Institut für Angewandte Mathematik
Abt. Stochastische Analysis
Endenicher Allee 60
D53115 Bonn
Tel:  +49 228 73 62274 
Room:  3.031 
Email:  fischer[at]iam.unibonn.de 
Research Interests
 Theory of linear and quasilinear Schrödinger operators on infinite graphs, especially
 Potential theory
 Martin boundary theory
 Spectral theory
Publications
Published Papers
 On the Optimality and Decay of pHardy Weights on Graphs (Calculus of Variations and Partial Differential Equations, 2024)
 An Improved Discrete pHardy Inequality (with Matthias Keller and Felix Pogorzelski, Integral Equations and Operator Theory, 2023)
 A NonLocal QuasiLinear 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

QuasiLinear Criticality Theory and Green's Functions on Graphs (accepted for publication in Journal d'Analyse Mathematique)

Sharp Hardytype inequalities for noncompact harmonic manifolds and DamekRicci spaces (with Norbert Peyerimhoff, accepted for publication in Israel Journal of Mathematics)

Capacity of infinite graphs over nonArchimedean ordered fields (with Matthias Keller, Anna Muranova and Noema Nicolussi)
Reports
Doctoral Thesis
 Hardy Inequalities on Graphs (Potsdam, 2024)
Seminars, Conferences and Workshops
2024  Sep.  Conference [upcoming]  Metric Measure Spaces, Ricci Curvature, and Optimal Transport Talk: Sharp Hardytype inequalities on noncompact harmonic manifolds  Varenna, Italy 
Sep.  Workshop  Calculus of Variations: a New Generation  Bonn, Germany  
June  Workshop  Walkshop on Mathematical Physics Talk: pParabolic Graphs  Hagen, Germany  
May  Seminar  Talk: Hardytype inequalities for noncompact harmonic manifolds and graphs  Como, Italy  
Mar.  Conference  Analysis on fractals and networks, and applications Talk: Hardytype inequalities for noncompact harmonic manifolds and graphs  CIRM, France  
2023  Nov.  Seminar  Talk: On the Optimality and Decay of pHardy Weights on Locally Finite Graphs  Wrocław, Poland 
Nov.  PhD Seminar  Talk: pParabolic Graphs  Wrocław, Poland  
Oct.  Seminar  Talk: On the Optimality and Decay of pHardy 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 Hardytype inequalities for noncompact harmonic manifolds and DamekRicci spaces  Potsdam, Germany  
Apr.  Workshop  Geometric Aspects of Evolution and Control Talk: Optimal pHardy Weights on Locally Finite Graphs  Hagen, Germany  
2022  Dec.  Seminar  Talk: Optimal pHardy Weights on Locally Finite Graphs  Bonn, Germany 
Dec.  Seminar  Talk: Optimal pHardy 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 pHardy Weights on Graphs  Potsdam, Germany  
Jun.  Conference (online)  OTAMP Talk: Characterisations of Criticality for QuasiLinear Schrödinger Operators on Graphs  Stockholm, Sweden  
Apr.  Seminar  Talk (Analysis and PDE Seminar): Criticality Theory for QuasiLinear Schrödinger Operators on Graphs  Durham, UK  
2021  Dec.  Conference  QGraph 2021 Talk: A NonLinear Ground State Representation On Graphs  Stockholm, Sweden 
Sep.  Conference (online)  DMVÖMG Jahrestagung 2021 Talk: Hardy Inequalities on Graphs  Passau, Germany  
Jan.  Conference (online)  Geometry, Dynamics and Spectrum of Operators on Discrete Spaces Talk: A FatouNaimDoobtype Theorem for Schrödinger Operators on Graphs  Oberwolfach, Germany  
2020  Dec.  Seminar (online)  Talk: Reduced Functions, Minimally Thin Sets and a FatouNaimDoobtype 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 pHardy 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 pHardy 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 