This conference, which is part of a long-standing tradition of French-Japanese collaboration in arithmetic geometry, will honor two leading figures of this partnership: Professor Takeshi Saito, on the occasion of his retirement, and Professor Takeshi Tsuji, on the occasion of his 60th birthday.

The main topics of the conference will include:

• p-adic Hodge theory, including the p-adic Simpson correspondence, geometric Sen theory, p-adic Galois representations and (φ,Γ)-modules, prismatic cohomology, and their applications;
• Ramification theory, including singular support and characteristic cycles of l-adic étale sheaves (in equal and mixed characteristic), compatibility with proper higher direct images, Swan conductors, and epsilon-factors;
• Geometric Langlands theory, l-adic, p-adic, and for modules with integrable connections, in characteristic p and in characteristic 0.

Numerous arithmetico-geometric invariants of spaces have been defined and characterized through the homotopic Galois action. The study of these invariants has driven significant progress in both the diophantine study of abelian varieties through their Tate module and in anabelian geometry as a whole. An important theme in both settings is how the constraints imposed by the Galois action have led to finiteness results - for example the different proofs of Mordell's conjecture.

This workshop focuses on the recent developments surrounding such invariants, with a particular emphasis on the Rasmussen-Tamagawa conjecture. The participants are encouraged to discuss related subjects during the workshop.

Keywords: Diophantine properties, abelian varieties, anabelian properties, Galois action, section conjecture, heavenly property, Rasmussen-Tamagawa conjecture.

※ This event is part of the special year ``Arithmetic, Homotopy, and Geometry 2027-28''.

The program will highlight both foundational developments, and new directions at the crossroads of multiple areas, such as arithmetic dynamics, complex degenerations, K-stability, tropical geometry, and anabelian geometry.

The aim is to encourage exchanges across these closely related areas and to promote new interactions within the growing community interested in homotopical and analytic methods in arithmetic geometry.

Organizers: E. Lepage (IMJ-PRG, FR), J. Poineau (Caen, FR)

※ This event is part of the special year ``Arithmetic, Homotopy, and Geometry 2027-28''.

This workshop aims to bring together experts in the field to share their recent results on cutting-edge topics. Key topics include homological stability for Hurwitz spaces and the stacky perspective on counting problems. The workshop will also cover motivic approaches to counting and the new challenges of generalizing classical results to the wild case. We encourage participants to discuss ways to unify these ideas for further development.

Keywords: Hurwitz spaces (Homological stability), Malle's conjecture (for function fields), Rational points of stacks, Brauer-Manin obstruction (for stacks), Wild Galois extensions of function fields and power series fields (counting results, moduli spaces), Motivic counting of Galois extensions.

This event is part of the special year "Arithmetic, Homotopy, and Geometry 2027-28".

A one-week conference broadly focused on the topics of the L-functions and modular forms database (LMFDB), mathematical databases, computation, and number theory.

The Faculty of Applied Mathematics at the AGH University of Krakow is organizing the second edition of the conference Dynamics, Equations and Applications (DEA). It will take place from 28 June to 2 July 2027, in Kraków, which is often regarded as one of the most exciting cities in Europe.

The conference will be organized in 16 parallel sessions covering four research fields: dynamical systems & ergodic theory, partial differential equations, number theory, and probability theory & stochastic processes, together with their interactions and applications, particularly in mathematical physics.

In addition to keynote and contributed talks within the parallel sessions, there will be 10 longer invited talks in each field given by the world's leading experts as well as plenary lectures delivered by Artur Avila, Alex Eskin, Ben Green, Martin Hairer, Adam Kanigowski, Jean-François Le Gall, Pierre-Louis Lions, Peter Sarnak, and Sylvia Serfaty.

More information (including scientific committee, main speakers and parallel sessions) about DEA 2027 can be found on its website http://www.dea.agh.edu.pl.

Aim

By bringing together the leading experts and promising young researchers and giving them the opportunity to present their latest results and their view on the field in general, we hope to provide a fertile basis for animated discussions. As a result, we hope to achieve a better understanding of the current state of the art and, more importantly, to identify and explore the most promising directions for future work.

Format

This is a workshop with about 40-45 participants. Participation is by invitation only. Every participant is expected to contribute actively to the success of the event, by giving talks and/or by taking part in the discussions. There will be two invited talks every morning (9:30-10:30 and 11:15-12:15); the afternoons will be available for shorter invited talks, discussions, informal talks and collaboration. Wednesday afternoon is free.

Spring 2028 semester program at the Institute for Computational and Experimental Research in Mathematics