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diff --git a/research/talks.json b/research/talks.json index a126e36..9f734c5 100644 --- a/research/talks.json +++ b/research/talks.json @@ -16,6 +16,7 @@ {"id":"aristoteMonotoneWeakDistributive2025a","abstract":"In both the category of sets and the category of compact Hausdorff spaces, there is a monotone weak distributive law that combines two layers of non-determinism. Noticing the similarity between these two laws, we study whether the latter can be obtained automatically as a weak lifting of the former. This holds partially, but does not generalize to other categories of algebras. We then characterize when exactly monotone weak distributive laws over powerset monads in categories of algebras exist, on the one hand exhibiting a law combining probabilities and non-determinism in compact Hausdorff spaces and showing on the other hand that such laws do not exist in a lot of other cases.","author":[{"family":"Aristote","given":"Quentin"}],"citation-key":"aristoteMonotoneWeakDistributive2025a","event-place":"Jena, Germany","event-title":"42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)","genre":"conference","issued":{"date-parts":[["2025",3,5]]},"language":"en","note":"slides: https://stacs2025.gitlab.io/slides/monotone-weak-distributive-laws-over-the-lifted-powerset-monad-in-categories-of-algebras.pdf","publisher-place":"Jena, Germany","title":"Monotone weak distributive laws over the lifted powerset monad in categories of algebras","type":"speech","URL":"https://stacs2025.de/"}, {"id":"aristoteMonotoneWeakDistributive2025b","abstract":"Within the study of the semantics of programming languages, computational effects may be modelled with monads, and weak distributive laws between monads are then a tool to combine two such effects.\n\nIn both the category of sets and the category of compact Hausdorff spaces, there is a monotone weak distributive law that combines two layers of non-determinism. Noticing the similarity between these two laws, we study whether the latter can be obtained automatically as some sort of lifting of the former.\n\nMore specifically, we show how a framework for constructing monotone weak distributive laws in regular categories lifts to categories of algebras, giving a full characterization for the existence of monotone weak distributive laws therein. We then exhibit such a law, combining probabilities and non-determinism, in compact Hausdorff spaces; but we also show how such laws do not exist in a lot of other cases.","author":[{"family":"Aristote","given":"Quentin"}],"citation-key":"aristoteMonotoneWeakDistributive2025b","event-place":"Marseille, France","event-title":"LSC Seminar (LiS)","genre":"seminar","issued":{"date-parts":[["2025",3,27]]},"language":"en","note":"slides: https://gitlab.math.univ-paris-diderot.fr/-/project/1062/uploads/02cd7ed45cdac419f5cf315fdde2200a/monotone-wdl-algebras.pdf","publisher-place":"Marseille, France","title":"Monotone weak distributive laws over the lifted powerset monad in categories of algebras","type":"speech","URL":"https://lsc.lis-lab.fr/lsc-seminar/"}, {"id":"aristoteMonotoneWeakDistributive2025c","abstract":"When studying the semantics of programming languages, monads are a tool to model computational effects. Given two monads modelling two effects, a natural question is whether one can build a composed monad modelling the combination of these two effects. There is a generic way to do this when there exists a monotone weak distributive law between the two monads.\n\nMonotone weak distributive laws are a recently-developed mathematical tool, and the first part of the talk will focus on introducing them and giving several examples. The second part of the talk will then focus on the main result from [1], which gives a full characterization for the existence of monotone weak distributive laws in certain categories of algebras.\n\n[1] https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2025.10","author":[{"family":"Aristote","given":"Quentin"}],"citation-key":"aristoteMonotoneWeakDistributive2025c","event-place":"Palaiseau, France","event-title":"Theoretical Cosynus Seminar (LIX)","genre":"seminar","issued":{"date-parts":[["2025",4,8]]},"language":"en","publisher-place":"Palaiseau, France","title":"Monotone weak distributive laws in categories of algebras","type":"speech","URL":"https://www.lix.polytechnique.fr/proofs-algorithms/tcs/"}, + {"id":"aristoteMonotoneWeakDistributive2025d","abstract":"In both the category of sets and the category of compact Hausdorff spaces, there is a monotone weak distributive law that combines two layers of non-determinism. Noticing the similarity between these two laws, we