# PKU/BICMR Number Theory Seminar - 2023

## Venue

• Until further notice, the offline or hybrid talks will be held in room 77201, BICMR.
• For online or hybrid talks, the Zoom number is 743 736 2326, and the password is 013049.

## Schedule

The series is also announced on researchseminars.org

 Time and Date Speaker Topic Slides / Recording March 15 15:00-16:00 Yupeng Wang (Chinese Academy of Sciences) Integral $$p$$-adic non-abelian Hodge theory for small representations April 5 15:30-16:30 Li Lai (Tshinghua University) On the irrationality of certain $$2$$-adic zeta values Let $$\zeta_2(\cdot)$$ be the Kubota-Leopoldt $$2$$-adic zeta function. We prove that, for every nonnegative integer $$s$$, there exists an odd integer $$j$$ in the interval $$[s+3,3s+5]$$ such that $$\zeta_2(j)$$ is irrational. In particular, at least one of $$\zeta_2(7),\zeta_2(9),\zeta_2(11),\zeta_2(13)$$ is irrational. Our approach is inspired by the recent work of Sprang. We construct explicit rational functions. The Volkenborn integrals of the (higher order) derivatives of these rational functions produce good linear combinations of $$1$$ and $$2$$-adic Hurwitz zeta values. The most difficult step is to prove that certain Volkenborn integrals are nonzero, which is resolved by careful manipulation of the binomial coefficients. April 12 Fan Gao (Zhejiang University) TBA April 26 King Fai Lai TBA May 24 Si Ying Lee (Bonn University) TBA