Marcel Schmidt

Currently I am a deputy professor for Functional Analysis and Dynamical Systems at the University of Leipzig. I will  keep this website updated. 

Publications and Preprints Eintrag erweitern

Preprints

  • Recurrent and (strongly) resolvable graphs (arXiv) (with Daniel Lenz, Simon Pucher), submitted,  36pp.
  • Boundary representations of intermediate forms between a regular Dirichlet form and its active main part (arXiv) (with Matthias Keller, Daniel Lenz, Michael Schwarz, Melchior Wirth), submitted, 24pp.
  • Blow-up of nonnegative solutions of an abstract semilinear heat equation with convex source (arXiv(with Daniel Lenz, Ian Zimmermann), submitted, 16pp.
  • Topological Poincaré type inequalities and lower bounds on the infimum of the spectrum for graphs (arXiv(with Daniel Lenz, Peter Stollmann), submitted, 23pp.
  • Geometric properties of Dirichlet forms under order isomorphisms (arXiv(with Daniel Lenz, Melchior Wirth), submitted, 30pp.

Publications        

  • (Weak) Hardy and Poincaré inequalities and criticality theory  (journal, arXiv)      Dirichlet forms and related topics,  421–459, Springer Proc. Math. Stat., 394, Springer, Singapore, [2022].
  • On Lp Liouville theorems for Dirichlet forms (journal, arXiv(with Bobo Hua, Matthias Keller,  Daniel Lenz),  Dirichlet forms and related topics, 201-221, Springer Proc. Math. Stat., 394, Springer, Singapore, [2022].
  • Uniqueness of form extensions and domination of semigroups (journal, arXiv)
    (with Daniel Lenz, Melchior Wirth), J. Funct. Anal. 280 (2021), no. 6,, 27 pp.
  • On the uniqueness class, stochastic completeness and volume growth for graphs (journal,arXiv(with Xueping Huang, Matthias Keller), Trans. Amer. Math. Soc. 373 (2020), no. 12, 8861-8884.
  • On the existence and uniqueness of self-adjoint realizations of discrete (magnetic) Schrödinger operators (journal,arXivin Analysis and Geometry on Graphs and Manifolds, 250 - 327, eds. Matthias Keller, Daniel Lenz, Radoslaw Wojciechowski, London Mathematical Society Lecture Note Series, 461. Cambridge University Press, Cambridge, 2020.
  • A note on the surjectivity of operators on vector bundles over discrete spaces (journal,arXiv(with Jannis Koberstein), Arch. Math. (Basel) 114 (2020), no. 3, 313-329.
  • Domination of quadratic forms (journal,arXiv(with Daniel Lenz, Melchior Wirth), to appear in Math. Z., 24pp.
  • A generalized conservation property for the heat semigroup on weighted manifolds (journalarXiv)(with Jun Masamune), Math. Ann. 377 (2020), no. 3-4, 1673-1710.
  • A note on reflected Dirichlet forms (journalarXiv) Potential Anal. 52 (2020), no. 2, 245-279.
  • Boundary representation of Dirichlet forms on discrete spaces (journal, arXiv(with Matthias Keller, Daniel Lenz, Michael Schwarz), J. Math. Pures Appl. (9) 126 (2019), 109-143. 
  • The Ihara Zeta function for infinite graphs (journal, arXiv(with Daniel Lenz, Felix Pogorzelski), Trans. Amer. Math. Soc. 371 (2019), no. 8, 5687-5729.
  • Global properties of Dirichlet forms in terms of Green's formula (journal, arXiv(with Sebastian Haeseler, Matthias Keller, Daniel Lenz, Jun Masamune), Calc. Var. Partial Differential Equations 56 (2017), no. 5, Art. 124, 43 pp.
  • Global properties of Dirichlet forms on discrete spaces (journal, arXiv) (based on my Diploma thesis) Dissertationes Math. (Rozprawy Mat.) 522 (2017), 1-43.
  • Note on short time behavior of semigroups associated to selfadjoint operators (journal, arXiv(with Matthias Keller, Daniel Lenz, Florentin Münch, Andras Telcs), Bull London Math Soc (2016) 48 (6): 935-944.
  • Note on uniformly transient graphs (journal, arXiv(with Matthias Keller, Daniel Lenz, Radoslaw Wojciechowski), Rev. Mat. Iberoam. 33 (2017), no. 3, 831-860.
  • A Feynman-Kac-Ito Formula for magnetic Schrödinger operators on graphs (journal, arXiv(with Batu Güneysu, Matthias Keller),  Probability Theory and Related Fields, 165 (2016), no. 1-2, 365-399.
  • Diffusion determines the recurrent graph (journal, arXiv) (with Matthias Keller, Daniel Lenz, Melchior Wirth), Advances in Mathematics, Volume 269 (2015), 364-398.

