“He who seeks for methods without having a definite problem in mind seeks for the most part in vain.” (David Hilbert)
Scientific Interests
 stochastic partial differential equations
 (stochastic) variational calculus
 singular and degenerate stochastic diffusion equations in Hilbert space
 nonlocal and local nonlinear stochastic evolution equations
 linear growth functionals and variational convergence
 ergodic theory and invariant distributions
 Dirichlet forms and their geometry
 Models from biology, ecology and neuroscience
Coauthors
(in chronological order)
Links
Google Scholar, arXiv, Orcid, ResearcherID.
List of Publications
for Jonas M. Tölle
updated March 28, 2020
Erdős number: 3
P. Erdős — C. J. Colbourn — M. Scheutzow — J. M. Tölle
Submitted for peer review
 J. M. Tölle (with M. Hinz and L. Viitasaari). Variability of paths and differential equations with BVcoefficients. Preprint, submitted (2020), 68 pp., arXiv:2003.11698.
Abstract.
show abstractWe define compositions φ(X) of Hölder paths X in ℝ^{n} and functions of bounded variation φ under a relative condition involving the path and the gradient measure of φ. We show the existence and properties of generalized LebesgueStieltjes integrals of compositions φ(X) with respect to a given Hölder path Y. These results are then used, together with Doss’ transform, to obtain existence and, in a certain sense, uniqueness results for differential equations in ℝ^{n} driven by Hölder paths and involving coefficients of bounded variation. Examples include equations with discontinuous coefficients driven by paths of twodimensional fractional Brownian motions.
 J. M. Tölle (with E. Hausenblas). The stochastic Klausmeier system and a stochastic SchauderTychonoff type theorem. Preprint, submitted (2019), 27 pp., arXiv:1912.00996.
Abstract.
show abstractWe investigate the existence of a pair of nonnegative solutions to the stochastic system of advectiondiffusion equations proposed by Klausmeier with Gaussian multiplicative noise. The proof of existence is based upon a stochastic version of the SchauderTychonoff fixed point theorem, which is also proved here.
Journal Publications
 J. M. Tölle. Stochastic evolution equations with singular drift and gradient noise via curvature and commutation conditions. Stochastic Processes and their Applications, 130 (2020), no. 5, 3220–3248, https://doi.org/10.1016/j.spa.2019.09.011, preprint available at arXiv:1803.07005.
 J. M. Tölle (with C. Kuehn). A gradient flow formulation for the stochastic Amari neural field model. Journal of Mathematical Biology, 79 (2019), no. 4, 1227–1252, https://doi.org/10.1007/s0028501901393w, preprint available at arXiv:1807.02575.
 J. M. Tölle (with B. Gess). Ergodicity and local limits for stochastic local and nonlocal pLaplace equations. SIAM J. Math. Anal. 48 (2016), no. 6, 4094–4125, http://dx.doi.org/10.1137/15M1049774, preprint available at arXiv:1507.04545.
 J. M. Tölle (with I. Ciotir). Nonlinear stochastic partial differential equations with singular diffusivity and gradient Stratonovich noise. J. Funct. Anal. 271 (2016), no. 7, 1764–1792, http://dx.doi.org/10.1016/j.jfa.2016.05.013, preprint available at arXiv:1507.02576.
 J. M. Tölle (with B. Gess). Stability of solutions to stochastic partial differential equations. J. Differential Equations 260 (2016), no. 6, 4973–5025, http://dx.doi.org/10.1016/j.jde.2015.11.039, preprint available at arXiv:1506.01230.
 J. M. Tölle (with B. Gess). Multivalued, singular stochastic evolution inclusions. J. Math. Pures Appl. 101 (2014), no. 6, 789–827, http://dx.doi.org/10.1016/j.matpur.2013.10.004, preprint available at arXiv:1112.5672.
 J. M. Tölle (with A. EsSarhir, M. Scheutzow and O. van Gaans). Invariant measures for monotone SPDEs with multiplicative noise term. Appl. Math. Optim. 68 (2013), no. 2, 275–287, http://dx.doi.org/10.1007/s0024501392064, preprint available at arXiv:0910.0960.
 J. M. Tölle (with I. Ciotir). Corrigendum to “Convergence of invariant measures for singular stochastic diffusion equations” [Stochastic Process. Appl. 122 (2012) 1998–2017.] Stochastic Process. Appl. 123 (2013), no. 3, 1178–1181, http://dx.doi.org/10.1016/j.spa.2012.10.009, preprint available at arXiv:1211.4404.
 J. M. Tölle. Uniqueness of weighted Sobolev spaces with weakly differentiable weights. J. Funct. Anal. 263 (2012), no. 10, 3195–3223, http://dx.doi.org/10.1016/j.jfa.2012.08.002, preprint available at arXiv:1110.2888.
 J. M. Tölle (with I. Ciotir). Convergence of invariant measures for singular stochastic diffusion equations. Stochastic Process. Appl. 122 (2012), no. 4, 1998–2017, http://dx.doi.org/10.1016/j.spa.2011.11.011, preprint available at arXiv:1201.2839.
 J. M. Tölle (with M.K. von Renesse). On an EVI curve characterization of Hilbert spaces. J. Math. Anal. Appl. 385 (2012), 589–598, http://dx.doi.org/10.1016/j.jmaa.2011.06.080.
 J. M. Tölle (with W. Liu). Existence and uniqueness of invariant measures for stochastic evolution equations with weakly dissipative drifts. Electr. Comm. Probab. 16 (2011), 447–457, https://doi.org/10.1214/ECP.v161643, preprint available at arXiv:1109.2437.
Published in peer reviewed proceedings
 J. M. Tölle. Estimates for nonlinear stochastic partial differential equations with gradient noise via Dirichlet forms. In: Eberle A., Grothaus M., Hoh W., Kassmann M., Stannat W., Trutnau G. (eds) Stochastic Partial Differential Equations and Related Fields. SPDERF 2016. Springer Proceedings in Mathematics & Statistics, vol 229. Springer, Cham. https://doi.org/10.1007/9783319749297_14.
Other works
 J. M. Tölle (with P. Beissner). A compact topology for σalgebra convergence. Working paper, (2018), 23 pp., arXiv:1802.05920.
 J. M. Tölle. Convergence of solutions to the pLaplace evolution equation as p goes to 1. Preprint, http://arxiv.org/abs/1103.0229v2, 2011, 11 pp.
Theses
 J. M. Tölle. Stochastic partial differential equations with singular drift. Habilitation thesis, Universität Augsburg, 2019, 232 pp.
 J. M. Tölle. Variational convergence of nonlinear partial differential operators on varying Banach spaces. Dissertation, Universität Bielefeld, published online on BieSOn, Universitätsbibliothek Bielefeld, urn:nbn:de:hbz:36116758, 2010, 250 pp, pdf.
 J. M. Tölle. Convergence of nonsymmetric forms with changing reference measures. Diploma thesis, Universität Bielefeld, BiBoSPreprint E0609234, http://www.math.unibielefeld.de/~bibos/preprints/E0609234.pdf, 2006, 81 pp.
Coorganization of Workshops
 Minisymposium “Nonlocal phenomena and regularity for stochastic evolution equations” (at the annual meeting of the German mathematical society (DMV), TU Chemnitz, September 14 — 17, 2020.)

