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Currently, I am a PostDoc in the research group of René L. Schilling and Anita Behme at the TUD Dresden University of Technology. Until March 2024, I was a PostDoc with Matthias Schwarz at the University of Leipzig and before in the research group of Max v. Renesse. In January 2021, I defended my thesis as a PhD assistant in the research group of Anton Thalmaier at the University of Luxembourg. My research is concerned with Stochastic Differential Geometry, i.e. the interplay of stochastic analysis und differential geometry. As a relatively young and interdisciplinary subject this area uses stochastic methods in order to explore classical analytical problems on manifolds. The deep connection between the Laplacian as generator of Brownian motion seemlessly opens ways to study the whole manifold by virtue of the paths of this stochastic process. Moreover, stochastic methods can be used to solve problems where analytic methods may fail.From March 2017 to February 2020, I was the PhD represenative of the mathematics research unit in the Doctoral Programme Mathematics and Applications at the University of Luxembourg and created a little, responsive website covering all coordinates about our PhD seminar.
Talks & Notes
2023
- 14th December 2023Moment estimates, concentration inequalities and exit times estimates on evolving manifoldsProbability & Statistics Seminar
Université du Luxembourg, Luxembourg
2021
- 11th June 2021Scattering Theory for the Hodge LaplacianStochastic Differential Geometry and Mathematical Physics
Centre Henri Lebesgue, Rennes
2020
- 13th February 2020Covariant Riesz transforms and the Calderón-Zygmund inequalityYoung researchers between geometry and stochastic analysis
VilVite, Bergen, Norway
2019
- 19th October 2019 What is a martingale?PhD Away Days
Université de Bordeaux, Bordeaux, France - 11th July 2019 Scattering theory for the Hodge-Laplacian without assumptions on the injectivity radiusThe 41st Conference on Stochastic Processes and their Applications 2019 - SPA 2019
Northwestern University, Evanston, IL, United States of America - 9th April 2019Scattering theory for the Hodge-Laplacian without assumptions on the injectivity radiusMini-Workshop 1915a: Recent Progress in Path Integration on Graphs and Manifolds
Oberwolfach, Germany - 7th March 2019An Introduction to Stochastic Differential GeometryPhD seminar
Université du Luxembourg, Luxembourg
2018
- 26th May 2018Scattering Theory - New Integral Criterion for Existence & Completeness of Wave Operators by Stochastic AnalysisPhD Away Days
Heidelberg, Germany
2017
- 29th September 2017Stochastic Differential GeometryPhD Away Days
Durbuy, Belgium - 7th May 2017Stochastic Flow Processes and Brownian Motion on ManifoldsPhD Seminar
Université du Luxembourg, Luxembourg
2016
- 14th September 2016Brownian Motion on Manifolds and Gradient Estimates via the Bismut-Elworthy-Li FormulaForschungsseminar Analysis, Stochastik und Mathematische Physik der Professur Analysis und der Professur Stochastik
TU Chemnitz, Germany - 4th July 2016Brownian Motion on Manifolds and the Bismut-Elworthy-Li FormulaMax-Planck-Institut für Mathematik in den Naturwissenschaften
Leipzig - 10th June 2016Birne ohne Perspektive? – Raumvorstellungen in der Mathematik: Euklidische und projektive GeometrieLange Nacht der Wissenschaften
TU Dresden, Germany
Conferences
2023
- December 14–15, 2023Representation Theory and Harmonic Analysis on (Locally) Symmetric Spaces - In honour of the 60th birthday of Martin OlbrichUniversité du Luxembourg, Esch-sur-Alzette, Luxembourg
- November 23-24, 2023Workshop START 2023: STochastic Analysis and Related TopicsTechnische Universtität Dresden, Dresden, Germany
- June 12-16, 2023International Conference on Malliavin Calculus and Related TopicsUniversité du Luxembourg, Luxembourg
- March 29-30, 2023Geometry Day 2023 in LeipzigLeipzig University, Leipzig, Germany
- February 15-17, 2023Luxembourg Workshop in Stochastic AnalysisUniversité du Luxembourg, Esch-sur-Alzette, Luxembourg
2022
