Fachbereich Mathematik und Informatik Angewandte Mathematik Münster

Private Homepage	https://www.uni-muenster.de/AMM/weber/index.html
Selected Publications	• Bruno, Stefano; Gess, Benjamin; Weber, Hendrik Optimal regularity in time and space for stochastic porous medium equations. Annals of Probability Vol. 50 (6), 2022 online • Chandra, Ajay; Gunaratnam, Trishen S.; Weber, Hendrik Phase Transitions for ϕ^4_3. Communications in Mathematical Physics Vol. 392, 2022 online • Chandra, Ajay; Moinat, Augustin; Weber, Hendrik A Priori Bounds for the Φ4 Equation in the Full Sub-critical Regime. Archive for Rational Mechanics and Analysis Vol. 247 (3), 2023 online • Grazieschi, Paolo; Matetski, Konstantin; Weber, Hendrik Martingale-driven integrals and singular SPDEs. Probability Theory and Related Fields Vol. 190, 2024 online • Hairer, Martin; Weber, Hendrik Rough Burgers-like equations with multiplicative noise. Probability Theory and Related Fields Vol. 157 (3-4), 2013 online • Moinat, Augustin; Weber, Hendrik Space-time localisation for the dynamic Phi-4/3 model. Communications on Pure and Applied Mathematics Vol. 73 (12), 2020 online • Mourrat, Jean-Christophe; Weber, Hendrik Convergence of the Two-Dimensional Dynamic Ising-Kac Model to Φ24. Communications on Pure and Applied Mathematics Vol. 70 (4), 2017 online • Mourrat, Jean-Christophe; Weber, Hendrik Global well-posedness of the dynamic Φ4 model in the plane. Annals of Probability Vol. 45 (4), 2017 online • Mourrat, Jean-Christophe; Weber, Hendrik The Dynamic Phi-4/3 Model Comes Down from Infinity. Communications in Mathematical Physics Vol. 356 (3), 2017 online • Otto, Felix; Weber, Hendrik Quasilinear SPDEs via Rough Paths. Archive for Rational Mechanics and Analysis Vol. 232 (2), 2019 online
Topics in Mathematics Münster	T6: Singularities and PDEs T7: Field theory and randomness T10: Deep learning and surrogate methods
Current Publications	• Song, Chunqiu; Weber, Hendrik; Wulkenhaar, Raimar Stochastic quantization of λϕ^4_2-theory in 2-d Moyal space. , 2025 online • de Lima Feltes, Guilherme; Weber, Hendrik Brownian particle in the curl of 2-d stochastic heat equations. Journal of Statistical Physics Vol. 191, 2024 online • Chevyrev, I.; Gerasimovičs, A.; Weber, H. Feature Engineering with Regularity Structures. Journal of Scientific Computing Vol. 98 (13), 2024 online • Chandra, Ajay; de Lima Feltes, Guilherme; Weber, Hendrik A priori bounds for 2-d generalised Parabolic Anderson Model. , 2024 online • Grazieschi, Paolo; Matetski, Konstantin; Weber, Hendrik The dynamical Ising-Kac model in 3D converges to Φ4/3. Probability Theory and Related Fields Vol. 190 (1-2), 2024 online • Otto, Felix; Sauer, Jonas; Smith, Scott; Weber, Hendrik A priori bounds for quasi-linear SPDEs in the full sub-critical regime. Journal of the European Mathematical Society Vol. online first, 2024 online • Esquivel, Salvador; Weber, Hendrik A priori bounds for the dynamic fractional Φ4 model on T3 in the full subcritical regime. , 2024 online • Grazieschi, Paolo; Matetski, Konstantin; Weber, Hendrik Martingale-driven integrals and singular SPDEs. Probability Theory and Related Fields Vol. 190, 2024 online • Chandra, Ajay; Moinat, Augustin; Weber, Hendrik A Priori Bounds for the Φ4 Equation in the Full Sub-critical Regime. Archive for Rational Mechanics and Analysis Vol. 247 (3), 2023 online
Current Projects	• Global Estimates for non-linear stochastic PDEs Semi-linear stochastic partial differential equations: global solutions’ behaviours Partial differential equations are fundamental to describing processes in which one variable is dependent on two or more others – most situations in real life. Stochastic partial differential equations (SPDEs) describe physical systems subject to random effects. In the description of scaling limits of interacting particle systems and in quantum field theories analysis, the randomness is due to fluctuations related to noise terms on all length scales. The presence of a non-linear term can lead to divergencies. Funded by the European Research Council, the GE4SPDE project will describe the