potentials at Sufficiently High Temperatures [arXiv]-with Eric O. Endo. (to appear in the Journal of Statistical Physics).
  6. Perturbations of Simultaneously Growing Multiple Schramm-Loewner Evolutions [arXiv]-with Jiaming Chen.(to appear in Stochastic Processes and their Applications).
  7. Convergence of Splitting and Linear Interpolation Schemes to Schramm-Loewner Evolutions [arXiv]- with Jiaming Chen.
  8. Law of the SLE tip [arXiv]- with Oleg Butkovsky and Yizheng Yuan.(to appear in Electronic Journal of Probability.
  9. 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).
  10. 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).
  11. An asymptotic radius of convergence for the Loewner equation and simulation of SLE traces via splitting [arXiv] - with James Foster and Terry Lyons. (to appear in the Journal of Statistical Physics)
  12. 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.(to appear in Statistics and Probability Letters).
  13. 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).
Work in preparation
  1. Random Matrices, Multiple SLEs and connections with Machine Learning [PDF]
  2. Weak symmetries/Transversal Calculus [PDF]
Videos, slides and posters
  • [New] Talk at the '10th World Congress in Probability and Statistics' 2021 [video]
  • 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
  • An invitation to SLE Theory [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

UNC Charlotte:

Spring 2024: Probability Theory I (graduate course, part of Qual Exams) , 'STAT 2122 Introduction to Probability and Statistics' (Fall 2023).

CU Boulder:

Lector for 'Introduction to Probability and Statistics' (Fall 2022) and 'Linear Algebra for Non-Maths majors' (Fall 2022). Mini-course in 'Schramm-Loewner Evolutions' (Summer 2022).

NYU Shanghai:

Lector for Calculus (Summer course 2022) and 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).

Links on my activity