Takayuki Kihara

Graduate School of Mathematics | Nagoya University

• Front Page
• Publications
• Seminar / Teaching
• Open Questions
• _

Contact Information

Takayuki Kihara, Professor (Curriculum Vitae)
Graduate School of Mathematics
Nagoya University, Japan
Email: kihara (at) i (dot) nagoya-u (dot) ac (dot) jp
Office: Graduate School of Mathematics Building, Room 505 [Campus map]

News

• Dr. Satoshi Nakata joined our group as a JSPS Postdoctoral Fellow! (April 2025)
• We held the 3rd Logic Winter School in Japan (Feb. 2025)
  Lectures: Homotopy Type Theory/Univalent Foundations, Model Theory and Bounded Reverse Mathematics
• Dr. Ming Ng joined our group as a JSPS Postdoctoral Fellow! (Dec. 2024)
• 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)

For Students in the Age of AI

Do not be satisfied with merely solving an open problem. Strive to understand in depth why the problem was solved. Try to develop the underlying theory that explains the solution as well. That is where your own originality will truly emerge.

• For example, if you find a counterexample to an open problem, investigate thoroughly what makes it a counterexample. Try to collect as many counterexamples as possible and identify the structural features they have in common; doing so may lead you to formulate a new theory based on them.

Selected Papers (see also the List of Publications)

1. The game-theoretic Katetov order and idealised effective subtoposes (with M. Ng)
   preprint, 59 pages. [arXiv]
   
2. The arithmetical hierarchy: A realizability-theoretic perspective
   preprint, 43 pages. [arXiv]
   
3. Lawvere-Tierney topologies for computability theorists
   Transactions of the American Mathematical Society, Series B, 10 (2023), 48-85. [arXiv]
   
4. Topological reducibilities for discontinuous functions and their structures
   Israel Journal of Mathematics, 252 (2022), pp. 461-500. [arXiv]
   
5. 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]
6. 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]
7. 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]
8. Point degree spectra of represented spaces (with Arno Pauly)
   Forum of Mathematics, Sigma, 10 (2022) e31, pp. 1-27. [arXiv]

Events Organized

1. LWSJ IV, The 4th Logic Winter School in Japan, Kitakami, Iwate, Japan, March 13-17, 2026.
2. RIMS 2025, RIMS Symposium on "New Horizons in Proof Theory and Computability Theory", Kyoto, Japan, December 22-25, 2025.
3. LWSJ III, The 3rd Logic Winter School in Japan, Saitama, Japan, February 17-21, 2025.
4. Proof 2024, Proof Theory Symposium in Japan 2024, Nagoya, December 16-18, 2024.
5. CCR 2024, Seventeenth International Conference on Computability, Complexity and Randomness, March 11-15, 2024, Nagoya, Japan
6. LWSJ II, The 2nd Logic Winter School in Japan, Ehime, Japan, December 26-29, 2023.
7. FoMSS 2023, Foundations of Mathematics Summer School in Japan 2023, Tokyo, Japan, September 11-15, 2023.
8. LWSJ I, The 1st Logic Winter School in Japan, Okinawa, Japan, February 20-24, 2023.
9. Sirius 2022, Sirius workshop on Computing in Topological Structures: Foundations and Implementations, Sirius Mathematical center, Sochi, Russia, July, 2022
10. JPRU 2022, The 2nd Japan-Russia Workshop on Effective Descriptive Set Theoty, Computable Analysis and Automata, Akita, Japan, March 2-5, 2022
11. JPRU 2021, Japan-Russia Workshop on Effective Descriptive Set Theoty, Computable Analysis and Automata, JAIST, Japan, March 17-19, 2021
12. SLS 2018, Sendai Logic School 2018, Akiu, Sendai, Japan, December 7-9, 2018

Program Committee, etc.

ICALP 2027, CiE 2026, CCC 2026, CCA 2025, ALC 2025, CCC 2025, CiE 2025, CCR 2024, CCC 2023, WDCM 2022, CCA 2022, ASL 2021, CCA 2018, CiE 2017