PhD thesis

  • Energy forms (arXiv), 196pp.

Diploma thesis

  • Global properties of Dirichlet forms on discrete spaces (arXiv), 49pp.
Talks Eintrag erweitern

Talks

  • August 2022, International Workshop on Dirichlet Forms and Related Topics, Kansai University Osaka, Weak Hardy/Poincaré inequalities and criticality theory.
  • June 2022, N-cities seminar, TU Chemnitz, Weak Hardy/Poincaré inequalities and criticality theory.
  • December 2021, Mini-Workshop Variable Curvature Bounds, Analysis and Topology on Dirichlet Spaces, MFO Oberwolfach, Weak Hardy/Poincaré inequalities and criticality theory.
  • November 2021, Research Seminar Analyis, Universität Leipzig, On the uniqueness class, stochastic completeness and volume growth for graphs.
  • September 2021, Online Seminar, Fudan University Shanghai, Graph limits, measurable
    graphs and Ihara’s zeta function.
  • July 2021, Summer school Dirichlet forms on graphs, Salerno, minicourse on Dirichlet forms on discrete graphs.
  • February 2021, Workshop of the working group Variational methods on graphs and networks within COST-Action Mathematical models for interacting dynamics on networks, Poincaré inequalities on graphs.
  • January 2021, Workshop Geometry, Dynamics and Spectrum of Operators on Discrete Spaces, MFO Oberwolfach, On the uniqueness class, stochastic completeness and volume growth for graphs.
  • September 2020, Mini-Simposium Spectral theory of operators and matrices and partial differential equations, DMV Annual Meeting 2020, On the uniqueness class, stochastic completeness and volume growth for graphs.
  • April 2019, Mini-Workshop Recent Progress in Path Integration on Graphs and Manifolds, MFO Oberwolfach, On the uniqueness class, stochastic completeness and volume growth for graphs.
  • April 2019, SPP Conference Geometry at Infinity, Münster, On the uniqueness class, stochastic completeness and volume growth for graphs.
  • September 2018,  Research Seminar 'Analysis' at Fernuniversität Hagen, On the uniqueness class, stochastic completeness and volume growth for graphs.
  • March 2018,  Research Seminar 'PDE and Applied Mathematics' at Technion Haifa, Does diffusion determine the geometry? 
  • January 2018,   Research Seminar 'Analysis' at Universität Leipzig, Does diffusion determine the geometry? 
  • November 2017, Conference  'Discrete and Continuous Models in the Theory of Networks' at ZIF Bielefeld, Boundary representations of Dirichlet forms on discrete spaces.
  • September 2017, Workshop 'Potential Analysis and its Related Fields' at Hokkaido University Sapporo, Does diffusion determine the geometry?
  • July 2017,  Research Seminar 'Analysis' at Hokkaido University Sapporo, Does diffusion determine the geometry? 
  • May 2017,  Research Seminar 'Geometric Analysis' at Universität Bielefeld, Energy forms - basic theory  and Energy forms - Silverstein extensions.
  • April 2017,  Operator Semigroups in Analysis: Modern Developments in  Bedlewo, Uniqueness of form extensions and domination of semigroups.
  • March 2017,  Workshop Interfacebetween Comutative and Non-Commutative Stochastic Analysis  at  Hokkaido University Sapporo,   Uniformly transient graphs.
  • March 2017,  Workshop on Dirichlet forms and their geometry at  Tohoku University Sendai, Minicourse on Energy forms.
  • January 2017, Miniworkshop on operator theoretic aspects of ergodic theory at Universität Leipzig, Does diffusion determine the geometry?
  • August 2016, Workshop on discrete analysis at Fudan University Shanghai, Does diffusion determine the geometry?
  • May 2016, PhD Seminar  Jena University, Uniformly transient and canoncially compactifiable graphs.
  • March 2016, Research seminar 'Differential geometry' at the graduate center of CUNY New York, Does diffusion determine the geometry?
  • January 2016, Workshop on spectral geometry at Universität Potsdam, Energy forms.
  • November 2015, Reseach Seminar 'Diskrete Spektraltheorie' at Universität Potsdam, Energy forms.
  • November 2015, Workshop on stochastic analysis and related topics at TU Dresden, Does diffusion determine the geometry?
  • November 2014, PhD Seminar  Jena University,  Minicourse on Benjamini-Schramm convergent graph sequences and Iharas' Zeta function.
  • September 2014, 11th Aoba-Yama PDE seminar at Tohoku University Sendai, Minicourse on Benjamini-Schramm convergent graph sequences and Iharas' Zeta function.
  • August 2014, StochasticProcesses, Analysis and Mathematical Physics, at Kansai University Osaka,  Does diffusion determine the geomtry?
  • June 2014, PhD Seminar  Jena University,  Does diffusion determine the geomery?
  • March 2014, Fractal Geometry and Stochastics V in Tabarz  The Ihara Zeta function for infinie graphs.
  • February 2014, Workshop Stochastic Processes and Mathematical Finance at Kansai University Osaka,  Does diffusion determine the geomtry?
  • February 2014, Research seminar at Tohoku University Sendai , Global properties of Dirichlet forms in terms of Green's formula.
  • February 2014, Colloquium of GSIS at the  Tohoku University Sendai, Does diffusion determine the geomtry?
  • October 2013, Research Seminar 'Analysis, Geometry and Stochastics' at Jena University, Global properties of Dirichlet forms in terms of Green's formula.
  • June 2013, PhD Seminar  Jena University, A Feynman-Kac-Ito formula for magnetic Schrödinger operators on graphs.
  • December 2012, Workshop 'Dirichlet forms, operator theory and mathematical physics' in Djerba, Global properties of Dirichlet forms in terms of Green's formula.
  • September 2012, Workshop on Probability at Kansai University Osaka, Asymptotic stability of Markovian semigroups on $\ell^1$.
  • September 2012, Conference Stochastic Analysis and Applications at Okayama University, Global properties of Dirichlet forms in terms of Green's formula.
  • September 2012, German Student conference in Saarbrücken, Global properties of Dirichlet forms on discrete spaces.
Curriculum Vitae Eintrag erweitern

