Tobias Fritz

Research Interests

I work on a broad range of topics in pure and applied mathematics, theoretical physics and computer science.

Currently, my main projects are concerned with developing a new foundation for probability theory and statistics based on category theory (see in particular arXiv:1908.07021) as well as the development of new algebraic tools and results for application to classical and quantum information theory in the context of resource theories (see in particular arXiv:2003.13835). I also have two ongoing projects on the mathematical structure of spacetime and field theory.

Recent Publications

• Partial Evaluations and the Compositional Structure of the Bar Construction, with Carmen Constantin, Paolo Perrone and Brandon Shapiro, arXiv: 2009.07302
• The asymptotic comparison of random walks on topological abelian groups, arXiv: 2004.13655
• A local-global principle for preordered semirings and abstract Positivstellensätze, arXiv: 2003.13835
• Infinite products and zero-one laws in categorical probability, with Eigil Fjeldgren Rischel, arXiv: 1912.02769
• There is no good way to quantify fat tailed distributions, with Omer Tamuz, arXiv: 1912.01733
• Probability, valuations, hyperspace: Three monads on Top and the support as a morphism, with Paolo Perrone and Sharwin Rezagholi, arXiv: 1910.03752
• A synthetic approach to Markov kernels, conditional independence, and theorems on sufficient statistics, arXiv: 1908.07021
• The universal property of infinite direct sums in C*-categories and W*-categories, with Bas Westerbaan, arXiv: 1907.04714
• A unified construction of semiring-homomorphic graph invariants, arXiv: 1901.01090
• A generalization of Strassen's Positivstellensatz and its application to large deviation theory, arXiv: 1810.08667
• Antisymmetry of the stochastic order on all ordered metric spaces, arXiv: 1810.06771
• Monads, partial evaluations, and rewriting, with Paolo Perrone, arXiv: 1810.06037
• A Criterion for Kan Extensions of Lax Monoidal Functors, with Paolo Perrone, arXiv: 1809.10481
• Stochastic order on metric spaces and the ordered Kantorovich monad, with Paolo Perrone, arXiv: 1808.09898
• Curious properties of free hypergraph C*-algebras, arXiv: 1808.09220
• Optimal bounds on the positivity of a matrix from a few moments, with Gemma de las Cuevas and Tim Netzer, arXiv: 1808.09462
• Bimonoidal Structure of Probability Monads, with Paolo Perrone, arXiv: 1804.03527
• A Probability Monad as the Colimit of Finite Powers, with Paolo Perrone, arXiv: 1712.05363
• The Inflation Technique for Causal Inference with Latent Variables, with Elie Wolfe and Robert W. Spekkens, arXiv: 1609.00672
• Spectrahedral Containment and Operator Systems with Finite-Dimensional Realization, with Tim Netzer and Andreas Thom, arXiv: 1609.07908
• Quantum logic is undecidable, arXiv: 1607.05870
• A Resource Theory for Work and Heat, with Carlo Sparaciari and Jonathan Oppenheim, arXiv: 1607.01302
• (Almost) C*-algebras as sheaves with self-action, with Cecilia Flori, arXiv: 1512.01669
• Plausibility measures on test spaces, with Matthew Leifer, arXiv: 1505.01151
• Resource convertibility and ordered commutative monoids, arXiv: 1504.03661
• A mathematical theory of resources, with Bob Coecke and Robert W. Spekkens, arXiv: 1409.5531
• Notes on Triangulated Categories, arXiv: 1407.3765
• Beyond Bell's Theorem II: Scenarios with arbitrary causal structure, arXiv: 1404.4812
• A Bayesian Characterization of Relative Entropy, with John C. Baez, arXiv: 1402.3067
• All joint measurability structures are quantum realizable, with Ravi Kunjwal and Chris Heunen, arXiv: 1311.5948
• Exploring the Local Orthogonality Principle, with Ana Belén Sainz, Remigiusz Augusiak, Jonatan Bohr Brask, Rafael Chaves, Anthony Leverrier and Antonio Acín, arXiv: 1311.6699
• Quantum theory realises all joint measurability graphs, with Chris Heunen and Manuel Reyes, arXiv: 1310.3698
• Compositories and Gleaves, with Cecilia Flori, arXiv: 1308.6548
• Probabilistic models on contextuality scenarios, with Anthony Leverrier and Ana Belén Sainz, arXiv: 1307.0145
• A Combinatorial Approach to Nonlocality and Contextuality, with Anthony Leverrier and Ana Belén Sainz, arXiv: 1212.4084
• Velocity Polytopes of Periodic Graphs and a No-Go Theorem for Digital Physics, arXiv: 1109.1963
• Local orthogonality: a multipartite principle for correlations, with Ana Belén Sainz, Remigiusz Augusiak, Jonatan Bohr Brask, Rafael Chaves, Anthony Leverrier and Antonio Acín, arXiv: 1210.3018
• Entropic Inequalities and Marginal Problems, with Rafael Chaves, arXiv: 1112.4788
• Can you compute the operator norm?, with Tim Netzer and Andreas Thom, arXiv: 1207.0975