EXTENDED PROCEEDINGS OF
Oxford (CMI and C&S) workshop on IUT theory of Shinichi Mochizuki
December 7-11 2015, L3 Math Institute Univ. Oxford
Letter to participants (I. Fesenko)
Scienti c report on the workshop (I. Fesenko)

December 7
9:00-9:20 Ivan Fesenko Foreword0

9:20-10:10 Shou-Wu Zhang A proof of geometric Szpiro inequality inspired by Bogomolov

1

10:40-11:40 Ulf Kühn Arithmetic of elliptic curves in general position2

13:30-14:30 Ariyan Javanpeykar Reducing the conjectures to one theorem of IUT

3

15:00-16:00 Yuichiro Hoshi An approximate statement of the main theorem of IUT

4

16:15-17:15 Yuichiro Hoshi Mono-anabelian transport

4

17:20-18:00 Discussions
December 8
9:00-11:00 Skype session with Shinichi Mochizuki
11:30-12:30 Fucheng Tan Absolute anabelian geometry

5

13:50-14:50 Fucheng Tan Absolute anabelian geometry

5

15:20-16:20 Jakob Stix Reconstruction of elds using Belyi cuspidalization

6

16:35-17:35 Lars Kuehne Archimedean aspects of absolute anabelian geometry

7

17:35-18:00 Discussions

9:00-9:45 Oren Ben-Bassat Frobenioids 1

810:00-10:45 Weronika Czerniawska Frobenioids 29fifiDecember 911:15-12:15 Tamás Szamuely Geometry and semi-graphs of anabelioids10

14:10-15:10 Emmanuel Lepage Tempered fundamental group of semi-graphs of anabelioids

11

15:45-16:15 Go Yamashita Motivation from Hodge-Arakelov theory

12

16:30-17:30 Kiran Kedlaya Etale theta function

13

17:30-18:00 Discussions
December 10
9:00-10:00 Kiran Kedlaya Etale theta function

13

10:15-11:15 Chung Pang Mok IUT, Introduction to (Hodge) theatres

14

11:45-12:45 Chung Pang Mok IUT, Introduction to (Hodge) theatres

14

13:50-14:50 Chung Pang Mok IUT, Multiradiality of the theta environment

15

15:20-16:20 Yuichiro Hoshi IUT, Hodge-Arakelov-theoretic evaluation

16

16:35-17:35 Yuichiro Hoshi IUT, Hodge-Arakelov-theoretic evaluation

16

17:35-18:00 Discussions
December 11
9:00-10:00 Go Yamashita IUT, [IUT-III]17

10:15-11:15 Go Yamashita IUT, [IUT-III]

17

11:45-12:45 Go Yamashita IUT, [IUT-III]

17

13:40-15:40 Skype session with Shinichi Mochizuki

18

16:10-17:10 Go Yamashita IUT, [IUT-III-IV], with some remarks on the language of species

19

17:10-17:30 Ivan Fesenko Summary and what's next

0 see this page for survey texts of IUT which you may nd useful to read rst
1 this proof can be viewed as an elementary guide or blueprint for IUT, see [B] and also this table; the key inequality is
actually the Milnor-Wood inequality, see e.g. this paperfifi

2 [NB] and [AE]

3 Sect. 1-2 of [IUT-IV] without proof of Th 1.10 of [IUT-IV]
4 these follow a very recent survey of IUT by Yuichiro Hoshi, in Japanese.
One can also recommend three slide talks of the same speaker at a RIMS conference in December 2015 available
from section Lectures of this page
5 [TAAG-I-II]
6 sect.1 of [TAAG-III]
7 sect. 2 and 4 of [TAAG-III]
8 [F], see also Responses to questions on Frobenioids by Shinichi Mochizuki, in particular Response 8
9 [F], see also Responses to questions on Frobenioids by Shinichi Mochizuki, in particular Response 8
10 [A]
11 [A] and sect. 2 of [IUT-I]
12 [HAT] and slides 12-23 of a talk by Go Yamashita at RIMS in March 2015
13 [ET], picture of covers
14 [IUT-I]
15 sect. 1 of [IUT-II]
16 sect. 2-4 of [IUT-II]
17 [IUT-III]
18 see in particular Response on a question of Fucheng Tan by Shinichi Mochizuki
19 [IUT-III] and sect. 1 of [IUT-IV], with some remarks on the language of species, sect. 3 of [IUT-IV]

All papers below are authored by Shinichi Mochizuki and available, often with comments, from this page[A] 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[AE] Arithmetic elliptic curves in general position, Math. J. Okayama Univ. 52 (2010), 1–28
[B] Bogomolov's proof of the geometric version of the Szpiro conjecture from the point of view of inter-universal
Teichmüller theory,
preprint 2015
[ET] The étale theta function and its frobenioid-theoretic manifestations, Publ. Res. Inst. Math. Sci. 45 (2009), 227–349[F] 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

[HAT] A survey of the Hodge–Arakelov theory of elliptic curves I, in Proc. of Symp. Pure Math. 70, AMS (2002), 533–569;
A survey of the Hodge–Arakelov theory of elliptic curves II, Adv. Stud. Pure Math. 36, Math. Soc. Japan (2002), 81–114[IUT] Inter-universal Teichmüller theory I: Constructions of Hodge theaters, preprint 2012–2015;
Inter-universal Teichmüller theory II: Hodge-Arakelov-theoretic evaluation, preprint 2012–2015;
Inter-universal Teichmüller theory III: Canonical splittings of the log-theta-lattice, preprint 2012–2015;
Inter-universal Teichmüller theory IV: Log-volume computations and set-theoretic foundations, preprint 2012–2015[NB] Noncritical Belyi maps, Math. J. Okayama Univ. 46 (2004), 105–113[TAAG] Topics in absolute anabelian geometry I: Generalities, J. Math. Sci. Univ. Tokyo 19 (2012), 139–242;
Topics in absolute anabelian geometry II: Decomposition groups and endomorphisms, J. Math. Sci. Univ. Tokyo 20(2013), 171–269;
Topics in absolute anabelian geometry III: Global reconstruction algorithms, J. Math. Sci. Univ. Tokyo 22 (2015),
939-1156