The study of L-invariants started since the work of Mazur-Tate-Teitelbaum, in which the L-invariants appeared as an important constant in the exceptional zero phenomenon of p-adic L-functions (of modular forms). There were later several definitions of L-invariants via different approaches. By the work of many people, these L-invariants turned out to be all the same in the modular form case. The proofs of the equality witnessed the profound development of the p-adic arithmetic, including the p-adic comparison theorems, p-adic Galois deformations, p-adic Langlands program etc.

The workshop aims to explore recent developments on several different type L-invariants in more general setting. And it offers a chance for the researchers working on different type L-invariants to exchange ideas. We expect the workshop can help to start new projects and collaborations. The workshop consists of 4 lecture series, with the first talk of each lecture series being introductory.  

Speaker: Yiwen Ding (BICMR)

Title: L-invariants and p-adic Langlands program

Abstract: A basic problem in p-adic Langlands program is to find the information of p-adic Galois representations in p-adic automorphic representations. Let V be a semi-stable non-crystalline p-adic Galois representation. By p-adic Hodge theory, V is determined by the associated Weil-Deligne representation, the Hodge-Tate weights, and its associated Fontaine-Mazur L-invariants. In the talks, we give a description of the Fontaine-Mazur L-invariants in terms of Galois deformations. We then explain a strategy to find their counter part in p-adic automorphic representations, including our work on simple L-invariants and also the joint work with Christophe Breuil on higher L-invariants.

Speaker：Lennart Gehrmann (Universitat Duisburg-Essen)

Title: Automorphic L-invariants for reductive groups

Abstract: Automorphic L-invariants were first constructed by Henri Darmon for modular forms of weight 2. The construction was generalized by various authors to modular forms of higher weight, Hilbert and Bianchi modular forms. In this lecture series I will review Darmon's construction of L-invariants, the connection to exceptional zeroes of p-adic L-functions and their behaviour under cyclic base change and the Jacquet-Langlands correspondence. I will also give a generalization of Darmon's consctruction of L-invariants to cohomological, cuspidal automorphic representations of arbitrary reductive groups.

Speaker：Shanwen Wang (Fudan University)

Title: Perrin-Riou p-adic L-functions and exceptional zeros

Abstract: We will explain the machine of p-adic L-function of Perrin-Riou, the exceptional zero conjectures of p-adic L-functions formulated by Denis Benois and the compatibility of them. 

Speaker：Bingyong Xie (East China Normal University) 

Title: Hodge-like decomposition and Teitelbaum type L-invariants

Abstract: In this talk, we discuss Teitelbaum L-invariants and its generalization by Chida-Mok-Park. Then following Iovita and Spiess method we use Hodge-like decompositions of de Rham cohomology over p-adic symmetric space to compare Teitelbaum type L-invariants and Fontaine-Mazur L-invariants.