2013-05-12
　・(Papers) Updated the comments concerning:
　　Topics Surrounding the Combinatorial Anabelian Geometry of
　　Hyperbolic Curves I: Inertia Groups and Profinite Dehn Twists.
2013-05-02
　・(Travel and Lectures) Posted the lecture notes for a lecture to be
　　given at the University of Tokyo on June 13, 2013. These lecture
　　notes are based on the survey
　　　　A Panoramic Overview of Inter-universal Teichmuller Theory.
　　that I released a few months ago.
　・(Past and Current Research) Posted "FAQ on 'Inter-Universality' "
　　by Go Yamashita.
2013-04-24
　・(Papers) Revised version (list of revisions):
　　Inter-universal Teichmuller Theory III: Canonical Splittings of
　　　　the Log-theta-lattice.
2013-04-12
　・Uploaded ``Cherry Blossoms around RIMS 2013''.
　・(Papers) Updated the comments concerning:
　　A Combinatorial Version of the Grothendieck Conjecture.
　・(Papers) Revised version (list of revisions):
　　Topics in Absolute Anabelian Geometry II.
　・(To Prospective Students and Visitors) Updated "To Prospective
　　Students and Visitors".
2013-03-26
　・(Papers) Revised version (list of revisions):
　　A Panoramic Overview of Inter-universal Teichmuller Theory.
　・(Papers) Revised version (list of revisions):
　　Inter-universal Teichmuller Theory I: Construction of Hodge Theaters.
　　Inter-universal Teichmuller Theory III: Canonical Splittings of
　　　　the Log-theta-lattice.
　　Inter-universal Teichmuller Theory IV: Log-volume Computations
　　　　and Set-theoretic Foundations.
2013-03-01
　・(Papers) Revised version (list of revisions):
　　A Panoramic Overview of Inter-universal Teichmuller Theory.
2013-02-21
　・(Papers) Revised version (list of revisions):
　　A Panoramic Overview of Inter-universal Teichmuller Theory.
2013-02-20
　・(Papers) New paper (survey of IUTeich):
　　A Panoramic Overview of Inter-universal Teichmuller Theory.
　・(Papers) Revised version (slightly modified the discussion of [Lch] and
　　updated the references):
　　Topics Surrounding the Combinatorial Anabelian Geometry of
　　　　Hyperbolic Curves II: Tripods and Combinatorial Cuspidalization.
　　Topics Surrounding the Combinatorial Anabelian Geometry of
　　　　Hyperbolic Curves III: Tripods and Tempered Fundamental Groups.
　・(Papers) Revised version (list of revisions):
　　Inter-universal Teichmuller Theory I: Construction of Hodge Theaters.
　　Inter-universal Teichmuller Theory II: Hodge-Arakelov-theoretic
　　　　Evaluation.
　　Inter-universal Teichmuller Theory III: Canonical Splittings of
　　　　the Log-theta-lattice.
2013-02-04
　・(Papers) Updated the comments concerning:
　　The Etale Theta Function and its Frobenioid-theoretic Manifestations.
　・(Papers) Revised version (list of revisions):
　　Topics in Absolute Anabelian Geometry III.
　・(Paper) Revised version (list of revisions):
　　Inter-universal Teichmuller Theory I: Construction of Hodge Theaters.
　　Inter-universal Teichmuller Theory II: Hodge-Arakelov-theoretic
　　　　Evaluation.
2013-01-14
　・(Papers) Revised version (list of revisions):
　　Inter-universal Teichmuller Theory III: Canonical Splittings of
　　　　the Log-theta-lattice.
2012-12-26
　・(Papers) Revised version (list of revisions):
　　Inter-universal Teichmuller Theory III: Canonical Splittings of
　　　　the Log-theta-lattice.
2012-12-20
　・(Papers) Updated/posted comments concerning:
　　The Geometry of Frobenioids I: The General Theory.
　　The Geometry of Frobenioids II: Poly-Frobenioids.
　　The Geometry of Anabelioids.
　　Semi-graphs of Anabelioids.
