Takayuki Kihara

Department of Mathematical Informatics | Graduate School of Informatics | Nagoya University

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Contact Information

Takayuki Kihara, Associate Professor (Curriculum Vitae)
Department of Mathematical Informatics
Graduate School of Informatics
Nagoya University, Japan
Email: kihara (at) i (dot) nagoya-u (dot) ac (dot) jp
Office: Graduate School of Informatics Building, Room 310 [Campus map]

News

• I have launched Logic Winter School in Japan. The first school was held in Okinawa (February 2023), and offered lectures on Categorical Logic, Constructive Mathematics, Descriptive Set Theory, Computability Theory and Models of Arithmetic.
• Computability Theory and Applications Online Seminar has started! (April 2020)
• With the support of the JSPS summer program, Mr. Paul-Elliot Angles d'Auriac (Paris-Est Créteil) is now visiting us! (From June to August 2018)
• Our Nagoya Logic Seminar webpage is now open! (May 2017)

Selected Papers (see also the List of Publications)

1. Rethinking the notion of oracle: A prequel to Lawvere-Tierney topologies for computability theorists
   preprint, 57 pages. [arXiv]
   
2. Lawvere-Tierney topologies for computability theorists
   Transactions of the American Mathematical Society, Series B, 10 (2023), 48-85. [arXiv]
   
3. Enumeration degrees and non-metrizable topology (with Keng Meng Ng, and Arno Pauly)
   preprint, 103 pages. [arXiv]
4. On the structure of the Wadge degrees of BQO-valued Borel functions (with Antonio Montalbán)
   Transactions of the American Mathematical Society 371 (11) (2019), pp. 7885-7923. [arXiv]
5. The uniform Martin's conjecture for many-one degrees (with Antonio Montalbán)
   Transactions of the American Mathematical Society 370 (12) (2018), pp. 9025-9044. [arXiv]
6. Turing degrees in Polish spaces and decomposability of Borel functions (with Vassilios Gregoriades and Keng Meng Ng)
   Journal of Mathematical Logic, 21 (2021), no. 1, 2050021, 41 pages. [arXiv]
7. Point degree spectra of represented spaces (with Arno Pauly)
   Forum of Mathematics, Sigma, 10 (2022) e31, pp. 1-27. [arXiv]
8. Decomposing Borel functions using the Shore-Slaman join theorem
   Fundamenta Mathematicae 230 (2015), pp. 1-13. [doi]

Selected Slides

1. Topos theoretic aspect of the degrees of unsolvability
2. Lawvere Tierney topologies for computability theorists
3. HYP with finite mind-changes
4. Wadge-like classifications of real-valued functions
5. De Groot duality in computability theory
6. Topological aspects of enumeration degrees
7. The uniform Martin conjecture and Wadge degrees
8. Degrees of unsolvability in topological spaces with countable cs-networks
9. The second-level Borel isomorphism problem: An encounter of recursion theory and infinite dimensional topology
10. An application of classical recursion theory to descriptive set theory via computable analysis
11. Counterexamples in computable continuum theory

Organized Workshops

1. CCR 2024, Seventeenth International Conference on Computability, Complexity and Randomness, Nagoya
2. LogWin 2023, Logic Winter School in Japan 2023, Okinawa, February 20-24, 2023.
3. Sirius 2022, Sirius workshop on Computing in Topological Structures: Foundations and Implementations, Sirius Mathematical center, Sochi, Russia, July, 2022
4. JPRU 2022, The 2nd Japan-Russia Workshop on Effective Descriptive Set Theoty, Computable Analysis and Automata, Akita, Japan, March 2-5, 2022
5. JPRU 2021, Japan-Russia Workshop on Effective Descriptive Set Theoty, Computable Analysis and Automata, JAIST, Japan, March 17-19, 2021
6. SLS 2018, Sendai Logic School 2018, Akiu, Sendai, Japan, December 7-9, 2018