Takayuki Kihara | Graduate School of Informatics

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

I supervised 6 Master theses:

(2023) The Reverse Mathematics Zoo of Hyperarithmetic Analysis
(2023) Subcategories of separated objects as regular-epireflective full subcategories
(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

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

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:

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