PhD Martin Schwald

About

Until recently, I worked in mathematical research and teaching. Below, you will find an overview of my academic activities from that period. For my software projects, visit my GitHub. Please feel free to reach out to me via LinkedIn.
10/2022-12/2025
University of Cologne, postdoc in the research group of Prof. Duc Viet Vu
05/2017-09/2022
Universität Duisburg-Essen, postdoc in the research group of Prof. Daniel Greb
10/2014-04/2017
University of Freiburg, PhD student in the Graduiertenkolleg Cohomological Methods in Geometry, supervised by Prof. Stefan Kebekus
Portrait of Martin Schwald

Research

Focus: Algebraic, Complex and Birational Geometry in the philosophy of the minimal model program. In particular irreducibel holomorphic symplectic manifolds, deformation theory, algebraic approximations.
11/2023
Moduli of K3 families over P^1, cycle spaces of IHS period domains, and deformations of complex-hyperkähler metrics,
Preprint: arXiv:2311.13420
03/2020
On the definition of irreducible holomorphic symplectic manifolds and their singular analogs,
International Mathematics Research Notices, 2021, rnab032, Preprint: arXiv:2003.06004
01/2020
(with Patrick Graf) The Kodaira problem for Kähler spaces with vanishing first Chern class,
Forum of Mathematics, Sigma, Volume 9, 2021, e24
10/2018
(with Tim Kirschner and Ana Brecan) Unobstructedness of hyperkähler twistor spaces,
Mathematische Zeitschrift (2021), doi:10.1007/s00209-021-02841-4
05/2018
(with Patrick Graf) On the Kodaira problem for uniruled Kähler spaces,
Arkiv för Matematik, Volume 58 (2020) Number 2, Preprint: arXiv:1805.02277
01/2017
Fujiki relations and fibrations of irreducible symplectic varieties,
Épijournal de Géométrie Algébrique, Volume 4 (2020), Article no. 7
12/2016
Low degree Hodge theory for klt varieties,
Preprint: arXiv:1612.01919

Given research talks

03/13/2024
Mexiko (UNAM), National Online Seminar Algebraic Geometry (Deformations of K3 twistor families)
12/05/2023
Chemnitz, Research Seminar Algebra und Theoretische Mathematik (Moduli of K3 families over P^1, cycle spaces of IHS period domains, and deformations of complex-hyperkähler metrics)
07/21/2022
Gdansk, Fourth Killing-Weierstrass Colloquium (Deformations of K3 twistor families)
02/08/2022
Lille, Algebraic Geometry Seminar (Deformations of K3 twistor families)
11/26/2021
Bochum, Joint Seminar on Complex Algebraic Geometry and Complex Analysis (On the definition of irreducible holomorphic symplectic manifolds and their singular analogues)
11/12/2021
Milan, Mini-workshop Singular irreducible Symplectic Varieties (On the definition of irreducible holomorphic symplectic manifolds and their singular analogues)
12/02/2020
Frankfurt, Oberseminar Algebra und Geometrie (On the definition of irreducible holomorphic symplectic manifolds and their singular analogues)
01/20/2020
Heidelberg, Symplectic Geometry Seminar (On the definition of irreducible holomorphic symplectic manifolds and their singular analogues)
07/17/2019
Bayreuth, Oberseminar Algebraische Geometrie (Unobstructedness of hyperkähler twistor spaces)
04/11/2019
Chemnitz, Research Seminar Algebra und Theoretische Mathematik (Fibrations of irreducible symplectic varieties)
07/07/2017
Cologne, Joint Seminar on Complex Algebraic Geometry and Complex Analysis (Fujiki relations and fibrations of irreducible symplectic varieties)

Teaching

WS 2025/26
Exercises on Differential Equations
SS 2025
Exercises on Complexe Geometry
WS 2024/25
Exercises on Analysis III
SS 2024
Exercises on Analysis II
WS 2023/24
Exercises on Analysis I
SS 2023
Exercises on Complex Analysis
WS 2022/23
Exercises on Ordinary Differential Equations
SS 2022
Exercises on Complex Geometry I
Exercises on Algebraic Geometry II
WS 2021/22
Seminar on Complex Analysis
Exercises on Algebraic Geometry I
SS 2021
Lecture on Complex Analysis
WS 2020/21
Lecture Riemann Surfaces
SS 2020
Lecture Analysis HRSGe (joint with Prof. Greb)
Exercises on Complex Geometry II
Master seminar on Complex Geometry
Global exercise session for Linear Algebra II
WS 2019/20
Exercises on Complex Geometry I
Lecture Mathematische Miniaturen
Global exercise session for Linear Algebra I
SS 2019
Lecture Analysis for HRSGe
Exercises on Algebraic Topology II
WS 2018/19
Exercises on Riemann Surfaces I
Seminar on Complex Analysis
SS 2018
Exercises on Complex Analysis
WS 2017/18
Proseminar on Gröbner bases
SS 2017
Proseminar on Symmetries
Masterseminar on Complex Tori and Abelian varieties
SS 2013
Complex Analysis, student assistant

Conferences and Summer Schools

07/18-07/22/2022
Fourth Killing-Weierstraß-Kolloquium, Gdansk
06/20-06/24/2022
Workshop on Complex Analysis and Geometry, Essen
11/11-11/12/2021
Mini-workshop Singular Irreducible Symplectic Varieties, Milan
09/06-09/12/2019
Summer school: o-Minimal Structures in Algebraic Geometry, Freiburg
06/11-06/13/2019
Final conference of the SFP/TRR45 Bonn/Essen/Mainz, Bonn
03/31-04/04/2019
Workshop: Higher Dimensional Complex Geometry, Saarbrücken
04/09-04/13/2018
French-German meeting in Complex Algebraic Geometry, Luminy
08/28-09/01/2017
Workshop Complex Analysis, Oberwolfach
02/08-02/10/2016
Differential forms in algebraic geometry, Freiburg
02/08-02/10/2016
An introductory Workshop on the Minimal Model Program, Hannover
07/13-07/31/2015
AMS Summer Institute in Algebraic Geometry, Salt Lake City
06/01-06/05/2015
GAel XXIII, Leuven
10/01-10/02/2014
DMV students' conference 2014, Bochum
06/30-07/04/2014
Differential forms on singular complex spaces, Bonn
10/28-11/01/2013
Around Torelli's theorem for K3-surfaces, Strassbourg
06/03-06/30/2012
Summer school of the Clay Math Institute, Obergurgl

Transregional Seminars

2017-2025
Joint Seminar on Complex Algebraic Geometry and Complex Analysis of Bochum, Essen, Cologne, Wuppertal
2017-2019
Seminars of the SFB/TR 45 of Bonn, Essen, Mainz
2014-2017
Joint Seminar in Algebraic and Complex Geometry of Basel, Freiburg, Nancy, Straßburg

Theses

03/2017
PhD thesis: Hodge theoretic methods in the study of symplectic varieties
06/2014
Master thesis: Entropy of automorphisms of compact Kähler surfaces
03/2012
Bachelor thesis: Resolution of complex projective surfaces by blowups