Attend a comprehensive international conference in arithmetic algebraic geometry held in memory of mathematician Jan Nekovář, featuring 20 expert presentations on cutting-edge research topics. Explore crystallinity properties and rigid flat connections, Iwasawa theory applications, BSD conjectures and class group estimates, geometric constructions of Artin representations, and plectic cohomology developments. Delve into uniform bounds for Chow groups, Galois groups of mixed Hodge-Tate structures, Kummer extensions with cross-ratio applications, eigenvarieties and completed cohomology theory, and Sato-Tate distributions for Bianchi modular forms. Examine Kolyvagin's conjecture connections to Iwasawa theory, L-function conjectures for varieties over function fields, de Rham cohomology in characteristic p, and cohomology of Shimura varieties with torsion coefficients. Discover hidden symmetries in Nekovář's mathematical contributions, Shimurian generalizations of truncated Barsotti-Tate groups, period relations for arithmetic automorphic periods on unitary groups, square root constructions from GSp_4 and GL(2) x GL(2), mock plectic points, and arithmetic applications of power series to irrationality problems. Gain insights from leading researchers including Hélène Esnault, David Loeffler, Jacob Tsimerman, Ana Caraiani, and other distinguished mathematicians presenting their latest findings in areas that were central to Jan Nekovář's mathematical interests and contributions to the field.

Syllabus

Hélène Esnault - Crystallinity properties and rigid flat connections revisited
David Loeffler - Iwasawa theory for Asai representations and the adjoint of a modular form
Jacob Tsimerman - BSD and Estimates for Class Groups of Number Fields
Tomoyuki Abe - On Geometric Construction of Artin Representation
Tony Scholl - Plectic cohomology
Alena Pirutka - Uniform bounds for Chow groups
Alexander Goncharov - The Galois Group of the Category of Mixed Hodge-Tate Structures
Spencer Bloch - Kummer Extensions, with Applications to Generalized Cross-Ratios, Functions on (...)
Matthew Emerton - Eigenvarieties and completed cohomology
James Newton - Sato-Tate for Bianchi modular forms
Giada Grossi - Kolyvagin’s conjecture and Iwasawa theory
Veronika Ertl - Conjectures on L-functions for varieties over function fields and their relations
Alexander Petrov - On de Rham Cohomology in Characteristic p
Ana Caraiani - On the cohomology of Shimura varieties with torsion coefficients
Olivier Fouquet - Hidden Symmetries of the Work of Jan Nekovář
Akhil Mathew - Shimurian generalizations of truncated Barsotti-Tate groups (after V. Drinfeld)
Jie Lin - Period Relations for Arithmetic Automorphic Periods on Unitary Groups
Vesselin Dimitrov - Square roots from GSp_4 or GL(2) x GL(2)
Michele Fornea - Mock Plectic Points
Yunqing Tang - The arithmetic of power series and applications to irrationality