　　The Profinite Grothendieck Conjecture for Closed Hyperbolic Curves
　　　　over Number Fields.
2012-12-16
　・(Papers) Revised version (list of revisions):
　　Inter-universal Teichmuller Theory I: Construction of Hodge Theaters.
　　Inter-universal Teichmuller Theory II: Hodge-Arakelov-theoretic
　　　　Evaluation.
　　Inter-universal Teichmuller Theory III: Canonical Splittings of
　　　　the Log-theta-lattice.
　　Inter-universal Teichmuller Theory IV: Log-volume Computations
　　　　and Set-theoretic Foundations.
2012-12-02
　・(Papers) Updated the comments concerning:
　　The Geometry of Frobenioids I: The General Theory.
2012-11-28
　・(Travel and Lectures) Updated the lecture notes for a lecture to be
　　given at a workshop scheduled for December 2012.
2012-11-21
　・(Travel and Lectures) Updated the lecture notes for a lecture to be
　　given at a workshop scheduled for December 2012.
　・(Papers) Updated the comments concerning:
　　The Geometry of Frobenioids I: The General Theory.
2012-11-14
　・(Papers) Updated the comments concerning:
　　The Geometry of Frobenioids I: The General Theory.
　・(Papers) Revised version (list of revisions):
　　Topics in Absolute Anabelian Geometry III.
2012-11-10
　・(Travel and Lectures) Posted the lecture notes for a lecture to be
　　given at a workshop scheduled for December 2012. I am scheduled to
　　write a survey of IUTeich based on these lecture notes by the end
　　of March 2013.
2012-11-07
　・(Papers) New papers:
　　Topics Surrounding the Combinatorial Anabelian Geometry of
　　　　Hyperbolic Curves II: Tripods and Combinatorial Cuspidalization.
　　Topics Surrounding the Combinatorial Anabelian Geometry of
　　　　Hyperbolic Curves III: Tripods and Tempered Fundamental Groups.
2012-10-25
　・(Papers) Posted comments concerning:
　　On the Combinatorial Anabelian Geometry of Nodally Nondegenerate
　　Outer Representations.
2012-10-20
　・(Papers) Posted comments concerning:
　　A Combinatorial Version of the Grothendieck Conjecture.
2012-10-18
　・(Papers) Revised version (list of revisions):
　　Topics in Absolute Anabelian Geometry III.
　・(Papers) Updated the comments concerning:
　　Absolute Anabelian Cuspidalizations of Proper Hyperbolic Curves.
　・(Papers) Posted comments concerning:
　　A Survey of the Hodge-Arakelov Theory of Elliptic Curves I.
　　A Survey of the Hodge-Arakelov Theory of Elliptic Curves II.
2012-10-14
　・(Papers) Posted comments concerning Theorem 1.10 of the following
　　paper:
　　Inter-universal Teichmuller Theory IV: Log-volume Computations
　　　　and Set-theoretic Foundations.
2012-10-08
　・(Papers) Updated the comments concerning:
　　Arithmetic Elliptic Curves in General Position.
2012-10-06
　・(Papers) Posted comments concerning:
　　Topics Surrounding the Combinatorial Anabelian Geometry of
　　Hyperbolic Curves I: Inertia Groups and Profinite Dehn Twists.
2012-10-02
　・(Papers) Updated the comments concerning:
　　The Etale Theta Function and its Frobenioid-theoretic Manifestations.
2012-08-30
　・(Papers) Revised version (the revisions are minor and unrelated to
　　the substantive content of the paper):
　　Topics Surrounding the Combinatorial Anabelian Geometry of
　　Hyperbolic Curves I: Inertia Groups and Profinite Dehn Twists.
　・(Papers) New papers:
　　Inter-universal Teichmuller Theory I: Construction of Hodge Theaters.
　　Inter-universal Teichmuller Theory II: Hodge-Arakelov-theoretic
　　　　Evaluation.
　　Inter-universal Teichmuller Theory III: Canonical Splittings of
　　　　the Log-theta-lattice.
　　Inter-universal Teichmuller Theory IV: Log-volume Computations
　　　　and Set-theoretic Foundations.
