Research Interests

• Logic
• Homotopy theory and higher categories
• Motivic homotopy theory
• Algebraic Geometry over deeper bases
• Number Theory
• Information Theory
• Applied Category Theory
• Machine Learning

Publications

• Arndt, Mariano, Pinto: Congruence Filter pairs, equational filter pairs and adjoints, Journal of Logic and Computation, vol. 34 (2), (2024)
• Arndt, Mariano, Pinto: Horn filter pairs and Craig interpolation in Propositional Logic, Boletín de Matemáticas 30 (2), (2023)
• Wagner, Arndt, Robine, Harmeling: Cyclophobic Reinforcement Learning, Transactions on Machine Learning Research, (2023)
• Arndt, Mariano, Pinto: Filter Pairs and natural extensions of logics, Archive for Mathematical Logic volume 62, pages 113–145 (2023)
• Arndt, Braunling: On the automorphic side of the K-theoretic Artin symbol, Selecta Mathematica, volume 25, Article number: 38 (2019)
• Arndt, Mariano, Pinto: Finitary Filter Pairs and propositional logics, South American Journal of Logic, vol. 4, Nr. 2 p. 257-280 (2018)
• Arndt, Mariano: The von Neumann-Regular Hull of (Preordered) Rings and Quadratic Forms, South American Journal of Logic, vol. 2, Nr. 2 p. 201-244 (2017)
• Arndt: Homotopical Categories of Logics, in "The road to Universal Logic", p.13-58, Festschrift for the 50th Birthday of Jean-Yves Béziau Volume I, Birkhäuser 2014
• Arndt: Homotopical Fibring, extended abstract for Topology, Algebra and Categories in Logic, Marseille 2011
• Arndt, Kapulkin: Homotopy Theoretic Models of Type Theory, Lecture Notes in Computer Science 6690, p. 45-60, Springer 2011
• Arndt, Freire, Luciano, Mariano: A Global Glance on Categories in Logic, Logica Universalis, Volume 1, Issue 1, p. 3-39, Springer 2007
• Arndt, Freire, Luciano, Mariano: On the category of algebraizable logics, CLE eprints, Vol. 6(1), 2006
• Arndt, Freire, Luciano, Mariano: Fibring and sheaves, Proceedings of the 2nd Indian International Conference on Artificial Intelligence, Pune, India, 2005