Current position

  • Since 10/2020 Deputy Professor for Functional Analysis and Dynamical Systems, Universität Leipzig.

Previous positions and education

  • 10/2018 - 09/2020 Deputy Professor for Analysis, Friedrich-Schiller-Universität Jena.
  • 05/2017 - 09/2018 Post Doc, Friedrich-Schiller-Universität Jena.
  • 2011-2017 PhD studies in mathematics, Friedrich-Schiller-Universität Jena.
  • 2007-2011 Diploma studies in mathematics, Friedrich-Schiller-Universität Jena.

Prizes

  • 2018 Prize of the President  of the Friedrich-Schiller-Universität Jena for best PhD thesis at Faculty for Mathematics and Computer Sciences.
  • 2012 Prize of the Rector of  the Friedrich-Schiller-Universität Jena for Diploma thesis at Faculty for Mathematics and Computer Sciences.
  • 2012 Prize at DMV Students' Conference for Diploma thesis: participation in workshop at Mathematisches Forschungsinstitut Oberwolfach (MFO).

(Co-)Organized Scientific Meetings

  • Workshop on Dirichlet forms and their geometry at Tohoku University Sendai, March 18th  - March 23rd 2017 (organized by Jun Masamune, Nobuaki Obata, Marcel Schmidt, Toshihiro Uemura and Masaki Wada).
  • One Day Workshop New Directions in Mathematical Physics and beyond at FSU Jena, Wednesday January 14th 2015 (organized by Gerhard Bräunlich, Matthias Keller, Markus Lange and Marcel Schmidt).
  • International Conference Fractal Geometry and Stochastics V in Tabarz, local organizing committee.
  • Ph.D. Symposium in Chemnitz within the Fall school Dirichlet forms, operator theory and mathematical physics, Wednesday October 2nd 2013 (organized by Siegfried Beckus, Marcel Hansmann, Felix Pogorzelski and Marcel Schmidt).
  • Geometric aspects in probability and analysis at FSU Jena, September 14th 2013 (organized by Matthias Keller, Daniel Lenz and Marcel Schmidt).