2012-06-18
　・(Papers) Posted comments concerning:
　　The Absolute Anabelian Geometry of Canonical Curves.
2012-04-14
　・Uploaded ``Cherry Blossoms around RIMS 2012''.
2012-04-12
　・(Papers) Revised version (made slight modifications to Theorem
　　1.8, (i); Corollary 1.11, (i); the Bibliography)
　　Topics in Absolute Anabelian Geometry II.
2012-04-06
　・(Papers) Revised version (the revisions are minor and unrelated to
　　the mathematical content of the paper):
　　Topics Surrounding the Combinatorial Anabelian Geometry of
　　Hyperbolic Curves I: Inertia Groups and Profinite Dehn Twists.
2012-04-05
　・(Top page) Replaced the photograph on the top page by a photograph
　　taken a few days ago.
2012-04-02
　・(To Prospective Students and Visitors) Updated "To Prospective
　　Students and Visitors".
2012-03-14
　・(Papers) Revised version (list of main revisions):
　　Topics in Absolute Anabelian Geometry I.
2012-02-12
　・(Papers) Revised version (list of main revisions):
　　Topics in Absolute Anabelian Geometry I.
　　Topics in Absolute Anabelian Geometry II.
　　Topics in Absolute Anabelian Geometry III.
2012-01-23
　・(Thoughts) Posted a report concerning my progress in writing up
　　my ideas on IUTeich theory.
2011-12-22
　・(Papers) Revised version (in which we corrected a misprint in
　　Lemma 1.5):
　　On the Combinatorial Anabelian Geometry of Nodally Nondegenerate
　　Outer Representations.
2011-11-25
　・(Papers) Updated the comments concerning:
　　The Geometry of Frobenioids I: The General Theory.
2011-11-08
　・(Papers) Upon receiving notification that in certain computing
　　environments the PDF files in the present site are unreadable, I
　　decided to replace most of the PDF files in the present site by
　　``font embedded versions''.
　・(Safety Confirmation Information) I added a ``Safety Confirmation
　　Information'' button to the present page in the hope that it might
　　be of use in emergency situations such as natural disasters.
2011-09-08
　・(Papers) Updated the comments concerning:
　　The Etale Theta Function and its Frobenioid-theoretic Manifestations.
2011-07-15
　・(Papers) Posted comments concerning:
　　A Theory of Ordinary p-adic Curves.
　・(Papers) Posted comments concerning:
　　Arithmetic Elliptic Curves in General Position.
2011-06-20
　・(Thoughts) Posted a report concerning my progress in writing up
　　my ideas on IUTeich theory.
2011-05-02
　・(Thoughts) I realized that the valuation-theoretic problem left
　　pending in my comments of 2011-03-03 may be resolved quite easily.
　　In particular, one may derive the main theorem obtained in Pop-Stix'
　　work on the p-adic Section Conjecture as a consequence of an entirely
　　elementary argument in graph theory and commutative algebra (i.e.,
　　without resorting to the use of difficult arithmetic results such
　　as Tamagawa's ``resolution of nonsingularities''). Click here for
　　more details. 　
2011-04-12
　・Uploaded ``Cherry Blossoms around RIMS 2011''.
2011-04-01
　・(Papers) New paper:
　　Topics Surrounding the Combinatorial Anabelian Geometry of
　　Hyperbolic Curves I: Inertia Groups and Profinite Dehn Twists.
　・(Papers) Posted comments concerning:
　　On the Combinatorial Cuspidalization of Hyperbolic Curves.
2011-03-03
　・(Thoughts) As I explained in a previous note, one may apply the work
　　of Pop-Stix on the p-adic Section Conjection to reduce the Profinite
　　p-adic Section Conjecture to its tempered counterpart (a remark
　　due to Y. Andre). On the other hand, I recently noticed that this
　　reduction may also be obtained as a consequence of an entirely
　　elementary graph-theoretic argument (i.e., without resorting to
　　the use of difficult arithmetic results such as Tamagawa's
　　``resolution of nonsingularities''). Click here for more details.
