Welcome to my website!
Teaching and Administration
I regularly offer lectures and seminars (see below for my current courses and courses from previous semesters). I also supervise theses. Feel free to contact me by e-mail for topics.
In addition to my activities in teaching and research, I coordinate the evaluation of the teaching of the Faculty of Mathematics. I am also responsible for maintaining the module handbooks for our faculty's Master's degree programs.
For students of economics, I review external academic records in mathematics for equivalency (more details on the procedure), and I prepare short reports on their achievements in mathematics. Please contact me by e-mail for such recommendation letters.
Current courses
Teaching in previous semesters
| Semester | Course title | Type |
|---|---|---|
| Summer semester 2025 | Seminar: Random graphs, complex networks and tessellations | Seminar |
| Introduction to fractal geometry | Proseminar | |
| Winter semester 2024/25 | Introduction to stochastics | Lecture |
| Mathematics 3 for the field of economics | Lecture | |
| Summer semester 2024 | Stochastic Geometry | Lecture |
| Magic with math | Proseminar | |
| Summer semester 2023 | Percolation | Lecture |
| Probability Theory and Statistics for Mechanical Engineering | Lecture | |
| Introduction to fractal geometry | Proseminar |
Research interests
Fractal Geometry, Geometric Measure Theory, Stochastic Geometry, Dynamical Systems, Applications in Physics and Earth Sciences
I am a member of the Spatial Stochastics and Stochastic Geometry group (see also the current website of our seminar). Until recently, I studied curvature concepts for fractals together with Prof. Martina Zähle (University of Jena) in the DFG project Scaling of Curvature Measures and the Modified Weyl-Berry Conjecture. I am a member of the DFG priority program 2265 Random Geometric Systems and in particular PI in project 12 Morphometric Roughness of Nanostructured Surfaces.
Preprints
Radunović, G.; Winter, S. (2025). Support measures in fractal geometry. arxiv. doi:10.48550/arxiv.2508.08780
Rozanova-Pierrat, A.; Teplyaev, A.; Winter, S.; Zähle, M. (2025). Fractal curvatures and short-time asymptotics of heat content. arxiv. doi:10.48550/arXiv.2502.02989
Rataj, J.; Winter, S.; Zähle, M. (2025). Mean Minkowski content and mean fractal curvatures of random self-similar code tree fractals. arxiv. doi:10.48550/arxiv.2505.04801
Published articles
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Rataj, J.; Winter, S.
On volume and surface area of parallel sets. II. Surface measures and (non)differentiability of the volume
2025. Bulletin of the London Mathematical Society, 57 (3), 895–912. doi:10.1112/blms.70006 -
Bosch, T.; Winter, S.
On the Radial Growth of Ballistic Aggregation and Other Aggregation Models
2024. Journal of Statistical Physics, 191 (4), Art.-Nr.: 42. doi:10.1007/s10955-024-03256-1 -
Klatt, M. A.; Winter, S.
Almost sure convergence and second moments of geometric functionals of fractal percolation
2023. Advances in Applied Probability, 55 (4), 1–33. doi:10.1017/apr.2023.48 -
Rataj, J.; Winter, S.; Zähle, M.
Mean Lipschitz–Killing curvatures for homogeneous random fractals
2023. Journal of Fractal Geometry, 10 (1), 1 – 42. doi:10.4171/JFG/124 -
Ernesti, F.; Schneider, M.; Winter, S.; Hug, D.; Last, G.; Böhlke, T.
Characterizing digital microstructures by the Minkowski‐based quadratic normal tensor
2022. Mathematical Methods in the Applied Sciences, 46 (1), 961–985. doi:10.1002/mma.8560 -
Gutjahr, T.; Hale, S.; Keller, K.; Blum, P.; Winter, S.
Quantification of Fracture Roughness by Change Probabilities and Hurst Exponents
2022. Mathematical Geosciences, 54, 679–710. doi:10.1007/s11004-021-09985-3 -
Klatt, M. A.; Winter, S.
Geometric functionals of fractal percolation
2020. Advances in applied probability, 52 (4), 1085–1126. doi:10.1017/apr.2020.33 -
Kombrink, S.; Winter, S.
Lattice self-similar sets on the real line are not Minkowski measurable
2020. Ergodic theory and dynamical systems, 40 (1), 221–232. doi:10.1017/etds.2018.26 -
Eichinger, T.; Winter, S.
Regularly varying functions, generalized contents, and the spectrum of fractal strings
2019. Horizons of fractal geometry and complex dimensions : 2016 Summer School on Fractal Geometry and Complex Dimensions, June 21–29, 2016, California Polytechnic State University, San Luis Obispo, California. Ed.: R. Niemeyer, 63–94, American Mathematical Society (AMS). doi:10.1090/conm/731/14673 -
Winter, S.
