, TBA

**Organizers:**

Ashay Burungale (California Institute of Technology)

Ming-Lun Hsieh (Academia Sinica)

Bharathwaj Palvannan (NCTS)

Sujatha Ramdorai (University of British Columbia)

**Aim & Scope:**

One fruitful approach in algebraic number theory and arithmetic geometry is to study arithmetic invariants varying over families. In Iwasawa theory, one obtains p-adic families, for example, by varying number fields (as in classical Iwasawa theory) or by considering p-adic families of modular forms (as in Hida theory). The fact that studying arithmetic invariants over families is an important perspective in number theory is highlighted by Galois deformation theory, which played a crucial role in Fermat’s last theorem. One of the central themes of this program, is whether interesting arithmetic invariants (such as Iwasawa mu-invariant) associated to L-functions are generically non-trivial over families, which are often encoded by whether analytic invariants (such as special values of L-functions) are generically non-trivial modulo p.

There have been numerous developments on the non-triviality of these arithmetic/analytic invariants, which have had various arithmetic applications (for instance, towards proving Iwasawa main conjectures). It is time to bring experts together to explore new ideas for the non-vanishing of L-values. Therefore, we plan to devote the first week of the program to a rigorous exposition of the ideas in the pioneering works, and the second week of the program will be devoted to the recent developments by some of the leading experts in the area.

**Mini Course Speakers:**

Ashay Burungale (California Institute of Technology)

Ching-Li Chai (University of Pennsylvania)

Haruzo Hida (University of California Los Angeles)

Ming-Lun Hsieh (Academia Sinica)

Vinayak Vatsal (The University of British Columbia)

**Invited Speakers:**

Li Cai (YMSC Tsinghua University)

Francesc Castella (University of California, Santa Barbara)

Ellen Eischen (University of Oregon)

Fabian Januszewski (Karlsruhe Institute of Technology)

Dimitar Jetchev (École polytechnique fédérale de Lausanne)

Mahesh Kakde (King's College London)

Chao Li (Columbia University)

Zheng Liu (University of California, Santa Barbara)

Yiannis Petridis (University College London)

Dinakar Ramakrishnan (California Institute of Technology)

Hae-Sang Sun (Ulsan National Institute of Science and Technology)

Ye Tian (Chinese Academy of Sciences)

Jacques Tilouine (Université Paris 13)

Masao Tsuzuki (Sophia University)

Eric Urban (Columbia University)

Xin Wan (Morningside Center of Mathematics)

Registration Link:https://forms.gle/QG7SnKQVdtoXMXbSA

**Please kindly note that Deadline for registration and funding: Feb 28, 2020**

**Contact:** Peggy Lee (ncts2020arithmetic@gmail.com)