# Shu Sasaki

Since November 2012, I am a research fellow at Universitat Duisburg-Essen.

Fakultat fur Mathematik,
Universitat Duisburg-Essen,
Thea-Leymann-Strasse 9
45127 Essen,
Germany.

Until October 2012, I was an EPSRC postdoctoral fellow hosted by Fred Diamond at King's College London.

I was a Ph.D student of Kevin Buzzard. Which does not mean that I should have a website identical to his, but I ended up having one :-) Spooky.

## Publications/Pre-prints

"p-adic Gross-Zagier formula at critical slope and a conjecutre of Perrin-Riou-II", with K.Büyükboduk and R.Pollack, in preparation.

"p-adic Gross-Zagier formula at critical slope and a conjecutre of Perrin-Riou-I", with K.Büyükboduk and R.Pollack, pre-print, pdf.

"p-adic automorphic cohomology of Shimura varieties and weight one forms, in preparation (available on request). This ms, for example, proposes a criterion for identifying p-adic *classical* (holomorphic) weight one forms inside p-adic completed cohomology groups.

"A Jacquet-Langlands relation between mod p Hilbert and quaternionic modular forms", with F. Diamond and P. Kassaei, in preparation. Fred gave a talk in the ICM satellite conderence (Rio 2018) on automorphic forms and Galois representations and here are his notes.

"A Serre weight conjecture for geometric Hilbert modular forms in characteristic p", with F. Diamond, pre-print, pdf.

"Buzzard-Taylor and subsequent developments (in Japanese)", to appear in Proceedings of Number Theory Summer School 2016 "Introduction to p-adic theory of modular forms", pdf.

"Integral models of Hilbert modular varieties in the ramified case, deformations of modular Galois representations, and weight one forms II", pre-print, pdf.

"Integral models of Hilbert modular varieties in the ramified case, deformations of modular Galois representations, and weight one forms", Invent. Math. 215 (2019), 171-264, pdf. Here is the link.

"Modular lifting results in parallel weight one and applications to the Artin conjecture: the tamely ramified case", with P. Kassaei and Y. Tian, Forum of Mathematics, Sigma, 2 (2014). Here is the link.

"On Artin representations and nearly ordinary Hecke algebras over totally real fields", Documenta Math. 18 (2013), 997-1038, pdf.

"\mu_{Aut} <= \mu_{Gal}", here. I was asked to write up notes for the lecture (90 minuites) I gave at the workshop "Around the Breuil-Mezard conjecture", organised by A.David and G.Wiese at University of Luxembourg (17/12/2012-18/12/2012). Apparently they are going to peer-review and publish these notes.

"Coleman's theory of p-adic modular forms", Proceedings of Number Theory Summer School 2009 "l-adic Galois representations and deformations of Galois representations", dvi. (Written primarily as a "reading aid" to some of the Coleman's papers for (under)graduate students in Japan who participated in the summer school. To the organisers' horror, however, I wrote this in English! Hopefully it serves more people though... According to Naoki, apparently I am the first one in the long history of Number Theory Summer School who committed the sin ;-))

Analytic continuation of overconvergent Hilbert eigenforms", Compositio Math. 146 (2010), 541-560, dvi.

## Lectures

I gave a course (3 hours in total) on Hida theory and Coleman theory for graduate students in Germany. I texted up lecture notes. If you are interested, they are here.

I was teaching a course (2 hours per week for 5 weeks) on the p-adic numbers at London Taught Course Centre in January 2011 and 2010. It was meant to be introductory and accessible to first year graduate students in pure mathematics. Nowhere near complete (I did tex up what I had said and written on the boards though) but, *for those of you who needed to take the exam in the end*, I had been instructed by LTCC to type up lecture notes and upload them on a website. They are here, here, and here. I run out of steam by just typing them up and haven't read them again since. Let me know if you find typos or errors.

I gave a 50-mins talk in Antalya (Turkey) about a conjecture of Artin. Here are the slides I had prepared for the talk if you are interested.