Workshop on “Nonlinear, nonlocal problems and stochastic methods” at Aalto University, Finland, December 7 — 9, 2016.
Workshop homepage: NNPSM2016.
Workshop poster.
Selected past Talks
Meeting  Location  Date  Title of Talk  Slides 

8th Austrian Stochastic Days 2020  Graz, Austria  September 10 — 11, 2020  Variability of paths and differential systems with BVcoefficients  
SIAM Conference on Analysis of Partial Differential Equations (PD19)  La Quinta, CA, U.S.A.  December 11 — 14, 2019  Gradient flows for the stochastic Amari neural field model  pdf, video 
9th International Conference on Stochastic Analysis and Its Applications  Bielefeld University  September 3 — 7, 2018  Gradient flows for the stochastic Amari neural field model  
Workshop on Stochastic Systems: their Analysis, Geometry and Perturbation  Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing, China  July 10 — 15, 2018  Stochastic nonlinear PDEs with singular drift and gradient noise  
Stochastic Partial Differential Equations  CIRM, Luminy, Marseille, France  May 14 — 18, 2018  Gradient flows for the stochastic Amari neural field model  
13th German Probability and Statistics Days  Uni Freiburg, Freiburg im Breisgau, Germany  Feb 27 — March 2, 2018  The set of subσalgebras is a compact metric space.  
19th ÖMG Congress and Annual DMV Meeting  ParisLodron University of Salzburg, Salzburg, Austria  Sep 11 — 15, 2017  The pLaplace evolution equation as p goes to 1 — Toward a general convergence result for parabolic minimizers  
19th ÖMG Congress and Annual DMV Meeting  ParisLodron University of Salzburg, Salzburg, Austria  Sep 11 — 15, 2017  Nonlinear SPDE with gradient noise via curvaturedimension conditions  
JapaneseGerman Open Conference on Stochastic Analysis 2017  University of Kaiserslautern, Germany  Sep 4 — 8, 2017  A compact topology for σalgebra convergence  
Oberseminar Mathematische Modellierung und partielle Differentialgleichungen  Augsburg University, Augsburg, Germany  May 30, 2017  The pLaplace evolution equation as p goes to 1: Toward a general convergence result for parabolic minimizers  
Stochastic Partial Differential Equations and Related Fields  Bielefeld University, Bielefeld, Germany  Oct 10 — 14, 2016  Nonlinear, singular SPDE perturbed by noise acting along infinitesimal motions on domains with symmetries  
7th European Congress of Mathematics  Technical University of Berlin, Berlin, Germany  Jul 18 — 22, 2016  Nonlinear stochastic partial differential equations with singular diffusivity and gradient Stratonovich noise  
Stochastic Partial Differential Equations and Applications – X  Levico Terme, Trento, Italy  Apr 30 — May 3, 2016  Nonlinear, singular SPDE with gradienttype Gaussian noise driving infinitesimal vector field actions 
Lectures
Course  Institution  Semester 