Supervision Eintrag erweitern

(Co-) Supervision

Phd Theses
  • Simon Puchert, Topic on harmonic functions on Dirichlet spaces, ongoing, joint with Daniel Lenz.
  • Oleksiy Sukaylo, Topic on boundaries of graphs, ongoing, joint with Daniel Lenz.
  • Ian Zimmermann, Topic on properties of nonlinear heat equations, ongoing, joint with Daniel Lenz.
Masters's and Diploma theses
  • Karl Strobel, Liouville theorems for spherically symmetric operators, ongoing.
  • Mirjam Brunner, Fujita exponent for semilinear heat equations on Heisenberg group, ongoing.
  • Aldo Popert, Weak Poincaré inequalities, ongoing.
  • Tobias Hössel, L^∞ -Liouville property and stochastic completeness, ongoing.
  • Simon Murmann, L^p -positivity preserving property on manifolds, ongoing.
  • Oleksiy Sukaylo, Boundaries of hyperbolic graphs, 2019.
  • Simon Puchert, Resolvable graphs and harmonic funtions, 2019.
  • Michael Schwarz, Boundary representation of Dirichlet forms on discrete spaces, joint with Daniel Lenz, 2015.
  • Jannis Koberstein, Surjectivity of graph Laplacians, 2016.
  • Melchior Wirth, Uniqueness of form extensions and domination of semigroups, joint with Daniel Lenz, 2015.
Bachelor's Theses
  • Simon Murmann, Characterizations of W^1_0 in different geometries, 2020.
  • Ian Zimmermann, Spectral distances on graphs, joint with Daniel Lenz, 2017.
  • Julian Weigt, Measurable equidecomposition, 2015.
  • Jula McGibbon, Spektraltheorie irreduzibler Operatoren (Spectral theory of irreducible operators), 2014.
  • Jannis Koberstein, Integraldarstellungen von Halbgruppen auf L^p (Integral representations of semigroups on L^p),  joint with Daniel Lenz, 2013.
  • Frank Nußbaum, Construction of Markov processes on graphs and the Feynman-Kac formula, joint with Daniel Lenz,  2013.

Staatsexamen Lehramt

  • Adrian Voit, Die Colin de Verdière Invariante, ongoing.

 

Teaching Eintrag erweitern

Aktuell

  • WiSe 22/23 Vorlesung 26th Internet Seminar “Graphs and Discrete Dirichlet Spaces”(Universität Leipzig)
  • WiSe 22/23 Vorlesung Funktionalanalysis I (Universität Leipzig)

Frühere Semester

  • SoSe 2022 Seminar Spectral Theory (Universität Leipzig)
  • SoSe 2022 Vorlesung C^*-Algebras (Universität Leipzig)
  • SoSe 2022 Vorlesung Functional Analysis II (Universität Leipzig)
  • WiSe 21/22 Vorlesung Spectral Theory (Universität Leipzig)
  • WiSe 21/22 Vorlesung Funktionalanalysis I (Universität Leipzig)
  • SoSe 2021 Vorlesung Functional Analysis II (Universität Leipzig)
  • SoSe 2021 Vorlesung Analysis auf Mannigfaltigkeiten - globale Analysis (Universität Leipzig)
  • WiSe 20/21 Vorlesung Funktionalanalysis I (Universität Leipzig)
  • WiSe 20/21 Vorlesung Analysis und Geometrie endlicher Graphen (Universität Leipzig)
  • SoSe 2020 Vorlesung Analysis und Geometrie endlicher Graphen
  • SoSe 2020 Seminar Das Buch der Beweise
  • WiSe 19/20 Vorlesung Spektraltheorie diskreter Operatoren
  • WiSe 19/20 Vorlesung Analysis III (Lehramt Gymnasium)
  • SoSe 2019 Vorlesung Analysis II (Lehramt Gymnasium)
  • SoSe 2019 Seminar Anwendungen von Funktionalanalysis
  • WS 18/19 Vorlesung Analysis I (Lehramt Gymnasium)
  • WS 18/19 Vorlesung und Übung Globale Analysis auf Mannigfaltigkeiten,
  • SoSe 18 Seminar Rang Eins Störungen selbstadjungierter Operatoren
  • WS 17/18 Übung Analysis III (Physik Bachelor)
  • SoSe 17 Vorlesung Operatoren auf Mannigfaltigkeiten (Math. Master)
  • WS 16/17 Übung Analysis I (Math. Bachelor)
  • WS 15/16 Vorlesung Analysis II (Physik Bachelor)
  • WS 14/15 Seminar Das Banach-Tarski-Paradoxon
  • WS 13/14  Seminar Analysis on metric measure spaces
  • SoSe 13 Vorlesung + Übung Einführung in die Statistik für Wirtschaftsingenieure (Fachhochschule Jena)
  • WS 12/13 Übung Analysis I (Physik Bachelor) und Seminar Banachverbände
  • SoSe 12 Übung Höhere Analysis I (Math. Bachelor)
  • WS 11/12 Übung Elementare Wahrscheinlichkeitstheorie und math. Statistik (Math. Lehramt Gymnasium)
  • SoSe 11 Übung Analysis II (Math. Bachelor)
  • WS 10/11 Übung Elementare Wahrscheinlichkeitstheorie und math. Statistik (Math. Lehramt Gymnasium)
  • WS 09/10 Übung Einführung in die Stochastik (Math. Lehramt Regelschule)