Shun ISHII's website

Welcome to my homepage!

About me

I’m Shun ISHII (石井 竣), a JSPS research fellow at Keio University. My CV is available here.

I am fascinated by Galois groups and fundamental groups. Broadly speaking, my research interests lie in a mixture of arithmetic, geometric and topological aspects of low-dimensional objects (e.g. Drinfeld modules, once-punctured elliptic curves, etc…) and moduli spaces of them.

email address : (my lastname).(my firstname)@keio.jp

Papers

・ The $\mathfrak{p}$-primary Uniform Boundedness Conjecture for Drinfeld Modules, accepted for publication in International Journal of Number Theory [RIMS Preprints].

・ Drinfeld 加群の$\mathfrak{p}$冪ねじれ点に対する普遍上界予想について (survey article, written in Japanese), accepted for publication in RIMS Kokyuroku Bessatsu.

・ On isogeny characters of Drinfeld modules of rank two, Mathematische Zeitschrift,301, 455–470 (2022), available here. A preprint is also available [RIMS Preprints].

Preprints

・On the kernels of the pro-$p$ outer Galois representations associated to once-punctured CM elliptic curves, submitted [arXiv].

・On Kummer characters arising from Galois actions on the pro-$p$ fundamental groups of once-punctured CM elliptic curves, submitted [arXiv].

Talks (date/name/place/title)

・2023.12.12, Algebraic Number Theory and Related Topics 2023 [Link], Research Institute for Mathematical Sciences (RIMS), On the kernels of pro-$p$ outer Galois representations associated to once-punctured CM elliptic curves.

・2023.09.26, MFO-RIMS Tandem workshop 2023 - Arithmetic Homotopy and Galois Theory [Link], Research Institute for Mathematical Sciences (RIMS) and Oberwolfach Research Institute for Mathematics (MFO), On pro-$p$ outer Galois representations associated to once-punctured CM elliptic curves.

・2023.07.12, 22th Hiroshima-Sendai Workshop on Number Theory [Link], Hiroshima University, On pro-$p$ outer Galois representations associated to once-punctured CM elliptic curves.

・2023.06.27, Keio Algebra seminar (慶應代数セミナー), Keio University, 一点抜き CM 楕円曲線の副$p$外 Galois 表現から生じる数体について.

・2023.03.28, Low Dimensional Topology and Number Theory XIV [Link], Kyushu University, On pro-$p$ outer Galois representations associated to once-punctured CM elliptic curves.

・2022.02.07, Mathsci Freshman Seminor 2022 [Link], online, 虚数乗法を持つ楕円曲線引く原点の副$p$外 Galois 表現から生じる指標について.

・2020.12.04, Algebraic Number Theory and Related Topics 2020 [Link], Research Institute for Mathematical Sciences (RIMS), Drinfeld 加群の$\mathfrak{p}$冪ねじれ点に対する普遍上界予想について.

・2020.09.11, 19th Sendai-Hiroshima Number Theory Conference [Link], online, On a variant of the uniform boundedness conjecture for Drinfeld modules.

・2020.08.21, 2nd Kyoto-Hefei Workshop on Arithmetic Geometry [Link], online, On a variant of the uniform boundedness conjecture for Drinfeld modules.

・2020.08.09. Kyushu Algebraic Number Theory 2020 Summer on Zoom [Link], online, Drinfeld 加群の一次元族に対する普遍上界予想の類似について.