global behaviour of solutions of some of the most prominent examples of semi-linear SPDEs, building on the systematic treatment of the renormalisation procedure used to deal with these divergencies. online • EXC 2044 - B3: Operator algebras & mathematical physics The development of operator algebras was largely motivated by physics since they provide the right mathematical framework for quantum mechanics. Since then, operator algebras have turned into a subject of their own. We will pursue the many fascinating connections to (functional) analysis, algebra, topology, group theory and logic, and eventually connect back to mathematical physics via random matrices and non-commutative geometry. online • EXC 2044 - C3: Interacting particle systems and phase transitions The question of whether a system undergoes phase transitions and what the critical parameters are is intrinsically related to the structure and geometry of the underlying space. We will study such phase transitions for variational models, for processes in random environments, for interacting particle systems, and for complex networks. Of special interest are the combined effects of fine-scalerandomly distributed heterogeneities and small gradient perturbations. We aim to connect different existing variational formulations for transportation networks, image segmentation, and fracture mechanics and explore the resulting implications on modelling, analysis, and numerical simulation of such processes. We will study various aspects of complex networks, i.e. sequences of random graphs (Gn)n∈N, asking for limit theorems as n tends to infinity. A main task will be to broaden the class of networks that can be investigated, in particular, models which include geometry and evolve in time. We will study Ising models on random networks or with random interactions, i.e. spin glasses. Fluctuations of order parameters and free energies will be analysed, especially at the critical values where the system undergoes a phase transition. We will also investigate whether a new class of interacting quantum fields connected with random matrices and non-commutative geometry satisfies the Osterwalder-Schrader axioms. Further, we will study condensation phenomena, where complex network models combine the preferential attachment paradigm with the concept of fitness. In the condensation regime, a certain fraction of the total mass dynamically accumulates at one point, the condensate. The aim is a qualitative and quantitative analysis of the condensation. We willalso explore connections to structured population models. Further, we will study interacting particle systems on graphs that describe social interaction or information exchange. Examples are the averaging process or the Deffuant model. We will also analyse asymmetric exclusion processes (ASEP) on arbitrary network structures. An interesting aspect will be how these processes are influenced by different distribution mechanisms of the particles at networks nodes. If the graph is given by a lattice, we aim to derive hydrodynamic limits for the ASEP with jumps of different ranges for multiple species, and for stochastic interactingmany-particle models of reinforced random walks. Formally, local cross-diffusion syste ms are obtained as limits of the classical multi-species ASEP and of the many-particle random walk. We will compare the newly resulting limiting equations and are interested in fluctuations, pattern formation, and the long-time behaviour of these models on the microscopic and the macroscopic scale. Further, we will analyse properties of the continuous directed polymer in a random environment. online
E-Mail	hendrik dot weber at uni-muenster dot de
Phone	+49 251 83-35148
FAX	+49 251 83-32729
Room	120.017
Secretary	Sekretariat Lückert Frau Dr. Claudia Lückert Telefon +49 251 83-35154 Fax +49 251 83-32729 Zimmer 120.025
Address	Prof. Dr. Hendrik Weber Angewandte Mathematik Münster: Institut für Analysis und Numerik Fachbereich Mathematik und Informatik der Universität Münster Orléans-Ring 10 48149 Münster
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