Moritz Doll

Contact

Schoof of Mathematical and Physical Sciences
Macquarie University
Macquarie Park, NSW 2109, Australia

Position: Postdoctoral Researcher
Mail: firstname.surname@mq.edu.au

School of Mathematics and Statistics
The University of Melbourne
Parkville, VIC 3010, Australia

Position: Visitor
Office: G87
Mail: firstname.surname@unimelb.edu.au

Research

I work in microlocal analysis and applied mathematics together with Justin Tzou and Leo Tzou. My PhD supervisor was Elmar Schrohe. Previously, I was a postdoctoral researcher at the University of Melbourne with Jesse Gell-Redman and at the Universität Bremen with Anke Pohl.

My CV can be found here.

Publications

A list of preprints can be found on the arXiv and published versions are linked on my orcid page.

Journal articles

1. Refined Weyl Law for Homogeneous Perturbations of the Harmonic Oscillator, with O. Gannot and J. Wunsch, Comm. Math. Phys. 362 (2018)
2. Recurrence of Singularities for Second Order Isotropic Pseudodifferential Operators, Math. Nachr. 292 (2019)
3. Lagrangian distributions on asymptotically Euclidean manifolds, with S. Coriasco and R. Schulz, Ann. Mat. Pura App. 198 (2019)
4. A Partial Data Problem in Linear Elasticity, with A. Froehly and R. Schulz, Inverse Problems 36 (2020)
5. Schrödinger Trace Invariants for Homogeneous Perturbations of the Harmonic Oscillator, with S. Zelditch, J. Spectr. Theory 10 (2020)
6. Weyl Law on Asymptotically Euclidean Manifolds, with S. Coriasco, Ann. Henri Poincaré 22 (2021)
7. Counting Resonances on Hyperbolic Surfaces with Unitary Twists, with K. Fedosova and A. Pohl, Comm. Anal. Geom. 32 (2024)
8. Scattering Theory with Unitary Twists, with K. Fedosova and A. Pohl, J. Analyse Math. 153 (2024)

Preprints

9. The Klein-Gordon equation on asymptotically Minkowski spacetimes: causal propagators, with D. Baskin and J. Gell-Redman, preprint (2024)
10. The Klein-Gordon equation on asymptotically Minkowski spacetimes: the Feynman propagator, with D. Baskin and J. Gell-Redman, preprint (2025)
11. Formalizing Schwartz functions and tempered distributions, preprint (2025)

Thesis

• M. Doll. Fourier Integral Operators on Non-Compact Manifolds. Dissertation.

Events

Past

• Spectral Theory and Mathematical Relativity, Vienna, June 5-July 28, 2023
• Hyperbolic PDEs and Nonlinear Evolution Problems, Creswick, Sep 18-Sep 30, 2023
• HANDSDays 3, University of Bremen (Organizers: Doll, Pohl)
• Asymptotic analysis & Spectral theory, Orsay, Sep 30-Oct 4, 2019
• Recent developments in microlocal analysis, Berkeley, Oct 14-18, 2019
• Bremen-Oldenburg Analysis Seminar (Organizers: Doll, Grieser)
• Trimester Program "Dynamics: Topology and Numbers", Bonn, 2020

Interactive Proof Assistants

Recently I got interested in interactive proof assistants, especially Lean and mathlib. I have formalized the definition of the Schwartz space as a locally convex space and the fundamentals of unbounded operators.

A list of files that I have made significant contributions to can be found here.

Past Teaching

Leibniz Universität Hannover

Winter 2015/2016: Funktionalanalysis, Tutorial

Summer 2016: Partielle Differentialgleichungen, Assistant

Summer 2017: Distributionentheorie, Tutorial

Winter 2017/2018: Analysis 1, Tutorial

Summer 2018: Analysis 2, Tutorial

Universität Bremen

Winter 2018/2019 Seminar Differentialgeometrie

Summer 2019 Seminar Spektral- und Streutheorie

Summer 2019 Ergodentheorie, Assistant

Winter 2019/2020 Seminar Differentialgeometrie

Summer 2020 Spektralgeometrie

Winter 2021/2022 Semiklassische Analysis