**RIMS/Symmetries and Correspondences workshop****: **

**Inter-universal Teichmüller Theory Summit 2016 **

Organizers:* Ivan Fesenko, Shinichi Mochizuki, Yuichiro Taguchi*

Dates:* *July 18 – 27, 2016

Place:* *RIMS, Kyoto University, Room 420 (July 18 – 22), Room 111 (July 25 – 27)

Abstracts of talks are available from this page

For papers and materials see below

* *July 18, Monday

* *09:30 – 09:40 Opening address

* ***Part I** Preparatory talks

09:45 – 10:45 *Koichiro Sawada*

Uchida’s theorem for one-dimensional function fields over finite fields

11:00 – 12:00* Kazumi Higashiyama*

Mono-anabelian geometry I: Reconstruction of function fields via Belyi cuspidalization

12:15 – 13:15 *Arata Minamide *

Mono-anabelian geometry II: Mono-anabelian geometry over mixed characteristic local fields

14:45 – 15:45 *Ippei Nagamachi*

Log-shell, log-volume, and log-link I

16:00 – 17:00 *Ippei Nagamachi*

Log-shell, log-volume, and log-link II

17:15 – 18:15 *Weronika Czerniawska *

* *July 19, Tuesday

09:30 – 10:30 *Weronika Czerniawska *

10:45 – 11:45 *Arata Minamide *

* *Étale theta functions and mono-theta environments I

12:00 – 13:00 *Arata Minamide*

Étale theta functions and mono-theta environments II

14:30 – 15:30 *Seidai Yasuda*

* *Étale theta functions, mono-theta environments, and [IUTch-I], §1-§3, I

15:45 – 16:45 *Seidai Yasuda*

* *Étale theta functions, mono-theta environments, and [IUTch-I], §1-§3, II

* ***Part II** Overall survey

17:00 – 18:00 *Shinichi Mochizuki*

* ***July 20, Wednesday*** *

09:30 – 10:30 *Shinichi Mochizuki *

* *10:45 – 11:45 *Shinichi Mochizuki *

* *12:00 – 13:00 *Shinichi Mochizuki *

14:30 – 15:30 *Shinichi Mochizuki*

15:45 – 16:45 *Shinichi Mochizuki *

* ***Part III** [IUTch-I-II] * *

17:00 – 18:00* Seidai Yasuda*

* *Étale theta functions, mono-theta environments, and [IUTch-I], §1-§3, III

* ***July 21, Thursday **

** Part II** Overall survey (continued)

09:30 – 10:30 *Shinichi Mochizuki*

10:45 – 11:45 *Shinichi Mochizuki*

** Part III** [IUTch-I-II] (continued)

* *12:00 – 13:00 *Fucheng Tan*

* *IUT-I: Hodge theaters and label classes of cusps 1

14:30 – 15:30 *Fucheng Tan*

* *IUT-I: Hodge theaters and label classes of cusps 2

15:45 – 16:45 *Taylor Dupuy*

* *Functors to and from mono-theta environments

17:00 – 18:00 *Emmanuel Lepage*

19:00 – 21:00 Buffet style dinner

** July 22, Friday**

* *09:30 – 10:30 *Taylor Dupuy *

* *Multiradiality

10:45 – 11:45 *Emmanuel Lepage*

* ***Part IV** [IUTch-III-IV] from the point of view of mono-anabelian transport

12:00 – 13:00 *Yuichiro Hoshi *

* *[IUTch-III-IV] from the point of view of mono-anabelian transport I

14:30 – 15:30 *Yuichiro Hoshi *

[IUTch-III-IV] from the point of view of mono-anabelian transport II

15:45 – 16:45 *Yuichiro Hoshi*

[IUTch-III-IV] from the point of view of mono-anabelian transport III

17:00 – 18:00 *Yuichiro Hoshi*

[IUTch-III-IV] from the point of view of mono-anabelian transport IV

* ***July 25, Monday**

* ***Part V** Related topics

* *09:30 – 10:30 *Yuki Wada*

Near miss abc-triples in compactly bounded subsets

* *10:45 – 11:45 *Vesselin Dimitrov *

Notes on the epsilon term in the abc conjecture

* *12:00 – 13:00* Kobi Kremnitzer *

Milnor-Wood inequality and bounded cohomology

* *14:30 – 15:30 *Ivan Fesenko *

15:45 – 16:45* Boris Zilber*

Model theory of anabelian geometry

* *17:00 – 18:00 Free discussion

* ***July 26, Tuesday**

* ***Part VI** [IUTchIII-IV] with remarks on the function-theoretic roots of the theory

09:30 – 10:30 *Go Yamashita*

[IUTchIII-IV] with remarks on the function-theoretic roots of the theory I

10:45 – 11:45 *Go Yamashita*

[IUTchIII-IV] with remarks on the function-theoretic roots of the theory II

12:00 – 13:00 *Go Yamashita*

[IUTchIII-IV] with remarks on the function-theoretic roots of the theory III

14:30 – 15:30 *Go Yamashita*

[IUTchIII-IV] with remarks on the function-theoretic roots of the theory IV

15:45 – 16:45 Free discussion

17:00 – 18:00 Free discussion

* ***July 27, Wednesday**

* ***Part VII** Overall discussion and impromptu talks

09:30 – 10:10 *Adam Topaz*

* *Kummer theory and anabelian geometry over algebraically closed fields

10:25 – 10:45 *Dinesh Thakur*

* *Diophantine approximation and deformation hierarchies in finite characteristic

11:00 – 12:00 *Paul Vojta*

* *On changes to the Thue-Siegel method

12:15 – 13:00 Free discussion

14:30 – 15:30 Free discussion

15:45 – 16:45 Free discussion

17:00 – 18:00 Free discussion

18:00 – 18:15 Closing remarks

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**Papers and materials for the workshop**

*Surveys of IUT*

The mathematics of mutually alien copies: from Gaussian integrals to inter-universal Teichmuller theory, by Shinichi Mochizuki, preprint 2016

Invitation to inter-universal Teichmüller theory (lecture note version), by Shinichi Mochizuki

Introduction to inter-universal Teichmüller theory (in Japanese), by Yuichiro Hoshi, preprint 2015

*Materials of the Oxford workshop on IUT*

* **Papers*

All the papers below are authored by Shinichi Mochizuki and available, often with comments, from this page

The geometry of anabelioids, Publ. Res. Inst. Math. Sci. 40 (2004), 819–881

Semi-graphs of anabelioids, Publ. Res. Inst. Math. Sci. 42 (2006), 221–322

Arithmetic elliptic curves in general position, Math. J. Okayama Univ. 52 (2010), 1–28

The geometry of frobenioids I: The general theory, Kyushu J. Math. 62(2008), 293–400

The geometry of frobenioids II: Poly-Frobenioids, Kyushu J. Math. 62 (2008), 401–460

Inter-universal Teichmüller theory I: Constructions of Hodge theaters, preprint 2012–2016 - [IUTch-I]

Inter-universal Teichmüller theory II: Hodge-Arakelov-theoretic evaluation, preprint 2012–2016 - [IUTch-II]

Inter-universal Teichmüller theory III: Canonical splittings of the log-theta-lattice, preprint 2012–2016 - [IUTch-III]

Inter-universal Teichmüller theory IV: Log-volume computations and set-theoretic foundations, preprint 2012–2016 - [IUTch-IV]

Noncritical Belyi maps, Math. J. Okayama Univ. 46 (2004), 105–113

Topics in absolute anabelian geometry I: Generalities, J. Math. Sci. Univ. Tokyo 19 (2012), 139–242

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