Takayuki Kihara

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

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Research Seminars

I'm co-organizing an international Zoom seminar for computability theorists:
Computability Theory and Applications Online Seminar

I'm also co-organizing a local seminar with Prof. Matsubara and Prof. Yoshinobu:
Nagoya Logic Seminar

Theses Supervised

I supervised 4 Master theses:

• (2022) Mathematical Universe based on Quantum Logic
• (2022) Analysis of Weak Negation Based on Modal Semantics
• (2020) Wadge-like Hierarchies under Determinacy Hypothesis
• (2020) A Survey on Categorical Semantics of Linear Logic

I supervised 5 Bachelor theses:

• (2021) Model-theoretic independence proofs for Ramsey-type combinatorial statements in first-order Peano arithmetic
• (2021) On derivations of incompleteness theorems and related topics
• (2020) The hierarchy of computability and logical principles in analysis
• (2020) A formal model and a concrete encoding scheme for certain pragmatic aspects of horological data representation, and a reference implementation in OCaml
• (2018) Theoretical foundations and practice of concatenative programming

Are you interested in joining us?

If you are interested in joining us as a student, please see the following admissions informations:

• Application for admission as a Graduate Student
• Application for admission as a Research Student

For a short visit, we can also host the following program offered by the JSPS:

• JSPS Summer Program (for graduate students and post-doctoral researchers, 2 months from June to August)

If you are interested in joining us as a post-doctoral researcher:

• Please see JSPS Standard Postdoctoral Fellowship for Overseas Researchers (2 years)
• See also other JSPS Postdoctral fellowship programs.

Teaching

FY 2021:

• Fall 2021: Theory of Computability 2
  Topos Theory: Presheaf, sheaf, Heyting-valued set, effective topos
  
• Fall 2021: Theory of Computability 1
  Computable analysis, represented space, realizability
  
• Fall 2021: Mathematical Informatics 10
  Theory of Computation: Temporal logic, omega-automaton, decidability
• Fall 2021: Mathematical Informatics 9
  Theory of Computation: combinatory logic, lambda calculus, Curry-Howard correspondence
  Course Notes (52 pages, in Japanese)
• Fall 2021: Mathematical Informatics 6
  Measure-Theoretic Probability Theory
• Fall 2021: Mathematical Informatics 5
  Probability Theory, and Statistics
• Spring 2021: Mathematical Informatics 1
  Googology and Logic: Kruskal's tree theorem, WQO theory, the Veblen hierarchy
  Course Notes (72 pages, in Japanese)
• Spring 2021: Survey on Pure Mathematical Informatics 2
  Primitive recursive functions of higher types, Goedel's system T
• Spring 2021: Advanced Calculus 1
• Spring 2021: Advanced Calculus 2

FY 2020:

• Fall 2020: Mathematical Informatics 10
  Theory of Computation: undecidable problem, limit computability, arithmetical hierarchy
  (A part of) Course Notes (24 pages, in Japanese)
• Fall 2020: Mathematical Informatics 9
  Theory of Computation: combinatory logic, lambda calculus, Curry-Howard correspondence
  Course Notes (52 pages, in Japanese)
• Fall 2020: Mathematical Informatics 6
  Measure-Theoretic Probability Theory
• Fall 2020: Mathematical Informatics 5
  Probability Theory, and Statistics
• Spring 2020: Mathematical Informatics 1
  Googology and Logic: Kruskal's tree theorem, WQO theory, the Veblen hierarchy
  Course Notes (72 pages, in Japanese)
• Spring 2020: Survey on Pure Mathematical Informatics 2
  Primitive recursive functions of higher types, Goedel's Dialectica interpretation
  Course Notes (39 pages, in Japanese)
• Spring 2020: Advanced Calculus 1
• Spring 2020: Advanced Calculus 2

FY 2019:

• Fall 2019: Theory of Computability 2
  Category Theory: adjoint, monad, Eilenberg-Moore algebra, categorical logic
  Course Notes (110 pages, in Japanese)
• Fall 2019: Theory of Computability 1
  Partial combinatory algebra, realizability, computable analysis
  Course Notes (97 pages, in Japanese)
• Fall 2019: Mathematical Informatics 6
  Statistics
• Fall 2019: Mathematical Informatics 5
  Probability Theory
• Spring 2019: Mathematical Informatics 1
  Googology and Logic: unprovability, fast growing hierarchy, proof-theoretic ordinals
• Spring 2019: Survey on Pure Mathematical Informatics 2
  Primitive recursive functions of higher types, Goedel's Dialectica interpretation
  Course Notes (39 pages, in Japanese)
• Spring 2019: Advanced Calculus 1
• Spring 2019: Advanced Calculus 2

FY 2018:

• (No lectures in the fall semester due to a visit to Singapore.)
• Spring 2018: Mathematical Informatics 1
  Googology and Logic: unprovability, fast growing hierarchy, proof-theoretic ordinals
• Spring 2018: Mathematical Informatics 6
  Introduction to Mathematical Logic
  Course Notes (70 pages, in Japanese)
• Spring 2018: Survey on Pure Mathematical Informatics 2
  Theory of Recursive Functions
• Spring 2018: Advanced Calculus 1
• Spring 2018: Advanced Calculus 2
• Spring 2018: Linear algebra 1

FY 2017:

• Fall 2017: Theory of Computability 2
  Representated space, computable analysis, algorithmic randomness
  Course Notes (43 pages, in Japanese)
• Fall 2017: Theory of Computability 1
  Turing machine, decision problem, partial combinatory algebra
  Course Notes (52 pages, in Japanese)
• Spring 2017: Mathematical Informatics 1
  Introduction to Randomness
  Course Notes (9 pages, in Japanese)
• Spring 2017: Mathematical Informatics 6
  Introduction to Mathematical Logic
  Course Notes (35 pages, in Japanese)
• Spring 2017: Survey on Pure Mathematical Informatics 2
  Theory of Recursive Functions
• Spring 2017: Linear algebra 1