Lukas Wessels

About Me

I am currently a visiting scholar at the Georgia Institute of Technology in Atlanta hosted by Andrzej Święch and funded by a fellowship of the German Academic Exchange Service (DAAD). Previously, I completed my PhD at Technische Universität Berlin and the Berlin Mathematical School. My supervisor was Wilhelm Stannat.

Contact

wessels (at) math.tu-berlin.de

Research Interests

• Stochastic Optimal Control in Infinite Dimensions
• Backward Stochastic (Partial) Differential Equations
• Fully Nonlinear Partial Differential Equations
• Mean Field Control and Mean Field Games

Publications

• L. Wessels, Semilinear Feynman-Kac Formulae for B-Continuous Viscosity Solutions, submitted, arXiv:2303.10038.
• W. Stannat, A. Vogler and L. Wessels, Neural Network Approximation of Optimal Controls for Stochastic Reaction-Diffusion Equations, submitted, arXiv:2301.11926.
• W. Stannat and L. Wessels, Necessary and Sufficient Conditions for Optimal Control of Semilinear Stochastic Partial Differential Equations, minor revision required for Ann. Appl. Probab., arXiv:2112.09639.
• W. Stannat and L. Wessels, Peng’s Maximum Principle for Stochastic Partial Differential Equations, SIAM J. Control Optim. 59, 3552-3573 (2021), arXiv:2105.05194.
• W. Stannat and L. Wessels, Deterministic Control of Stochastic Reaction-Diffusion Equations, Evol. Equ. Control Theory 10, 701-722 (2021), arXiv:1905.09074.

Doctoral Thesis:

• L. Wessels, Optimal Control of Stochastic Reaction-Diffusion Equations, Technische Universität Berlin, 2022, http://dx.doi.org/10.14279/depositonce-16218.

See also my Google Scholar Profile.

Presentations

• Stochastic Control & Financial Engineering, Princeton University, Princeton, NJ, June 20 – 23, 2023.
• Mathematical Finance Seminar Series, Columbia University, New York, NY, April 6, 2023.
• Seminar on Stochastic Processes, University of Arizona, Tucson, AZ, March 8 – 11, 2023, (Poster).
• Math Finance Colloquium, University of Southern California, Los Angeles, CA, November 28, 2022, (Slides).
• 21st Northeast Probability Seminar, Columbia University, New York, NY, November 17 – 18, 2022, (Slides).
• Modern Topics in Probability, Brin Mathematics Research Center, College Park, MD, October 17 – 21, 2022, (Slides).
• PDE Seminar, Georgia Institute of Technology, Atlanta, GA, September 20, 2022, (Slides).
• PhD Defense, Technische Universität Berlin, July 19, 2022, (Slides).
• Oberseminar Dynamics, Technische Universität München, virtual, July 4, 2022, (Slides).
• 9th Colloquium on Backward Stochastic Differential Equations and Mean Field Systems, Annecy, June 27 – July 1, 2022, (Slides).
• Langenbach-Seminar, WIAS Berlin, virtual, December 1, 2021, (Slides).
• German Probability and Statistics Days, virtual, September 27 – October 1, 2021, (Slides, Link to the recording).
• International Conference on Control of Self-Organizing Nonlinear Systems, Potsdam, August 29 – September 2, 2021, (Slides).
• 9th BMS Student Conference, virtual, March 3 – 5, 2021, (Slides).
• Workshop on Control of Self-Organizing Nonlinear Systems, Lutherstadt Wittenberg, August 20 – 22, 2019 (Slides).
• International Conference on Control of Self-Organizing Nonlinear Systems, Warnemünde, Rostock, September 9 – 13, 2018 (Slides).

Courses Taught

• Winter semester 2020/2021: Differential Equations I, Institute of Mathematics, Technische Universität Berlin
• Winter semester 2018/2019: Calculus II for Engineering, Institute of Mathematics, Technische Universität Berlin
• Summer semester 2018: Stochastics for Computer Science, Institute of Mathematics, Technische Universität Berlin
• Winter semester 2017/2018: Calculus I for Engineering, Institute of Mathematics, Technische Universität Berlin
• Winter semester 2014/2015: Mathematics and Statistics for Biology, Institute of Mathematics, Rheinische Friedrich-Wilhelms-Universität Bonn

Book Recommendations

These are some books that speak to me as a mathematician and have informed the way I think about my career.

• Timothy Gowers, June Barrow-Green, and Imre Leader (eds.): Princeton Companion to Mathematics. Contains introductions to (almost) all areas of modern pure mathematics. Great to broaden the mathematical horizon.
• Paul R. Halmos: I Want to be a Mathematician (freely available). Paints a good picture of what it’s like to be a professional mathematician in the US: Starting from high school, going through undergrad, grad school, postdoc, all ranks of professor and a department chair.
• Allison K. Henrich, Emille D. Lawrence, Matthew A. Pons, and David G. Taylor (eds.): Living Proof (freely available). Tells the stories of 41 mathematicians and how they got to where they are now, highlighting obstacles they had to overcome on their journeys.