About me

I’m a mathematician working in applied topos theory. I obtained my PhD in October 2017 under the supervision of Marc Nieper-Wißkirchen at the University of Augsburg. Besides research, I love teaching mathematics at all levels and am passionate about doing mathematics with school students. Currently I’m back in Augsburg. During the academic year 2018/2019, I was working at the Università di Verona under the supervision of Peter Schuster. In the winter term 2017/2018, I was substituting a junior professor at the University of Augsburg, and during the summer of 2018, I was a guest at the Max Planck Institute for Mathematics in the Sciences in Leipzig.

I explore applications of the internal language of toposes, particularly in commutative algebra and in algebraic geometry.

• Short research summary
• Research statement
• PhD thesis: Using the internal language of toposes in algebraic geometry (large portions require only familiarity with scheme theory, not with topos theory; slides, more slides, 2015 talk at the IHÉS)

• Paper: An elementary and constructive proof of Grothendieck’s generic freeness lemma
• Paper: Flabby and injective objects in toposes
• Short note: A constructive Knaster–Tarski proof of the uncountability of the reals (joint with Matthias Hutzler)
• Paper: Exploring mathematical objects from custom-tailored toposes
• Preprint: Reflections on reflection for intuitionistic set theories (joint with Andrew Swan)
• Paper: A general Nullstellensatz for generalized spaces
• Expository paper: Generalized spaces for constructive algebra
• Paper: Maximal ideals in countable rings, constructively (joint with Peter Schuster)
• Paper: A constructive picture of Noetherian conditions and well quasi-orders (joint with Gabriele Buriola and Peter Schuster)
• Expository paper: A primer to the set-theoretic multiverse philosophy
• Paper: Reifying dynamical algebra: maximal ideals in countable rings, constructively (joint with Peter Schuster)

• UNILOG talk: Exploring the internal language of toposes
• Como talk: How topos theory can help commutative algebra (for topos theorists)
• Leipzig talk: How topos theory can help algebra and geometry (for a general mathematical audience)
• Colloquium Logicum/Münchenwiler/Padova talk: New reduction techniques in commutative algebra driven by logical methods
• PSSL104 talk: How not to constructivize cohomology (also see paper)
• 6WFTop/CT2019 talk: A general Nullstellensatz for generalised spaces (also see rough draft)
• Dagstuhl 2021 talk: Bridging the foundational gap: Updating algebraic geometry in face of current challenges regarding formalizability, constructivity and predicativity

I contribute to the nLab and to the Stacks Project, and encourage everyone to consider Eugenia Cheng’s manifesto for inclusivity in category theory and mathematics at large.

Recent results by Matthias Ritter (formerly Matthias Hutzler): The infinitesimal topos classifies the theory of quotients of local algebras by nilpotent ideals (master’s thesis), Syntactic presentations for glued toposes and for crystalline toposes (PhD thesis)

Recent result by Johannes Riebel: The undecidability of BB(748)

Travel plans

• April 2018: PSSL 103 in Brno
• April 2018: Oberseminar Mathematische Logik in Munich
• April 2018: Computational Approaches to the Foundations of Mathematics in Munich
• May 2018: Summer School on Types, Sets and Constructions in Bonn
• May 2018: Philosophy of mathematics: objects, structures, and logics in Mussomeli
• June 2018: UniLog in Vichy
• June 2018: Toposes in Como in Como
• July 2018: Jugendschülerakademie in Papenburg
• August 2018: Mathematics camp in Violau
• September 2018: Colloquium Logicum 2018 in Bayreuth
• September 2018: Proof and Computation in Fischbachau
• October 2018: PSSL 104 in Amsterdam
• October 2018: EUTYPES2018 in Aarhus
• October 2018: Münchenwiler Meeting in Münchenwiler
• February 2019: Motivic Verona in Verona
• March 2019: Compact course on proof interpretations in Verona
• April 2019: Workshop on Formal Topology in Birmingham
• Spring 2019: Warwick
• July 2019: Category Theory 2019
• September 2019: Proof and Computation in Herrsching