2010-11-23
　・(Papers) Updated the comments concerning:
　　Semi-graphs of Anabelioids.
2010-11-18
　・(Thoughts) Posted a report concerning my progress in writing up
　　my ideas on IUTeich theory.
2010-11-15
　・(Thoughts) Again I made slight modifications to my comments the
　　other day concerning the the theorem of Pop-Stix and updated the
　　various links for these comments to the latest version.
　・(Papers) Updated the comments concerning:
　　Semi-graphs of Anabelioids.
2010-11-11
　・(Thoughts) I made slight modifications to my comments the other
　　day concerning the the theorem of Pop-Stix. Click here for more
　　details.
　・(Papers) Revised version (in which we made slight modifications to
　　the discussion of the relationship to the work of Takao):
　　On the Combinatorial Anabelian Geometry of Nodally Nondegenerate
　　Outer Representations.
2010-11-02
　・(Thoughts) I realized, with regard to the relationship between the
　　``combinatorial section conjecture'' and the work of Pop-Stix on
　　the p-adic Section Conjection, that a similar argument holds over
　　more general fields and for more general sets of primes Σ. This
　　lead me to modify the argument I gave on 2010-10-29. Click here
　　for more details.
2010-10-29
　・(Thoughts) I recently realized that the work of Pop-Stix on the
　　p-adic Section Conjecture is related to the ``combinatorial
　　section conjecture'' that I proved in my paper ``Semi-graphs of
　　anabelioids'' a few years ago. Click here for more details.
2010-10-27
　・(Papers) Revised version (in which I replaced statements
　　concerning the ``genus'' by statements concerning the ``type'' in
　　Definition 1.9; Corollaries 1.10, 1.11):
　　Topics in Absolute Anabelian Geometry II.
2010-10-13
　・(Travel and Lectures) Posted the lecture notes for a lecture to be
　　given at a workshop scheduled for October 2010.
　・(To Prospective Students and Visitors) Updated "To Prospective
　　Students and Visitors".
2010-07-16
　・(Past and Current Research) Posted the abstract of a lecture to be
　　given at a workshop scheduled for October 2010.
2010-06-18
　・(Papers) Revised version (in which I made slight modifications to
　　Propositions 5.7, (ii); 5.8, (vi)):
　　Topics in Absolute Anabelian Geometry III.
2010-06-11
　・(Papers) Revised version (in which I made a slight modification to
　　Definition 5.4, (v)):
　　Topics in Absolute Anabelian Geometry III.
2010-06-01
　・(Papers) Revised version (in which I modified Corollary 2.8, (i),
　　and Remark 2.12.1):
　　Topics in Absolute Anabelian Geometry I.
2010-05-06
　・(Papers) Revised version (list of main revisions):
　　Topics in Absolute Anabelian Geometry I.
2010-04-12
　・(Thoughts) Posted a report concerning my progress in writing up
　　my ideas on IUTeich theory.
　・Uploaded ``Cherry Blossoms around RIMS 2010''.
2009-10-15
　・(Thoughts) Posted a report concerning my progress in writing up
　　my ideas on IUTeich theory.
　・(To Prospective Students and Visitors) Updated "To Prospective
　　Students and Visitors".
2009-10-01
　・(Papers) Revised version (in which we modified Lemma 1.6, Remark
　　1.6.1):
　　On the Combinatorial Anabelian Geometry of Nodally Nondegenerate
　　Outer Representations.
2009-09-13
　・(Papers) Revised version (in which we modified Theorem 6.1, Corollary 6.3):
　　On the Combinatorial Anabelian Geometry of Nodally Nondegenerate
　　Outer Representations.
2009-09-03
　・(Papers) Updated the comments concerning:
　　Semi-graphs of Anabelioids.
　・(Papers) Revised version (in which I made a slight modification
　　to Remark 2.11.1):
　　Topics in Absolute Anabelian Geometry II.
2009-08-19
　・(Papers) New paper:
　　On the Combinatorial Anabelian Geometry of Nodally Nondegenerate
　　Outer Representations.