- September 19-23, 2022Open Japanese-German conference on stochastic analysis and applicationsUniversity of Münster, Münster, Germany
- August 29 - September 2, 2022New Trends in Dirichlet Forms and Optimal TransportHCM Conference, Mathematics Center, Bonn, Germany
- August 29 - September 2, 2022HCM Conference - New Trends in Dirichlet Forms and Optimal TransportLipschitz lecture hall, Mathematics Center, Bonn, Germany
2021
- December 1-2, 2021Pseudo-Differential Operators and Markov Processes - Marking 40 Years of Contributions to Mathematics by Professor Niels JacobOnline Workshop
- November 15-19, 2021Problème de Schrödinger et systèmes d'EDP à champ moyen: avancées numériques et théoriquesCIRM - Centre International de Rencontres Mathématiques, Marseille, France
- September 27 - October 1, 2021German Probability & Statistics Days Mannheim 2021Hybrid conference, Mannheim, Germany
- June 16-18, 2021YRbGSA2021 - Young researchers between geometry and stochastic analysis 2021Online Summer School
- June 7-11, 2021Stochastic Differential Geometry and Mathematical PhysicsCentre Henri Lebesgue, Rennes (Online)
2020
- Winter term 2020, biweeklyStochastic Analysis under COVID - Year 2020Online conference
- August 24-28, 2020Bernoulli-IMS One World Symposium 2020Online conference
- April 04, 2020Miniconference on analysis and probability in sub-Riemannian spacesOnline conference
- March 24-27, 202014th German Probability and Statistics Days (GPSD) - Dresdner Stochastik-Tage 2020Technische Universtität Dresden, Dresden, Germany
- February 12-14, 2020Young researchers between geometry and stochastic analysis VilVite, Bergen, Norway
2019
- December 16-19, 2019Supergeometry, supersymmetry and quantizationUniversité du Luxembourg, Esch-sur-Alzette, Luxembourg
- September 2-6, 2019Japanese-German Open Conference on Stochastic Analysis 2019Fukuoka University, Fukuoka, Japan
- July 8-12, 2019The 41st Conference on Stochastic Processes and their Applications 2019 - SPA 2019Northwestern University, Evanston, IL, United States of America
- April 7-13, 2019Mini-Workshop 1915a: Recent Progress in Path Integration on Graphs and ManifoldsOberwolfach, Germany
2018
- September 24-26, 2018Analysis of Differential Operators on ManifoldsUniversität Freiburg, Germany
- July 12-14, 2018Trierer Kolloquium zu Kants Religion innerhalb der Grenzen der bloßen VernunftTrier, Germany
- July 2-6, 201812th International Vilnius Conference on Probability Theory and Mathematical Statistics and 2018 IMS Annual Meeting on Probability and StatisticsVilnius, Lithuania
- June 11-15, 201840th Conference on Stochastic Processes and their Applications – SPA 2018Göteborg, Sweden
2017
- December 14-15, 2017Supergeometry and ApplicationsUniversité du Luxembourg, Luxembourg
- September 4-23, 2017Intense Activity Period on Metric Measure Spaces and Ricci CurvatureMax-Planck Institute for Mathematics, Bonn
- August 29-31, 2017Workshop on Asymptotics for Stochastic Dynamical SystemsSwansea University - Prifysgol Abertawe, United Kingdom
- July 10–14, 2017Conference GeoProb 2017 at LuxembourgUniversité du Luxembourg, Luxembourg
2015
- May 26-29, 2015ERASMUS 2015 - SummerschoolTechnische Universität Dresden, Germany
Research Profile
- Stochastic Differential Geometry
- Stochastic Analysis on Manifolds
- Stochastic Riemannian Geometry
- Geometry of Stochastic Differential Equations
- Lévy Processes on Manifolds
- Gradient estimates for Lévy Processes on Manifolds
Publications
Publications and accepted papers
- Estimates for the covariant derivative of the heat semigroup on differential forms, and covariant Riesz transforms (joint with Baptiste Devyver & Batu Güneysu), Mathematische Annalen Volume 386, (2023), 46 p. (pages 1753–1798), arxiv:2107.00311
- Scattering theory for the Hodge Laplacian, Journal of Geometric Analysis 32, 150 (2022), 52 p., arxiv:2007.06447
Preprints
Reports
- Scattering theory for the Hodge-Laplacian without assumptions on the injectivity radius, in: Mini-Workshop: recent progress in path integration on graphs and manifolds. Oberwolfach Rep. 16 (2019), no. 2, 1003–1042.
