Vadim Kulikov

I am a mathematician and a cognitive scientist working as a Senior Research Fellow at the University of Oulu, Faculty of Information Technology and Electrical Engineering, Center for Ubiquitous Computing (UBICOMP)  (Oulu, Finland). I am also affiliated as an Adjunct Professor at the Department of Mathematics and Statistics of the University of Helsinki. My main interest is in theoretical investigation on topics related to logic, set theory and model theory, cognitive modeling, computational cognitive neuroscience, philosophy of mind, enactivist and ecological theories of perception. I find applications to robotics, VR, machine learning and data-analysis exciting and important. Additionally to my main work as a scientist, I occasionally do consulting through the companies Bats and Seahorses and Tensoritulo Oy. As a hobby I am interested in connections between mathematics and art. I am enthusiastic about teaching and education on all levels from kindergarten to university (I am a contributor to the project NoBoxToday, have lectured around 10 university courses on mathematics and machine learning, and supervised a dozen BSc and MSc theses) . My other hobbies include floor acrobatics and drawing.

Previously I have worked at: University of Helsinki, Aalto University, University of Vienna (at the Kurt Gödel Research Center for Mathematical Logic), Mittag-Leffler Institute, as well as a U.S.-based hedgefund in New Jersey. See my full CV here.

Publications

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Books

  • S.-D. Friedman, T. and V. Kulikov. (2014). Generalized descriptive set theory and classification theory. Series: Memoirs of AMS, publisher: American Mathematical Society; ISBNs: 978-0-8218-9475-0 (print); 978-1-4704-1671-3 (online).
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Peer-reviewed scientific articles and books

  • V. Kulikov. (2020). Preferential Engagement and What Can We Learn From Online Chess? Minds and Machines. Springer Science and Business Media LLC
    Official website
  • T. Hyttinen, V. Kulikov, and M. Moreno. (2020). On Latex formula-completeness of quasi-orders on Latex formula . Fundamenta Mathematicae, 251(3):245–268.
    Official website PDF
  • D. Asperó, T. Hyttinen, V. Kulikov, and M. Moreno. (2019). Reducibility of equivalence relations arising from nonstationary ideals under large cardinal assumptions. Notre Dame Journal of Formal Logic, 60(4):665–682.
    Official website  PDF
  • M. Hannula, Å. Hirvonen, J. Kontinen, V. Kulikov, and J. Virtema.  (2019). Facets of distribution identities in probabilistic team semantics. In F. Calimeri, N. Leone, and M. Manna, editors, Logics in Artificial Intelligence, volume 11468 of Lecture Notes in Computer Science, pp. 304–320. Springer.
    Official website  PDF
  • T. Hyttinen and V. Kulikov. (2018). Borel* sets in the generalized Baire space and infinitary languages. In Jaakko Hintikka on Knowledge and Game-Theoretical Semantics, pp. 395–412. Springer.
    Official website PDF
  • T. Hyttinen, V. Kulikov, and M. Moreno. (2017). A generalized Borel-reducibility counterpart of Shelah’s main gap theorem. Archive for Mathematical Logic, 56(3-4):175–185.
    Official website PDF
  • V. Kulikov. A non-classification result for wild knots. (2017). Transactions of the American Mathematical Society, 369(8):5829–5853.
    Official website PDF
  • S.-D. Friedman, Y. Khomskii, and V. Kulikov. (2016). Regularity properties on the generalized reals. Annals of Pure and Applied Logic, 167(4):408–430.
    Official website
    PDF
  • S.-D. Friedman, T. Hyttinen, and V. Kulikov. (2015). On Borel reducibility in generalized Baire space. Fundamenta Mathematicae, 231(3):285–298.
    Official website PDF
  • T. Hyttinen and V. Kulikov. (2015). On Latex formula-complete equivalence relations on the generalized Baire space. Mathematical Logic Quarterly, 61(1-2):66–81.
    Official website  PDF
  • S.-D. Friedman and V. Kulikov. (2015). Failures of the Silver dichotomy in the generalized Baire space. The Journal of Symbolic Logic, 80(2):661–670.
    Official website  PDF
  • V. Kulikov. (2013). Borel reductions and cub games in generalised descriptive set theory. The Journal of Symbolic Logic, 78(2):439–458, 2013.
    Official website PDF
  • V. Kulikov. (2013). The class of purely unrectifiable sets in Latex formula is Latex formula-complete. Real analysis exchange, 39(2):323–334.
    Official website PDF
  • T. Hyttinen and V. Kulikov. (2011). Weak Ehrenfeucht-Fraı̈ssé games. Transactions of the American Mathematical Society, 363(6):3309–3334.
    Official website PDF

Conference proceedings (selected)

  • V. Kulikov. (2019) A mathematical approach to enactivism. In A. Newen, editor, Eurocogsci: Situated Minds and Flexible Cognition. Proceedings of EuroCogSci2019, Bochum
  • V. Kulikov. (2016). A Multicoding Theory of Cognitive Semantics. In Современная логика: проблемы теории, истории и применения в науке – Логический анализ языка (Contemporary logic: theory, history, and applications to science – logical analysis of language), 13(2):121-122.
    Official website PDF
  • V. Kulikov. (2015). Framework theory: A theory of cognitive semantics. In T. R. Besold and K.-U. Kühnberger, editors, Proceedings of the Workshop on Neural-Cognitive Integration (Dresden, NCI@Ki2015), pp. 8–18.
    Website PDF

Publications intended for the general public (in Finnish)

  • Vadim Kulikov (2020): Matematiikkaa taiteessa (Mathematics in Art), in ArchiMAD 1/2020.
  • Vadim Kulikov (2017): Voiko kone koskaa oppia ihmisen abstraktia ajattelua? (Can machines learn abstract thinking?) in Uutistamo.
  • Vadim Kulikov (2017): Miten viisi sekuntia vuodessa muuttuu pohjattomaksi motivaation lähteeksi: Prof. Olli Martion haastattelu. (How five seconds a year can turn into a bottomless source of motivation: an interview with Prof. Olli Martio) in Dimensio. PDF
  • Vadim Kulikov (2010): Solmut taiteessa ja matematiikassa (Knots in Art and Mathematics), Matematiikkalehti Solmu PDF
  • Matti Lehtinen ja Vadim Kulikov (2009): Emmy Noether mursi sukupuolirajan (Emmy Noether broke a gender barrier), Matematiikkalehti Solmu PDF
  • Vadim Kulikov (2009): Ensimmäisten kuuluisien naismatemaatikkojen henkilökuvia, Sofia Kovalevskaja (First women in mathematics, Sofia Kovalevskaya), Matematiikkalehti Solmu PDF

Theses

  • Master’s thesis, cognitive science (2016), U. Vienna. Supervisor Ulrich Ansorge, Unconscious inference: Understanding semantics through colour concept processing in verbal and visual modalities. PDF
  • PhD thesis (2011), mathematical logic U. Helsinki. Supervisor Tapani Hyttinen, Playing Games on Sets and Models  Official website  PDF
  • Master’s thesis (2009), mathematical logic, U. Helsinki. Supervisor Tapani Hyttinen Weak Ehrenfeucht-Fraïsse Games. Paper based on thesis

Contact Vadim


Phone: +358503444045