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Yamashita Lab
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The lab studies arithmetic geometry, including p-adic Hodge theory and multiple zeta values.
AboutAbout the lab
Arithmetic geometry, linking numbers and shapes.
The Yamashita Lab studies arithmetic geometry.
It lists p-adic Hodge theory, Iwasawa theory, multiple zeta values, Shimura varieties and the Langlands correspondence, and inter-universal Teichmüller theory among its research areas.
Students who choose Lecturer Yamashita as their academic advisor are generally expected to study and conduct research in arithmetic geometry.
After entering graduate school, students choose a text and present it at a seminar held about once a week, then find a research topic and proceed with their research.
Key terms
- Arithmetic geometry
- A field of mathematics that studies the properties of integers and of solutions to equations using the language of geometric objects (algebraic varieties)
- p-adic Hodge theory
- A theory that compares the cohomologies of varieties in the world of p-adic numbers, which are built from a prime number p
- Multiple zeta values
- Numbers obtained by extending values of the zeta function to multiple sums. They are connected to many areas of mathematics and physics
ResearchResearch themes
The lab studies arithmetic geometry. It works on p-adic Hodge theory, multiple zeta values and mixed Tate motives, modularity lifting theorems and the Langlands correspondence, and inter-universal Teichmüller theory.
*Illustrative imagep-adic Multiple Zeta Values
The lab jointly formulated a p-adic version of the conjecture on the dimensions of spaces of multiple zeta values. It has shown that there is a huge number of linear relations among p-adic multiple zeta values.
*Illustrative imageExtending the p-adic Lefschetz (1,1) Theorem
By extending the p-adic Lefschetz (1,1) theorem to the case of semistable reduction, and the Hyodo-Kato isomorphism to the case of families, the lab extended the results of earlier work on the Picard number jump loci.
*Illustrative imageMod p Reductions of Crystalline Representations
In modularity lifting theorems and the Langlands correspondence, the core is to study local universal deformation rings using integral p-adic Hodge theory.
*Illustrative imageDeveloping Inter-universal Teichmüller Theory
In collaboration with Shinichi Mochizuki, the lab is working to develop inter-universal geometry further. As a long-term plan, it aims to build a theory of the "inter-universal Mellin transform" and relate it to the Riemann zeta function.
MembersFaculty
- LecturerGo Yamashita
VoicesStudent voices
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Report an errorAbout the images
The top and research theme images are illustrative and were not taken at the lab. They are cropped from Wikimedia Commons images. Cropped CC BY-SA images are provided under the same CC BY-SA license as the original (version shown on each line).
- Top image: “Riemann zeta function absolute value vi” Conscious / CC BY 2.5 (cropped)
- p-adic Multiple Zeta Values: “Partial sums riemann zeta function” Åshild Telle / CC0 (cropped)
- Extending the p-adic Lefschetz (1,1) Theorem: “Kummer surface” Claudio Rocchini / CC BY-SA 3.0 (cropped)
- Mod p Reductions of Crystalline Representations: “Ulam spiral with prime numbers and divisor-based dot sizes” Marianoju / CC BY-SA 4.0 (cropped)
- Developing Inter-universal Teichmüller Theory: “Bers-Einbettung” Café Bene / CC BY-SA 3.0 (cropped)
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