# Razvan Mosincat

School of Mathematics
The University of Edinburgh
The King's Buildings, Peter Guthrie Tait Road
James Clerk Maxwell Building, EH9 3FD
Edinburgh, UK

office: JCMB, room 5210
e-mail: r.o.mosincat [at] sms.ed.ac.uk

### Research interests

I am interested in the analysis of nonlinear dispersive PDEs using tools from harmonic analysis, dynamical systems, probability, and operator theory. In particular, I address problems regarding the low-regularity analysis of (deterministic and stochastic) Schrödinger-type equations. My supervisor is Dr. Tadahiro Oh.

### Publications

1. (with O. Pocovnicu, L. Tolomeo, Y. Wang) Well-posedness of periodic three-dimensional stochastic nonlinear beam equations with space-time white noise
2. (PhD thesis) Well-posedness of the one-dimensional derivative nonlinear Schrödinger equation
3. (with H. Yoon) Unconditional uniqueness for the derivative nonlinear Schrödinger equation on the real line
4. (with K. Cheung) Stochastic nonlinear Schrödinger equations on tori, arXiv:1803.02817
5. Global well-posedness of the derivative nonlinear Schrödinger equation with periodic boundary condition in $$H^{\frac12}$$, arXiv:1608.06838, J. Differential Equations, 263 (2017) 4658-4722
6. (with T. Oh) A remark on global well-posedness of the derivative nonlinear Schrödinger equation on the circle, arXiv:1502.02261, C. R. Math. Acad. Sci. Paris, Ser. I 353 (2015) 837-841
7. (with C. Preda and P. Preda) Dichotomies with no invariant unstable manifolds for autonomous equations, J. Funct. Spaces Appl., vol. 2012, Article ID 527647, 23 pp.
8. (with C. Preda and P. Preda) A new version of a theorem of Minh-Rabiger-Schnaubelt regarding nonautonomous evolution equations, Appl. Anal., 90 (2011) 1405-1418.
9. (with C. Preda and P. Preda) Averaging theorems for the large-time behavior of the solutions of nonautonomous systems, Systems Control Lett., 60 (2011) 994-999.

### Talks

1. University of York (UK), Mathematical Finance and Stochastic Analysis Seminar, May 21, 2018:
Stochastic nonlinear Schrödinger equations on tori
2. University of Oxford (UK), Joint CDT Colloquium: Analysis and PDEs, April 20, 2018:
Unconditional uniqueness for the derivative nonlinear Schrödinger equation
3. Kyoto University (Japan), NLPDE seminar, Department of Mathematics, February 9, 2018:
Low-regularity well-posedness for the derivative nonlinear Schrödinger equation
and
Stochastic nonlinear dispersive equations: SNLB and SNLS
4. Fields Institute, Toronto (Canada), Focus Program on Nonlinear Dispersive Partial Differential Equations and Inverse Scattering, July 31 - August 23, 2017:
(poster) Low-regularity well-posedness for the derivative nonlinear Schrödinger equation
5. ICMS, Edinburgh (UK), Probabilistic Perspectives in Nonlinear PDEs, June 5-9, 2017 and Nonlinear PDEs, stochastic control and filtering: new methods and applications: in honour of Nikolai Krylov, May 29 - June 2, 2017
(poster) Well-posedness theory of the three-dimensional stochastic beam equation with additive space-time white noise forcing
6. University of Birmingham (UK), Analysis Seminar (School of Mathematics), October 31, 2016:
Global well-posedness for the derivative nonlinear Schrödinger equation on the torus
7. West University of Timisoara (Romania), The 23rd International Conference on Operator Theory, June 29 - July 4, 2010:
Some remarks on the asymptotic behaviour of the solutions of semilinear evolution equations
8. West University of Timisoara (Romania), Functional Analysis seminar, March 2010:
Discrete-time theorems for the continuous-time dichotomy of autonomus equations with no unstable invariant manifolds.
9. West University of Timisoara (Romania), Analysis seminar, November 2009:
Spectral properties of one-parameter semigroups
10. West University of Timisoara (Romania), Analysis seminar, October 2009:
On the abstract Cauchy problem

### Teaching

In past semesters, I served as a tutor for:
• Honours Complex Variables (Spring 2018, 1 section)
• Honours Complex Variables, skills (Spring 2018, 2 sections)
• Probability with Applications (Spring 2017, 2 sections)
• Honours Complex Variables (Spring 2017, 1 section)
• Honours Complex Variables, skills (Spring 2017, 1 section)
• Honours Differential Equations (Fall 2016, 1 section)
• Linear Analysis (Fall 2016, 1 section)
• Pure Analysis (SMSTC, graduate level), Module 1 (Fall 2016)
• Probability with Applications (Spring 2016, 2 sections)
• Engineering Mathematics (Fall 2015, 2 sections)
• Calculus and its Applications (Spring 2015, 2 sections)

### Organized events

Joint CDT Colloquium (joint meeting of the CDTs at University of Cambridge, University of Edinburgh and Heriot-Watt University, University of Oxford, and University of Warwick): co-organiser (with Tim Hurst, Anton Martinsson, Jenovah Rodrigues), April 18-21, 2017, ICMS, Edinburgh (UK).

### Misc.

While an undergraduate student at the Politehnica" University of Timisoara (Romania), I took some interest in developing optimized code for training artificial neural networks. I have worked under the supervision of Dr. Dan Ciresan. Nowadays, I am curious to hear about new developments in machine learning, pattern recognition, or more broadly in artificial intelligence.