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Momentan bin ich Postdoktorand in der Forschungsgruppe von René L. Schilling und Anita Behme an der Technischen Universität Dresden. Bis März 2024 war ich PostDoc in der Forschungsgruppe von Matthias Schwarz an der Universtität Leipzig, zuvor in der Forschungsgruppe von Max v. Renesse. Im Jaunar 2021 habe ich meine Dissertation als Doktorand in der Forschungsgruppe von Anton Thalmaier an der Université du Luxembourg verteidigt. Mein Forschungsinteresse gilt der Stochastischen Differentialgeometrie, d.h. der Verbindung von Stochastischer Analysis und Differentialgeometrie. Als ein relativ junges und interdisziplinäres Teilgebiet der Mathematik nutzen wir u.a. stochastische Methoden um klassische analytische Probleme auf Mannigfaltigkeiten zu lösen. Die tief gehende Verbindung zwischen der Brownschen Bewegung und dem Laplace-Operator als ihrem Erzeuger eröffnet Möglichkeiten über probabilistische Methoden die Mannigfaltigkeit als Ganzes zu analysieren und in vielen Bereichen Probleme zu lösen, wo Standard"tools" der PDE Theorie oder Differentialgeometrie nicht mehr greifen.Von März 2017 bis Februar 2020 war ich außerdem der Repräsentant der Doktoranden des Mathematischen Instituts im Doctoral Programme Mathematics and Applications an der Universität Luxembourg und habe in dieser Funktion eine kleine, responsive Website mit allen Eckdaten unseres PhD Seminars erstellt.
Vorträge & Slides
2025
- 14th March 2025Kato bounded Harnack inequality for Schrödinger operators on manifolds17th German Probability and Statistics Days (GPSD) 2025
Technische Universtität Dresden, Dresden, Germany
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
Konferenzen
2025
- 14-18 July 202544th Conference on Stochastic Processes and their ApplicationsWrocław University of Science and Technology, Wrocław, Poland
- 11-14 March 202517th German Probability and Statistics Days (GPSD) 2025Technische Universtität Dresden, Dresden, Germany
2024
- 25–29 November 2024Aux frontières de la géométrie sous-riemannienneCIRM - Centre International de Rencontres Mathématiques, Marseille, France
2023
- 14–15 December 2023Representation Theory and Harmonic Analysis on (Locally) Symmetric Spaces - In honour of the 60th birthday of Martin OlbrichUniversité du Luxembourg, Esch-sur-Alzette, Luxembourg
- 23-24 November 2023Workshop START 2023: STochastic Analysis and Related TopicsTechnische Universtität Dresden, Dresden, Germany
- 12-16 June 2023International Conference on Malliavin Calculus and Related TopicsUniversité du Luxembourg, Luxembourg
- 29-30 March 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
Forschungsinteressen
- 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
Veröffentlichungen
Veröffentlichte und angenommene Artikel
- 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
Preprint(s)
Reports(s)
- 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.
Abschlussarbeiten
- Scattering Theory for the Hodge Laplacian and Covariant Riesz Transforms (Dissertation)
- The Bismut-Elworthy-Li Formula and Gradient Estimates for Stochastic Differential Equations (Diplomarbeit)
Andere 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
Weitere Projekte
-
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.
Notizen
- 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
Lehre
Wissenschaftlicher Mitarbeiter / Postdoc, Technische Universität Dresden
- Vorlesung: Stochastik (Bachelor Math-Ba-ST10), Sommersemester 2025
- Kursassistenz: Mathematik für Elektrotechniker I/1, Wintersemester 2024-2025
- Kursassistenz: Mathematik für Elektrotechniker II/2, Sommersemester 2024
Wissenschaftlicher Mitarbeiter / Postdoc, Universtität Leipzig
- Übungen Diskrete Strukturen, Wintersemester 2023
- Übungen Lineare Algebra für Informatiker, Sommersemester 2023
- Übungen Lineare Algebra 1, Wintersemester 2022-2023
- Kursassistenz: Gewöhnliche Differentialgleichungen, Wintersemester 2022-2023
- Kursassistenz: Wahrscheinlichkeitstheorie I, Sommersemester 2022
- Kursassistenz: Wahrscheinlichkeitstheorie II, Wintersemester 2021-2022
- Übungen zum Mathematischen Propädeutikum, Sommersemester 2021
Assistant-doctorant (PhD assistant), Université du Luxembourg
- Kursassistenz: Probabilités et Statistique 2 , Sommersemester 2020
- Kursassistenz: Probabilités et Statistique 1, Wintersemester 2019-2020
- Kursassistenz: Probabilités et Statistique 2, Sommersemester 2019
- Kursassistenz: Probabilités et Statistique 1, Wintersemester 2018-2019
- Kursassistenz: Probabilités et Statistique 2, Sommersemester 2018
- Kursassistenz: Probabilités et Statistique 1, Wintersemester 2017-2018
Diplomand, Technische Universität Dresden
- Mathematik für Elektrotechniker II/2 (Übungsgruppenleiter/Tutor), Sommersemester 2015
- Lernraum Mathematik, Sommersemester 2015
- Mathematik für Elektrotechniker II/1 (Übungsgruppenleiter/Tutor), Wintersemester 2014-2015
- Lernraum Mathematik, Wintersemester 2014-2015
- Mathematik für Elektrotechniker I/2 (Übungsgruppenleiter/Tutor), Sommersemester 2014
- Lernraum Mathematik, Sommersemester 2014
- Mathematik für Elektrotechniker I/1 (Übungsgruppenleiter/Tutor), Wintersemester 2013-2014
- Lernraum Mathematik, Wintersemester 2013-2014
- Übung Maß und Integral (Korrektor), Wintersemester 2012-2013
- Mathematik für Elektrotechniker II/1 (Übungsgruppenleiter/Tutor), Wintersemester 2012-2013
- Mathematik für Elektrotechniker I/2 (Übungsgruppenleiter/Tutor), Sommersemester 2012
- Mathematik für Elektrotechniker I/1 (Übungsgruppenleiter/Tutor), Wintersemester 2011-2012