study whether the latter can be obtained automatically as a weak lifting of the former. This holds partially, but does not generalize to other categories of algebras. We then characterize when exactly monotone weak distributive laws over powerset monads in categories of algebras exist, on the one hand exhibiting a law combining probabilities and non-determinism in compact Hausdorff spaces and showing on the other hand that such laws do not exist in a lot of other cases.","author":[{"family":"Aristote","given":"Quentin"}],"citation-key":"aristoteMonotoneWeakDistributive2025d","event-place":"Paris, France","event-title":"PPS days (IRIF)","genre":"seminar","issued":{"date-parts":[["2025",7,3]]},"language":"en","note":"slides: https://gitlab.math.univ-paris-diderot.fr/-/project/1062/uploads/5d4b2a49c1a59a680d60bffa2b3ee01b/monotone-wdl-algebras.pdf","publisher-place":"Paris, France","title":"Monotone weak distributive laws over the lifted powerset monad in categories of algebras","type":"speech","URL":"https://www.irif.fr/rencontres/pps2025/index"}, {"id":"aristoteMulticategoricalFrameworkMinimization2024","abstract":"Joint work with Daniela Petrişan. This paper provides a unifying category-theoretic framework for minimization and learning algorithms for bottom-up tree automata with effects. Our aim is two-fold: encompass existing algorithms for various forms of tree automata – deterministic bottom-up tree automata, residual finite tree automata, tree automata weighted over a field – and instantiate the abstract framework in order to obtain new results – tree automata weighted over principal ideal domains (PIDs).","author":[{"family":"Aristote","given":"Quentin"}],"citation-key":"aristoteMulticategoricalFrameworkMinimization2024","event-place":"Bordeaux, France","event-title":"Highlights of Logic, Games and Automata (Highlights 2024)","genre":"conference","issued":{"date-parts":[["2024",9,18]]},"language":"en","note":"slides: https://gitlab.math.univ-paris-diderot.fr/-/project/1003/uploads/c415dcc8a1e22c5d91cb91cfd8d6d55f/minimal-tree-automata.pdf","publisher-place":"Bordeaux, France","title":"Multicategorical framework for minimization and learning of bottom-up tree automata with effects","type":"speech","URL":"https://highlights-conference.org/2024/"}, {"id":"aristoteNumberRingsAre2025","abstract":"We study automata weighted over number rings, that is, rings of integers in an algebraic number field.\n\nWe show that number rings are what we call \"almost strong Fatou\": if an n-state automaton weighted in a number field recognizes an integer-valued series, then it admits an equivalent n+1-state automaton weighted in the corresponding ring of integers.\n\nWe give a polynomial time procedure for computing such an n+1-state integer-weighted automaton, and show that deciding whether this automaton is minimal among all equivalent integer-weighted automata is as hard as PIP, a problem for which the best known algorithm is in quantum polynomial time.\n\nThis procedure provides a reduction between learning problems for automata weighted in number rings and in fields, and we show that it is an instance of a more general, abstract reduction procedure between learning problems for automata valued in two categories related by well-behaved functors.","author":[{"family":"Aristote","given":"Quentin"}],"citation-key":"aristoteNumberRingsAre2025","event-place":"Marseille, France","event-title":"Combinatorics, Automata and Number Theory 2025","genre":"conference","issued":{"date-parts":[["2025",9,29]]},"language":"en","note":"slides: https://gitlab.math.univ-paris-diderot.fr/-/project/996/uploads/73d3ba029f37d98b7090cce6fd81d8f1/number-rings-almost-strong-fatou.pdf\nposter: https://gitlab.math.univ-paris-diderot.fr/-/project/996/uploads/6c9a3e6d87931780518a540aabb432de/removing-fractions.pdf","publisher-place":"Marseille, France","title":"Number rings are almost strong Fatou","type":"speech","URL":"http://www.discmath.ulg.ac.be/CANT2025/"}, {"id":"aristoteOpenPowerObjectsCategories2025","author":[{"family":"Aristote","given":"Quentin"}],"citation-key":"aristoteOpenPowerObjectsCategories2025","event-place":"Brno, Czech Republic","event-title":"International Category Theory Conference (CT 2025)","genre":"conference","issued":{"date-parts":[["2025",7,18]]},"language":"en","note":"slides: https://gitlab.math.univ-paris-diderot.fr/-/project/1062/uploads/620105dfc6c8ec7fef78737368585a25/open-powerobjects-algebras.pdf\nabstract: https://conference.math.muni.cz/ct2025/data/uploads/abstracts/aristote.pdf","publisher-place":"Brno, Czech Republic","title":"Open Power-Objects in Categories of Algebras","type":"speech","URL":"https://conference.math.muni.cz/ct2025/"}, |