/sci/ - Science & Math

[Anonymous No.7022493]

Have you gotten ready for “Inter-universal Mellin transform” yet?

http://www.kurims.kyoto-u.ac.jp/~motizuki/Inter-universal%20Teichmuller%20Theory%20IV.pdf

Remark 2.2.1

Mochizuki hopes to solve the Riemann Hypothesis

[Anonymous No.7022502]

The old thread finally died? ;_;

[Anonymous No.7022520]

I am ready!

[Anonymous No.7022521]

Researchers around the world are already using IUTeich in other areas.

http://arxiv.org/abs/1411.1208

Acknowledgement
The author cannot express enough his sincere and deep gratitude to Professors Shinichi Mochizuki and Kirti Joshi. Without their philosophies and amazinginsights, his study of mathematics would have remained “dormant”. The author deeply appreciates Professor Yuichiro Hoshi giving him helpful suggestions, as well as reading preliminary versions of the present paper. Butthe author alone, of course, is responsible for any errors and misconceptions in the present paper. Also, the author would also like to thank Professor Go Yamashita, Mr. Katsurou Takahashi (for giving him heartfelt encouragements), and the various individuals (including pointed stable curves of positive characteristic!) with whom the author became acquainted in Kyoto. The author means the present paper for a gratitude letter to them.

[Anonymous No.7022522]

Go Yamashita is writing an independent survey of 200~300 pages in length about IUTeich and its initial results.
Hopefully that will give a big boost for its study. Should be ready in about 2 or 3 months.

[Anonymous No.7022523]

Looks like Chung Pang Mok is giving some seminars on the USA.

https://www.msri.org/seminars/21066
> Introductory remarks on Mochizuki's works on absolute anabelian geometry and inter-universal Teichmüller theory

http://www.math.ucsc.edu/seminars-colloquia/seminars/num-theory-Fall-14.html
> Introduction to Mochizuki's works on inter-universal Teichmuller theory

[Anonymous No.7022524]

>>7022523
Not only on Mathematical Sciences Research and UC Santa Cruz, but he's also going to give lectures at University of British Columbia and Duke University.

https://www.math.duke.edu/mcal?abstract-8848
https://www.math.ubc.ca/Dept/Events/index.shtml?period=future&series=69

Chung Pang Mok is definitely helping disseminate IUTeich in the USA.

I hope it begins to be taught all over the world so Mochizuki can focus on the Riemann Hypothesis.

[Anonymous No.7022526]

What are the pre-requisites in order to read the IUTeich papers?

[Anonymous No.7022530]

>>7022526
Hartshorne's Algebraic Geometry, a few analytic and algebraic number theory things and probably some of Grothendieck's work (EGA, SGA). Ask an expert in the field of arithmetic geometry, they would know more than me.

[Anonymous No.7022531]

What is Mochizuki claiming, exactly? That he has a new set of techniques, which he calls “inter-universal geometry”, generalizing the foundations of algebraic geometry in terms of schemes first envisioned by Grothendieck? And that these new theory is useful in many ways, including solving the abc conjecture and possibly the Riemann Hypothesis? Huge!

[Anonymous No.7022652]

So can any mathematician understand this guy's work? I heard recently about Mochizuki complaining that other mathematicians are really struggling to understand what he has done.

[Anonymous No.7022655]

>>7022652
Read his report about the status of the theory:

http://www.kurims.kyoto-u.ac.jp/~motizuki/IUTeich%20Verification%20Report%202014-12.pdf

[Anonymous No.7022705]

OOOOOOOOOHHHHHHHHH

NIP CHONG BING BONG IS GONNA STUDY REAR HARD AND SOLVE THE PROBREM I CAN TELL

[Anonymous No.7022726]

>>7022493

mochizuki is best waifu

[Anonymous No.7022732]

Callin' it now, this thread won't die for another 5+ weeks.

[Anonymous No.7022758]

stop posting this fucking thread im sick of seeing this ugly stupid cunt's face on the front page

fuck you

[Anonymous No.7022775]

>>7022758

not until everyone has read IUTEICH

[Anonymous No.7022777]

>>7022758
Because pseudoscience, homework, and maymay threads are somehow preferable to a thread on a legitimate development in the field of mathematics?

Fuck off to >>>/b/

[Anonymous No.7022779]

Is there a version of the Pontryagin duality on varieties?

[Anonymous No.7022780]

>>7022779
There's Cartier duality, which is like Pontryagin duality for group schemes.

[Anonymous No.7022781]

What role do moduli spaces play in this theory? Teichmüller theory is all about them, right? But then again, isn't Teichmüller theory not about complex Riemannian surfaces? That's weird, I don't see how this theory would be analogous.

[Anonymous No.7022783]

>>7022780

Neat, thanks for the answer.

[Anonymous No.7022785]

>>7022781
A moduli space is a space that parametrizes a family of distinct objects (e.g. the triangles in the plane, distinguished up to rigid motion). Teichmuller space is the moduli space of all complex structures on a given space (e.g. a torus), up to homeomorphism (in the connected component of the identity). This itself turns out to be a complex manifold. The case of the torus (i.e. elliptic curves) is the easiest to start off with, if I recall correctly this is given by the torus's lattice in <span class="math">\mathbb{C}[/spoiler] modulo rigid motions.

[Anonymous No.7022786]

Who here has a physical copy of the IUTeich papers? I printed mine some weeks ago, thinking about getting it into a brochure.

[Anonymous No.7022829]

>>7022786

my printer can't handle italics, so half his text didn't appear. oh well.

[Anonymous No.7022886]

>>7022777
Nice digits, /b/ro!

[Anonymous No.7022909]

>>7022530
How the fuck does anyone read Hartsthorne?

I read up to the definition of schemes in that online "Foundations of Algebraic Geometry" book (and really need to get back into trying to read more soon) but all of that together was easier than the first 20 pages of Hartshorne.