Research

Research interests

• Logic
• Topos Theory
• Homotopy theory and higher categories
• Motivic homotopy theory
• Algebraic Geometry over deeper bases
• Locally compact modules and number theory
• Quadratic forms and special groups

Publications

• Arndt, Mariano, Pinto: Finitary filter pairs and propositional logics , to appear in South American Journal of Logic, Proceedings of the EBL 2017
• Arndt, Bräunling: On the automorphic side of the K-theoretic Artin symbol, Selecta Mathematica (2019) 25:38, 47p, link to the preprint version
• Arndt, Mariano: The von Neumann-Regular Hull of (Preordered) Rings and Quadratic Forms, in South American Journal of Logic, 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, 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

Theses

• The equivalence of edge symmetric double groupoids with connection and crossed modules over groupoids, Diplom thesis (M.Sc.), 2005, in German, supervisor: Prof. Dr. K.H. Kamps, FernUniversität Hagen, Germany
• Finiteness in Toposes, master thesis, 2005, in Portuguese, supervisor: Prof. Dr. M. Coniglio, Unicamp, Campinas, Brazil
• Abstract motivic homotopy theory, PhD thesis, 2016, supervisor: Prof. Dr. M. Spitzweck, University of Osnabrück, Osnabrück, Germany

Upcoming preprints / works in progress

• Ranges of functors and elementary classes via topos theory (see video below)
• Kappa filter pairs and natural extensions, with H. Mariano and D. Pinto
• Horn filter pairs and Craig interpolation, with H. Mariano and D. Pinto
• From GAG to NAG - comparing Durov's and Haran's settings for generalized algebraic geometry, Abstract for a past talk on this at Osnabrück
• Motivic homotopy theory over deeper bases
• Homotopical fibring of logics, Abstract for a past talk at Marseille
• Models for cartesian algebra in infinity categories