Institut für Angewandte Mathematik
Abt. Stochastische Analysis
Endenicher Allee 60
D-53115 Bonn
| Tel: | +49 228 73 62274 |
| Room: | 3.031 |
| E-mail: | fischer[at]iam.uni-bonn.de |
Research Interests
- Theory of linear and quasi-linear Schrödinger operators on infinite graphs, especially
- Potential theory
- Martin boundary theory
- Spectral theory
Publications
Published Papers
- Capacity of infinite graphs over non-Archimedean ordered fields (with Matthias Keller, Anna Muranova and Noema Nicolussi, Journal of Mathematical Analysis and Applications, 2024)
- On the Optimality and Decay of p-Hardy Weights on Graphs (Calculus of Variations and Partial Differential Equations, 2024)
- An Improved Discrete p-Hardy Inequality (with Matthias Keller and Felix Pogorzelski, Integral Equations and Operator Theory, 2023)
- A Non-Local Quasi-Linear Ground State Representation and Criticality Theory (Calculus of Variations and Partial Differential Equations, 2023)
- Riesz Decompositions for Schrödinger Operators on Graphs (with Matthias Keller, Journal of Mathematical Analysis and Applications, 2021)
Preprints
-
Quasi-Linear Criticality Theory and Green's Functions on Graphs (accepted for publication in Journal d'Analyse Mathematique)
-
Sharp Hardy-type inequalities for non-compact harmonic manifolds and Damek-Ricci spaces (with Norbert Peyerimhoff, accepted for publication in Israel Journal of Mathematics)
Reports
Doctoral Thesis
- Hardy Inequalities on Graphs (Potsdam, 2024)
Seminars, Conferences and Workshops
| 2025 | Mar. | Workshop [upcoming] | DOGS 25 Talk: TBA | Jena, Germany |
| 2024 | Sep. | Conference | Metric Measure Spaces, Ricci Curvature, and Optimal Transport Talk: Sharp Hardy-type inequalities on non-compact harmonic manifolds | Varenna, Italy |
| Sep. | Workshop | Calculus of Variations: a New Generation | Bonn, Germany | |
| June | Workshop | Walkshop on Mathematical Physics Talk: p-Parabolic Graphs | Hagen, Germany | |
| May | Seminar | Talk: Hardy-type inequalities for non-compact harmonic manifolds and graphs | Como, Italy | |
| Mar. | Conference | Analysis on fractals and networks, and applications Talk: Hardy-type inequalities for non-compact harmonic manifolds and graphs | CIRM, France | |
| 2023 | Nov. | Seminar | Talk: On the Optimality and Decay of p-Hardy Weights on Locally Finite Graphs | Wrocław, Poland |
| Nov. | PhD Seminar | Talk: p-Parabolic Graphs | Wrocław, Poland | |
| Oct. | Seminar | Talk: On the Optimality and Decay of p-Hardy Weights on Graphs | Dortmund, Germany | |
| Oct. | Conference | Panorama of Mathematics II | Bonn, Germany | |
| June | Conference | ILAS2023 Talk: A Riesz Decomposition for Schrödinger Operators on Graphs | Madrid, Spain | |
| May | Seminar | Talk: Sharp Hardy-type inequalities for non-compact harmonic manifolds and Damek-Ricci spaces | Potsdam, Germany | |
| Apr. | Workshop | Geometric Aspects of Evolution and Control Talk: Optimal p-Hardy Weights on Locally Finite Graphs | Hagen, Germany | |
| 2022 | Dec. | Seminar | Talk: Optimal p-Hardy Weights on Locally Finite Graphs | Bonn, Germany |
| Dec. | Seminar | Talk: Optimal p-Hardy Weights on Locally Finite Graphs | Vienna, Austria | |
| Nov. | Seminar | Talk: Optimal Hardy Weights on Locally Finite Graphs | Como, Italy | |
| Okt. | Seminar | SIAM Chapter Potsdam Talk: Optimal p-Hardy Weights on Graphs | Potsdam, Germany | |
| Jun. | Conference (online) | OTAMP Talk: Characterisations of Criticality for Quasi-Linear Schrödinger Operators on Graphs | Stockholm, Sweden | |
| Apr. | Seminar | Talk (Analysis and PDE Seminar): Criticality Theory for Quasi-Linear Schrödinger Operators on Graphs | Durham, UK | |
| 2021 | Dec. | Conference | QGraph 2021 Talk: A Non-Linear Ground State Representation On Graphs | Stockholm, Sweden |
| Sep. | Conference (online) | DMV-ÖMG Jahrestagung 2021 Talk: Hardy Inequalities on Graphs | Passau, Germany | |
| Jan. | Conference (online) | Geometry, Dynamics and Spectrum of Operators on Discrete Spaces Talk: A Fatou-Naim-Doob-type Theorem for Schrödinger Operators on Graphs | Oberwolfach, Germany | |
| 2020 | Dec. | Seminar (online) | Talk: Reduced Functions, Minimally Thin Sets and a Fatou-Naim-Doob-type Theorem for Schrödinger Operators on Graphs | Leipzig, Germany |
| Dec. | Seminar (online) | Ph.D. Seminar Talk: What are Optimal Hardy Inequalities? | Potsdam, Germany | |
| Oct. | Workshop | Analysis on graphs Talk: Markov Semigroups associated with Graphs on l^p | Jena, Germany | |
| Sep. | Conference (online) | DMV Jahrestagung Talk: An Improved Discrete p-Hardy Inequality | Chemnitz, Germany | |
| 2019 | Sep. | Conference | DMV Jahrestagung Talk: A Riesz Decomposition for Schrödinger Operators on Graphs | Karlsruhe, Germany |
| July | Seminar | Ph.D. day Talk: An Improved Discrete p-Hardy Inequality | Potsdam, Germany | |
| June | Conference | Geometric aspects of harmonic analysis and spectral theory Talk: A Riesz Decomposition for Schrödinger Operators on Graphs | Haifa (Technion), Israel | |
| Apr. | Seminar | Talk: A Riesz Decomposition for Schrödinger Operators on Graphs | Hamburg (TUHH), Germany | |
| Apr. | Conference | Geometry at Infinity | Münster, Germany | |
| 2018 | Sep. | Summer School | Generalized Curvatures GenCurv2018 | Lausanne, Switzerland |
| July | Seminar | Ph.D. day Talk: A Riesz Decomposition for Schrödinger Operators on Graphs | Potsdam, Germany | |
| June | Workshop | Dirichlet forms on graphs, Talk: Infinite Graphs: The Setting in a Nutshell | Jena, Germany | |
| 2017 | Nov. | Conference | Discrete And Continuous Models in the Theory of Networks | Bielefeld, Germany |
| Oct. | Conference | Analysis and Geometry on Graphs and Manifolds | Potsdam, Germany | |
| 2016 | Dec. | Workshop | Dirichlet Forms, Operator Theory and Mathematical Physics Talk: Dirichlet Forms and Stochastic Completeness on Graphs | Hammamet, Tunisia |