Seminar on “Stochastic Differential Equations”  Augsburg University  2019 
Functional Analysis  Ulm University  2018/19 
Analysis III  Ulm University  2018/19 
Functional Analysis  Augsburg University  2018 
Seminar on “Convex Sets and Convex Functions” (together with Lisa Beck)  Augsburg University  2018 
Preparatory Course “Brückenkurs” in Mathematics  Augsburg University  2017/18 
First course in probability and statistics  Aalto University  2016/17 
Stochastic Analysis  University of Hamburg  2015/16 
Standin lectures  Institution  Semester 

Functional Analysis  Bielefeld University  2015 
Analysis II  Bielefeld University  2014 
Probability Theory I  Bielefeld University  2011 
Homework and exams
Homework and written exam coordinator  Institution  Semester 

Functional Analysis  Augsburg University  2018 
Ordinary Differential Equations  Augsburg University  2017/18 
Measure and Integration Theory  Bielefeld University  2014/15 
Analysis II  Bielefeld University  2014 
Analysis I  Bielefeld University  2013/14 
Analysis III for engineers  Technical University of Berlin  2012 
Analysis I for engineers  Technical University of Berlin  2011/12 
Exercise classes / teaching assistance  Institution  Semester 

Measure and Integral  University of Helsinki  2020 
Ordinary Differential Equations  Augsburg University  2017/18 
Measure and Integration Theory  Bielefeld University  2014/15 
Analysis II  Bielefeld University  2014 
Analysis I  Bielefeld University  2013/14 
Analysis III for engineers  Technical University of Berlin  2012 
Analysis I for engineers  Technical University of Berlin  2011/12 
MA 303 (Differential Equations and PDEs)  Purdue University  2006 
Probability Theory I  Bielefeld University  2005/06 
Measure Theory and Elements of Functional Analysis  Bielefeld University  2005 
Mathematics for Computer Scientists  Bielefeld University  2004/05 
Stochastics A  Bielefeld University  2003/04 
Analysis I  Bielefeld University  2003 
Linear Algebra I  Bielefeld University  2002/03 
First examiner in oral exams
Graduate level
 Functional Analysis
 Analysis III
 Stochastic Analysis
Second examiner in oral exams
Graduate level
 Actuarial Mathematics
 Mathematics for Finance I
 Probability Theory IIII
Undergraduate level
 Analysis I–II
 Analysis C
 Analysis IIII for engineers
 Integral Transforms and Differential Equations for engineers
 Measure and Integration Theory
 Statistics
Master and Diploma students
Nelli Schmelzer, Stochastische nichtlineare Schrödingergleichungen: Existenz und Eindeutigkeit von milden Lösungen in L^{2}, (First advisor: Prof. Dr. Michael Röckner), 2015, Bielefeld University.
Fadwa Mihad, Extrapolation stationärer stochastischer Prozesse, (First advisor: Lecturer Dr. Henrik Winkler), 2011, Technical University of Berlin.
2020  Habilitation in Mathematics (Title of Docent), Habilitation thesis: “Stochastic partial differential equations with singular drift”  Universität Augsburg 
2019 – now  Postdoc at the Geometric Analysis and Partial Differential Equations Research Unit  University of Helsinki 
2017 – 2019  Research Associate at the Nonlinear Analysis Chair  Universität Augsburg 
2018 – 2019  Visiting Professor at the Institute of Analysis  Universität Ulm 
2016 – 2017  Postdoc at the Nonlinear Partial Differential Equations (NPDE) Group  Aalto University 
2015 – 2016  Visiting Lecturer at the Center of Mathematical Statistics and Stochastic Processes  Universität Hamburg 
2014 – 2015  Postdoc at the Stochastic Analysis Group  Universität Bielefeld 
2011 – 2013  Postdoc at the DFG Research Group 718 “Analysis and Stochastics in Complex Physical Systems”  TU Berlin 
2010  Postdoc at the DFG Collaborative Research Center 701 “Spectral Structures and Topological Methods in Mathematics”  Universität Bielefeld 
2010  PhD in Mathematics, Supervisor: Prof. Michael Röckner (Genealogy), Dissertation: Summary & Download  Universität Bielefeld 
2007  Stay at the Chinese Academy of Sciences (CAS)  CAS Beijing 
2006 – 2010  PhD Studies in Mathematics at the DFG International Research Training Group 1132 “Stochastics and Real World Models”  Universität Bielefeld 
2006  Diploma in Mathematics (Supervisor: Prof. Michael Röckner)  Universität Bielefeld 
2006  Graduate School of Mathematics  Purdue University 
2002 – 2006  Study of Mathematics and Computer Science  Universität Bielefeld 
2002  PreDiploma in Mathematics  Universität Bielefeld 
2000 – 2002  Study of Mathematics, Philosophy and Computer Science  Universität Bielefeld 