Personal information:
I am a postdoc in the research
group of Professor
Dr. Vitali Wachtel at University of Bielefeld.
Email:
tuan.nguyen.math@gmail.com
Personal
website: [LINK]
Google
Scholar: [LINK]
MathSciNet:
[LINK]
CV:
[LINK]
Last
update: Nov. 17th 2024
Address at University of Bielefeld:
Faculty
of Mathematics
Telefon: +49 521 106-4783
Telefon
Sekretariat: +49 521 106-4797
Office: UHG V5-132
Current teaching:
Analysis
1 SS 2025
Bachelor
Seminar WS 2024-5 at Bielefeld University
Stochastik
2 SS 2024 at Bielefeld University
Current research:
Random walks in cones
Partial
differential equations
Stochastic Analysis
Multilevel
Monte Carlo approximations
McKean Vlasov stochastic
differential equations
Short CV:
Apr
2024 – : Postdoc at University of Bielefeld with
Professor Dr. Vitali Wachtel.
Jan
2023 – Mar 2024: Postdoc at Nanyang Technological
University, Singapore with Professor Dr. Ariel Neufeld.
Oct
2017 – Dec 2022: Postdoc at University of
Duisburg-Essen with Professor Dr. Martin Hutzenthaler.
Nov
2014 – Sept 2017: Ph. D. Mathematics at TU Berlin.
Ph. D. thesis: The random conductance model under degenerate
conditions.
Final result: summa cumme laude.
Supervisor:
Professor Dr. Jean-Dominique Deuschel.
Scholarship holder at
Berlin Mathematical School and RTG 1845.
Oct
2012 – Sept 2014: Master Mathematics at TU Berlin.
Phase 1 - Student at Berlin Mathematical School (qualifying
exam 1.3).
Master thesis: Invariance principle for the
random conductance model
(with Prof. Dr. Jean-Dominique
Deuschel and Dr. Martin Slowik).
Oct 2008 – Sept
2012: Bachelor Mathematics at TU Berlin. Nebenfach:
Makro-Ökonomik.
Bachelor thesis: Random Polymers - Pinning
for lazy walks.
(with Prof. Dr. Jean-Dominique Deuschel and
Dr. Martin Slowik).
Links (coauthors and mentors):
Prof.
Dr. Jean-Dominique Deuschel
Prof.
Dr. Martin Hutzenthaler
Prof.
Dr. Arnulf Jentzen
Prof.
Dr. Thomas Kruse
Prof.
Dr. Ariel Neufeld
Prof.
Dr. Martin Slowik
Prof.
Dr. Vitali Wachtel
Dr.
Sizhou Wu
Preprints:
Nguyen,
T. A.
Multilevel
Picard approximations overcome the curse of dimensionality when
approximating semilinear heat equations with gradient-dependent
nonlinearities in L^p-sense
Revision requested by Journal of
Computational and Applied Mathematics
arXiv:2410.00203,
2024
Neufeld,
A. & Nguyen, T. A.
Multilevel
Picard approximations and deep neural networks with ReLU, leaky
ReLU, and softplus activation overcome the curse of dimensionality
when approximating semilinear parabolic partial differential
equations in L^p-sense
arXiv:2409.20431,
2024
Neufeld,
A.; Nguyen, T. A. & Wu, S.
Multilevel
Picard approximations overcome the curse of dimensionality in the
numerical approximation of general semilinear PDEs with
gradient-dependent nonlinearities
Revision requested by
Journal of Complexity
arXiv:2311.11579,
2023
Hutzenthaler,
M. & Nguyen, T. A.
Multilevel
Picard approximations for high-dimensional decoupled
forward-backward stochastic differential
equations
arXiv:2204.08511,
2022
Hutzenthaler,
M. & Nguyen, T. A.
A
path-dependent stochastic Gronwall inequality and strong
convergence rate for stochastic functional differential
equations
arXiv:2206.01049,
2022
Hutzenthaler,
M.; Jentzen, A.; Kruse, T. & Nguyen, T. A.
Multilevel
Picard approximations for high-dimensional semilinear second-order
PDEs with Lipschitz nonlinearities
arXiv:2009.02484,
2020
Revision requested by
Numerical Methods for Partial Differential Equations
Nguyen, T. A.
A
Liouville principle for the random conductance model under
degenerate conditions
arXiv:1908.10691, 2019
Accepted papers:
Neufeld,
A.; Nguyen, T. A. & Wu, S.
Deep
ReLU neural networks overcome the curse of dimensionality in the
numerical approximation of semilinear partial integro-differential
equations
Accepted by Analysis and
Applications
arXiv:2310.15581,
2023
Neufeld,
A. & Nguyen, T. A.
Rectified
deep neural networks overcome the curse of dimensionality when
approximating solutions of McKean--Vlasov stochastic differential
equations
Journal
of Mathematical Analysis and Applications, 2025,
541, 128661 [DOI]
Neufeld,
A. & Nguyen, T. A.
Rectified
deep neural networks overcome the curse of dimensionality in the
numerical approximation of gradient-dependent semilinear heat
equations
Accepted by Communication in Mathematical
Sciences
arXiv:2403.09200,
2024
Hutzenthaler,
M.; Jentzen, A.; Kruse, T. & Nguyen, T. A.
Overcoming
the curse of dimensionality in the numerical approximation of
backward stochastic differential equations
Journal
of Numerical Mathematics, 2023,
31, 1-28 [DOI]
Hutzenthaler,
M. & Nguyen, T. A.
Multilevel
Picard approximations of high-dimensional semilinear partial
differential equations with locally monotone coefficient
functions
Applied
Numerical Mathematics, 2022,
181, 151-175 [DOI]
Hutzenthaler,
M.; Kruse, T. & Nguyen, T. A.
Multilevel
Picard approximations for McKean-Vlasov stochastic differential
equations
Journal
of Mathematical Analysis and Applications, 2022,
507, 125761 [DOI]
Hutzenthaler,
M. & Nguyen, T. A.
Strong
convergence rate of Euler-Maruyama approximations in
temporal-spatial Hölder-norms
Journal
of Computational and Applied Mathematics, 2022,
412, 114391 [DOI]
Hutzenthaler,
M.; Kruse, T. & Nguyen, T. A.
On
the speed of convergence of Picard iterations of backward
stochastic differential equations
Probability,
Uncertainty and Quantitative Risk, 2021,
7, 133-150 [DOI]
Hutzenthaler,
M.; Jentzen, A.; Kruse, T. & Nguyen, T. A.
A
proof that rectified deep neural networks overcome the curse of
dimensionality in the numerical approximation of semilinear heat
equations
SN
Partial Differential Equations and Applications, 2020,
1 [DOI]
Hutzenthaler,
M.; Jentzen, A.; Kruse, T.; Nguyen, T. A. & von Wurstemberger,
P.
Overcoming
the curse of dimensionality in the numerical approximation of
semilinear parabolic partial differential equations
Proceedings
of the Royal Society A: Mathematical, Physical and Engineering
Sciences, 2020,
476, 20190630
[DOI]
Nguyen,
T. A.
An
L^p-comparison, p1,, on the finite differences of a discrete
harmonic function at the boundary of a discrete box
Potential
Analysis, 2020,
56, 351-407 [DOI]
Deuschel,
J.-D.; Nguyen, T. A. & Slowik, M.
Quenched
invariance principles for the random conductance model on a random
graph with degenerate ergodic weights
Probability
Theory and Related Fields, 2018,
170, 363-386 [DOI]
Thesis:
Nguyen,
T. A.
The
random conductance model under degenerate conditions
Technical
University of Berlin, 2017
[DOI]