Melchior Wirth


I moved to the Maas group at IST Austria. My new contact information can be found hereExterner Link.

Research Interests

Roughly speaking, I am interested in the interplay between analysis, geometry and probability beyond the smooth world. More concretely, this includes the following topics and their interconnections:

  • discrete and noncommutative optimal transport
  • gradient flows and curvature in non-smooth settings
  • analysis and geometry of infinite graphs

Publications and Preprints

Peer-reviewed publications

Domination of quadratic formsExterner Link

(with Daniel Lenz, Marcel Schmidt), Mathematische Zeitschrift, accepted

Tilings of convex sets by mutually incongruent equilateral triangles contain arbitrarily small tilesExterner Link

(with Christian Richter), Discrete & Computational Geometry, 63(1), 2019

On the geometry of geodesics in discrete optimal transportExterner Link

(with Matthias Erbar, Jan Maas), Calculus of Variations and Partial Differential Equations, Volume 58 (2018)

Sobolev-Type Inequalities and Eigenvalue Growth on Graphs with Finite MeasureExterner Link

(with Bobo Hua, Matthias Keller, Michael Schwarz), Proceedings of the American Mathematical Society, accepted

Diffusion determines the recurrent graphExterner Link

(with Matthias Keller, Daniel Lenz, Marcel Schmidt), Advances in Mathematics, Volume 269 (2015), 364-398.


Self-Adjoint Extensions of Bipartite HamiltoniansExterner Link

(with Daniel Lenz, Timon Weinmann)

A Noncommutative Transport Metric and Quantum Markov Semigroups as Gradient Flows of the EntropyExterner Link


Geometric properties of Dirichlet forms under order isomorphismsExterner Link

(with Daniel Lenz, Marcel Schmidt), submitted

Stability of Kac regularity under domination of quadratic formsExterner Link


Uniqueness of form extensions and domination of semigroupsExterner Link

(with Daniel Lenz, Marcel Schmidt), submitted

Master's thesis

Uniqueness of form extensions and domination of semigroupsExterner Link

(FSU Jena 2015, Advisor: Prof. Daniel Lenz)

Bachelor's thesis

Does diffusion determine the graph structure?Externer Link

(FSU Jena 2013, Advisor: Prof. Daniel Lenz)

Talks and Posters


  • March 2018, Closing Workshop RTG Quantum and Gravitational Fields at FSU Jena: 'The Heat Flow as Gradient Flow of the Entropy'
  • March 2017, workshop 'Interface between Commutative and Non-Commutative Stochastic Analysis' at Hokkaido University Sapporo: 'A transport metric for Dirichlet forms and gradient flows of the entropy'
  • September 2016, summer school 'Spectral Theory, Differential Equations and Probability' at University of Mainz: 'Does Diffusion Determine the Geometry?'
  • June 2016, PhD SeminarExterner Link at Friedrich Schiller University Jena: 'Groups and C*-Algebras: Amenability, C*-Simplicity and the Unique Trace Property'
  • July 2015, PhD SeminarExterner Link at Friedrich Schiller University Jena: 'Uniqueness of extensions of magnetic Schrödinger forms'


Curriculum Vitae

Current position

PhD student, Friedrich Schiller University Jena


2014 - 2015

Master studies in mathematics, FSU Jena

2013 - 2014 Master studies in mathematics, WWU Münster
2011 - 2013 Bachelor studies in mathematics, FSU Jena
2010 - 2011 Bachelor studies in physics, FSU Jena


2016 Prize of the President of Jena University for master's thesis

2016 Prize at DMV Students' Conference for master's thesis: participation in workshop at Mathematisches Forschungsinstitut Oberwolfach (MFO)


since April 2017 PhD studies funded by the German Academic Scholarship Foundation (Studienstiftung des deutschen Volkes)

since April 2016 Member of the Research Training group (1523/2) Quantum and Gravitational Fields

2016 Oberwolfach Leibniz Graduate Student (OWLG)

2013 - 2015 Studies funded by the German Academic Scholarship Foundation (Studienstiftung des deutschen Volkes)


Scientific Meetings

One Day Workshop 2018Externer Link 'Nonlocal Models in Analysis and Probability', March 22, 2018 (together with Daniel Lenz and Ilya Pavlyukevich)

Young Researchers' SymposiumExterner Link within conference Analysis and Geometry on Graphs and ManifoldsExterner Link at Potsdam University, July 31 to August 3, 2017 (together with Michael Schwarz)



Fall 2019  Analysis III (exercise class)
Fall 2015  Functional Analsis II (exercise class)
Summer 2015  Ordinary Differential Equations (exercise classes)
Summer 2013  Functional Analysis I (exercise class)
Fall 2012  Analysis III (exercise class)
Summer 2012  Analysis II (exercise class)