Thesis
- Scattering Theory for the Hodge Laplacian and Covariant Riesz Transforms (PhD dissertation)
- The Bismut-Elworthy-Li Formula and Gradient Estimates for Stochastic Differential Equations (Diploma thesis (Diplomarbeit))
Other Publications / Notes
- Formen des starken & schwachen Gesetzes der großen Zahlen
- 𝖫2 as a Hilbert space and conditional expectations
- Convergence in Probability
- Lim sup and lim inf in three languages
- Infinitesimal Generator of a C0-contraction semigroups - a probabilistic approach
- On the Musical Isomorphisms
Other Projects
-
minflat Beamer Theme
The minflat theme is a Beamer theme in modern flat design, i.e. emphasising a minimal yet functional design, primarily designed for mathematical talks. You can choose between two colour schemes: a blue violet and a red purple variant. Corresponding colours used are green for the progress bar (and examples) and orange for alert elements. -
Tractatus logico-philosophicus - tractatus 2.0
The project tractatus 2.0 is an attempt to allow you to sort the paragraphs resp. its propositions flexible but relative to its priority which is scarcely possible in reality. The well-known visualisation as a hierarchic (tree) structure, as it is currently used, must be overcome, aiming at detaching every paragraph and being able to look at it individual. Accordingly, our aim is not to break structure of the Tractatus itself, but create you a platform to play and explore the overwhelming possibilities the paragraphs itself or in the variety of feasible options can be arranged and thus understood.
Notes
- Formen des starken & schwachen Gesetzes der großen Zahlen
- 𝖫2 as a Hilbert space and conditional expectations
- Convergence in Probability
- Lim sup and lim inf in three languages
- Infinitesimal Generator of a C0-contraction semigroups - a probabilistic approach
- On the Musical Isomorphisms
Teaching
Wissenschaftlicher Mitarbeiter / Postdoc, Technische Universität Dresden
- Teaching assistant: Mathematik für Elektrotechniker I/1, winter term 2024-2025
- Mathematik für Elektrotechniker II/2 (Übungsgruppenleiter), summer term 2024
Wissenschaftlicher Mitarbeiter / Postdoc, Universtität Leipzig
- Übungen Diskrete Strukturen, winter term 2023
- Übungen Lineare Algebra für Informatiker, summer term 2023
- Übungen Lineare Algebra 1, winter term 2022-2023
- Teaching assistant: Gewöhnliche Differentialgleichungen, winter term 2022-2023
- Teaching assistant: Wahrscheinlichkeitstheorie I, summer term 2022
- Teaching assistant: Wahrscheinlichkeitstheorie II, winter term 2021-2022
- Übungen zum Mathematischen Propädeutikum, summer term 2021
Assistant-doctorant (PhD assistant), Université du Luxembourg
- Teaching assistant: Probabilités et Statistique 2 , summer term 2020
- Teaching assistant: Probabilités et Statistique 1, winter term 2019-2020
- Teaching assistant: Probabilités et Statistique 2, summer term 2019
- Teaching assistant: Probabilités et Statistique 1, winter term 2018-2019
- Teaching assistant: Probabilités et Statistique 2, summer term 2018
- Teaching assistant: Probabilités et Statistique 1, winter term 2017-2018
Diplomand, Technische Universität Dresden
- Mathematik für Elektrotechniker II/2 (Übungsgruppenleiter/Tutor), summer term 2015
- Lernraum Mathematik, summer term 2015
- Mathematik für Elektrotechniker II/1 (Übungsgruppenleiter/Tutor), winter term 2014-2015
- Lernraum Mathematik, winter term 2014-2015
- Mathematik für Elektrotechniker I/2 (Übungsgruppenleiter/Tutor), summer term 2014
- Lernraum Mathematik, summer term 2014
- Mathematik für Elektrotechniker I/1 (Übungsgruppenleiter/Tutor), winter term 2013-2014
- Lernraum Mathematik, winter term 2013-2014
- Übung Maß und Integral (Korrektor), winter term 2012-2013
- Mathematik für Elektrotechniker II/1 (Übungsgruppenleiter/Tutor), winter term 2012-2013
- Mathematik für Elektrotechniker I/2 (Übungsgruppenleiter/Tutor), summer term 2012
- Mathematik für Elektrotechniker I/1 (Übungsgruppenleiter/Tutor), winter term 2011-2012