Localization results for Minkowski contents
2019. Journal of the London Mathematical Society, 99 (2), 553–582. doi:10.1112/jlms.12180 -
Kombrink, S.; Pearse, E. P. J.; Winter, S.
Lattice-type self-similar sets with pluriphase generators fail to be Minkowski measurable
2016. Mathematische Zeitschrift, 283 (3), 1049–1070. doi:10.1007/s00209-016-1633-x -
Winter, S.
Minkowski content and fractal curvatures of self-similar tilings and generator formulas for self-similar sets
2015. Advances in mathematics, 274, 285–322. doi:10.1016/j.aim.2015.01.005 -
Spodarev, E.; Straka, P.; Winter, S.
Estimation of fractal dimension and fractal curvatures from digital images
2015. Chaos, solitons & fractals, 75, 134–152. doi:10.1016/j.chaos.2015.02.011 -
Pokorný, D.; Winter, S.
Scaling exponents of curvature measures
2014. Journal of Fractal Geometry, Mathematics of Fractals and Related Topics, 1 (2), 177–219. doi:10.4171/JFG/5 -
Winter, S.; Zaehle, M.
Fractal curvature measures of self-similar sets
2013. Advances in Geometry, 13 (2), 229–244. doi:10.1515/advgeom-2012-0026 -
Rataj, J.; Winter, S.
Characterization of Minkowski measurability in terms of surface area
2013. Journal of Mathematical Analysis and Applications, 400 (1), 120–132. doi:10.1016/j.jmaa.2012.10.059 -
Lapidus, M. L.; Pearse, E. P. J.; Winter, S.
Minkowski measurability results for self-similar tilings and fractals with monophase generators
2013. Fractal Geometry and Dynamical Systems in Pure and Applied Mathematics. Vol. 1: Fractals in Pure Mathematics. Ed.: D. Carfi, 185, American Mathematical Society. doi:10.1090/conm/600/11951 -
Pearse, E. P. J.; Winter, S.
Geometry of canonical self-similar tilings
2012. Rocky Mountain Journal of Mathematics, 42 (4), 1327–1357. doi:10.1216/RMJ-2012-42-4-1327 -
Lapidus, M. L.; Pearse, E. P. J.; Winter, S.
Pointwise tube formulas for fractal sprays and self-similar tilings with arbitrary generators
2011. Advances in Mathematics, 227 (4), 1349–1398. doi:10.1016/j.aim.2011.03.004 -
Winter, S.
Lower S-dimension of fractal sets
2011. Journal of Mathematical Analysis and Applications, 375 (2), 467–477. doi:10.1016/j.jmaa.2010.09.047 -
Winter, S.
Curvature bounds for neighborhoods of self-similar sets
2011. Commentationes mathematicae Universitatis Carolinae, 52 (2), 205–226 -
Winter, S.
Geometric Measures for Fractals
2010. Recent Developments in Fractals and Related Fields. Ed.: J. Barral, 73–89, Birkhäuser Boston. doi:10.1007/978-0-8176-4888-6_6 -
Rataj, J.; Winter, S.
On Volume and Surface Area of Parallel Sets
2010. Indiana University Mathematics Journal, 59 (5), 1661–1685 -
Csörnyei, M.; Kirchheim, B.; O’Neil, T. C.; Preiss, D.; Winter, S.
Universal Singular Sets in the Calculus of Variations
2008. Archive for Rational Mechanics and Analysis, 190 (3), 371–424. doi:10.1007/s00205-008-0142-4 -
Winter, S.
Curvature measures and fractals
2008. Dissertationes Mathematicae, 453, 66 S. doi:10.4064/dm453-0-1 -
Olsen, L.; Winter, S.
Multifractal analysis of divergence points of deformed measure theoretical Birkhoff averages. II: Non-linearity, divergence points and Banach space valued spectra
2007. Bulletin des Sciences Mathématiques, 131 (6), 518–558. doi:10.1016/j.bulsci.2006.05.005 -
Llorente, M.; Winter, S.
A notion of Euler characteristic for fractals
2007. Mathematische Nachrichten, 280 (1-2), 152–170. doi:10.1002/mana.200410471 -
Keller, K.; Winter, S.
Combinatorics of distance doubling maps
2005. Fundamenta Mathematicae, 187, 35 S. doi:10.4064/fm187-1-1 -
Olsen, L.; Winter, S.
Normal and Non-Normal Points of Self-Similar Sets and Divergence Points of Self-Similar Measures
2003. Journal of the London Mathematical Society, 67 (01), 103–122. doi:10.1112/S0024610702003630
Edited books and proceedings
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Freiberg, U.; Hambly, B.; Hinz, M.; Winter, S. (Eds.)
Fractal Geometry and Stochastics VI
2021. Springer International Publishing. doi:10.1007/978-3-030-59649-1