Name: Asuka Shiga

Affiliation: Department of Mathematics, Graduate School of Science, Tohoku University

Research

I study the Tate–Shafarevich group (\Sha(E/K)) of an elliptic curve (E) over a number field (K). The Tate–Shafarevich group can be interpreted as the group of counterexamples to the local–global principle for genus-one curves, and it is also an important and fascinating object appearing in the Birch and Swinnerton-Dyer conjecture.

Following my recent work on elliptic curves sharing the same BSD invariants, I am currently studying the phenomenon of visibility, in which elements of the Tate–Shafarevich group become visible inside higher-dimensional abelian varieties. I am also investigating the extent to which an elliptic curve can be recovered from its BSD invariants.

Google Scholar:
https://scholar.google.com/citations?user=HFMRXU8AAAAJ

Upcoming Events

• Arithmetic Statistics, Paderborn, August 24–28, 2026

• Y-RANT 2026, Bristol, September 2–4, 2026

• L-functions and Motives in Niseko 2026, September 13–18, 2026

• Arithmetic Geometry in Sendai, November 2–6, 2026

 

 

 

 

 

 

 

 

 

 

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Favorite group: Tate-Shafarevich group

 

Favorite topologies: Fürstenberg topology, Krull topology

 

Favorite group scheme: Néron model

 

Favorite music: Makoto Ozone, "My Tomorrow," Sukashikao, "Tatoeba Asa no Bus-tei de" (For Example, at the Morning Bus Stop), Tia, "blue," Tokyo Jihen "Gunjou Biyori" (Ultramarine Weather), etc.

 

Favorite anime: Sonny Boy, Samurai Champloo

 

Favorite character: Nekojiru

 

Favorite painters: René Magritte, Van Gogh

 

Favorite coffee shops: Ramble (Shinjuku), Umeda Coffee-kan YC (Umeda)

 

Favorite books (non-mathematics): Bertrand Russell "The Conquest of Happiness," Eto Mori, "Colorful"

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