2009-07-06
　・(Papers) Revised version (in which I made a slight modification
　　concerning the term ``edge-paired'' in the case in which the
　　prime under consideration is equal to 2):
　　Topics in Absolute Anabelian Geometry II.
2009-06-16
　・(Papers) Updated the comments concerning:
　　Semi-graphs of Anabelioids.
2009-05-14
　・(Papers) Posted comments concerning:
　　The Etale Theta Function and its Frobenioid-theoretic Manifestations.
2009-04-21
　・(Papers) Revised version (in which I added Remark 2.11.1):
　　Topics in Absolute Anabelian Geometry II.
2009-04-12
　・Uploaded ``Cherry Blossoms around RIMS 2009''.
2009-04-05
　・(Papers) Revised version (in which I revised the definition of a log-shell):
　　Topics in Absolute Anabelian Geometry III.
2009-02-25
　・(Papers) Revised version:
　　On the Combinatorial Cuspidalization of Hyperbolic Curves.
　・(Papers) Posted comments related to the content of the following
　　paper:
　　The Algebraic and Anabelian Geometry of Configuration Spaces.
2009-02-17
　・(Papers) Revised version:
　　Arithmetic Elliptic Curves in General Position.
2009-02-11
　・(Thoughts) Posted a report concerning my progress in writing up
　　my ideas on IUTeich theory.
2009-01-22
　・(Papers) Revised version:
　　On the Combinatorial Cuspidalization of Hyperbolic Curves.
2008-12-12
　・(Papers) Updated the list of papers and posted revised version:
　　The Etale Theta Function and its Frobenioid-theoretic Manifestations.
2008-11-17
　・(Papers) Revised version:
　　The Etale Theta Function and its Frobenioid-theoretic Manifestations.
2008-09-05
　・(Papers) Posted comments concerning:
　　The Geometry of Frobenioids I: The General Theory.
2008-08-18
　・(Papers) Revised version:
　　Topics in Absolute Anabelian Geometry II.
2008-08-03
　・(Papers) Revised version:
　　Topics in Absolute Anabelian Geometry III.
2008-07-21
　・(Past and Current Research) ''So what is IUTeich theory about?''
　　an explanation via ``Sokkuri animation'' that was pointed out to
　　me by Fumiharu Kato.
2008-06-17
　・(Papers) Revised version:
　　Arithmetic Elliptic Curves in General Position.
2008-06-11
　・(Papers) New paper:
　　On the Combinatorial Cuspidalization of Hyperbolic Curves.
　・(Papers) Revised version:
　　The Geometry of Frobenioids I: The General Theory.
　・(Papers) Revised version:
　　The Geometry of Frobenioids II: Poly-Frobenioids.
　・(Thoughts) Added a report on recent research concerning
　　combinatorial cuspidalization and absolute pro-p anabelian
　　geometry.
2008-05-18
　・(Travel and Lectures) Posted the lecture notes for my lectures for
　　students and colloquium talk on ``Arithmetic Teichmuller Theory''
　　(in Japanese)
　・(Papers) Updated the picture in the paper as well as the comments
　　concerning:
　　Semi-graphs of Anabelioids.
2008-04-14
　・(Papers) Revised version:
　　Topics in Absolute Anabelian Geometry I, II, III.
2008-04-09
　・Uploaded ``Cherry Blossoms around RIMS 2008''.
　・(Thoughts) Added a report on research concerning a combinatorial
　　version of an injectivity theorem of Matsumoto.
　・(Papers) Posted comments concerning:
　　Foundations of p-adic Teichmuller Theory.
　・(Papers) Posted comments concerning:
　　Semi-graphs of Anabelioids.
2008-03-25
　・(Papers) New series of papers:
　　Topics in Absolute Anabelian Geometry I, II, III.
　・(Papers) New paper:
　　Arithmetic Elliptic Curves in General Position.
　・(Past and Current Research) Updated the report on my research up
　　till now.
2008-02-01
　・(Papers) Posted comments concerning:
　　Absolute Anabelian Cuspidalizations of Proper Hyperbolic Curves.
2008-01-05
　・(Papers) Revised version:
　　The Geometry of Frobenioids I: The General Theory.
　・(Papers) Revised version:
　　The Geometry of Frobenioids II: Poly-Frobenioids.
2007-07-27
　・(Papers) Revised version:
　　The Algebraic and Anabelian Geometry of Configuration Spaces.
2007-06-06
　・(Papers) Revised version:
　　Absolute Anabelian Cuspidalizations of Proper Hyperbolic Curves.
2007-05-16
　・(Papers) Revised version:
　　The Geometry of Frobenioids I: The General Theory.
　・(Papers) Revised version:
　　The Geometry of Frobenioids II: Poly-Frobenioids.
　・(Papers) Revised version:
　　The Etale Theta Function and its Frobenioid-theoretic Manifestations.
2007-04-12
　・Uploaded ``Cherry Blossoms around RIMS 2007''.
2007-04-06
　・(Papers) Revised version:
　　A Combinatorial Version of the Grothendieck Conjecture.
2007-01-31
　・(Papers) Revised version:
　　Absolute Anabelian Cuspidalizations of Proper Hyperbolic Curves.
　・(Papers) Revised version:
　　A Combinatorial Version of the Grothendieck Conjecture.
2007-01-20
　・(Papers) Revised version:
　　Absolute Anabelian Cuspidalizations of Proper Hyperbolic Curves.
2006-12-23
　・(Papers) Revised version:
　　Absolute Anabelian Cuspidalizations of Proper Hyperbolic Curves.
　・(Papers) Revised version:
　　The Geometry of Frobenioids I: The General Theory.
　・(Papers) Revised version:
　　The Geometry of Frobenioids II: Poly-Frobenioids.
　・(Papers) Revised version:
　　The Etale Theta Function and its Frobenioid-theoretic Manifestations.
2006-11-27
　・(Papers) Revised version:
　　The Algebraic and Anabelian Geometry of Configuration Spaces.
2006-11-18
　・(Travel and Lectures) Posted the lecture notes for my lecture at
　　the workshop on ``p-adic Arithmetic Geometry'' to be held next week.
2006-10-31
　・(Thoughts) Erratum concerning ``symmetrized configuration
　　spaces''.
2006-09-16
　・(Past and Current Research) Updated the report on my recent
　　research related to the ABC Conjecture.
2006-09-06
　・(Papers) New paper:
　　The Algebraic and Anabelian Geometry of Configuration Spaces.
2006-09-01
　・(Papers) Revised version:
　　The Etale Theta Function and its Frobenioid-theoretic Manifestations.
2006-08-25
　・(Thoughts) More on recent work in anabelian geometry.
　・(Papers) Revised version:
　　Conformal and Quasiconformal Categorical Representation of
　　Hyperbolic Riemann Surfaces.
2006-07-14
　・(Papers) Revised version:
　　Global Solvably Closed Anabelian Geometry.
2006-06-24
　・(Thoughts) Added a report on recent work in anabelian geometry.
2006-06-13
　・(Papers) Revised version:
　　The Geometry of Frobenioids I: The General Theory.
2006-06-03
　・(Papers) Revised version:
　　Global Solvably Closed Anabelian Geometry.
2006-06-02
　・(To Prospective Students and Visitors) Updated "To Prospective
　　Students and Visitors".
2006-05-22
　・(Curriculum Vitae) Added an mp3 file that contains the
　　pronunciation of my name.
2006-05-21
　・(Papers) Revised version:
　　Absolute Anabelian Cuspidalizations of Proper Hyperbolic Curves.
2006-04-22
　・(Papers) New paper:
　　The Etale Theta Function and its Frobenioid-theoretic Manifestations.
2006-04-11
　・(Papers) Revised version:
　　A Combinatorial Version of the Grothendieck Conjecture.
　・(Papers) Revised version:
　　The Geometry of Frobenioids I: The General Theory.
　・(Papers) Revised version:
　　The Geometry of Frobenioids II: Poly-Frobenioids.
2006-04-06
　・(Papers) Revised version:
　　Conformal and Quasiconformal Categorical Representation of
　　Hyperbolic Riemann Surfaces.