Weight Filtration on Log Crystalline Site
Explore advanced mathematical concepts in log crystalline site and weight filtration, focusing on p-adic Steenbrink complex construction for simple normal crossing log varieties.
Local Systems and Higgs Bundles in p-adic Geometry
Explore the algebraic nature of local systems and Higgs bundles in p-adic geometry, drawing parallels to complex varieties and characteristic p counterparts.
Motives and Super-Representation Theory: Principles and Case Studies
Découvrez les principes et études de cas des motifs et de la (super-)théorie des représentations, explorant la théorie de Galois motivique abstraite.
The Non-Abelian p-Curvature Conjecture
Explore a generalized p-curvature conjecture for non-linear ODEs, its implications for algebraic geometry, and proof techniques inspired by Katz and Esnault-Groechenig's work.
Secondary Invariants and Arithmetic Rigidity
Explore secondary Chern classes in complex local systems, their definitions, and arithmetic analogs. Delve into rigidity phenomena and motivic speculations in algebraic geometry.
Point-Counting and the Zilber-Pink Conjecture - Lecture 2
Explore the Zilber-Pink conjecture, its relation to classical conjectures, and point-counting strategies for proving cases, focusing on curves in modular curve powers.
Point-Counting and the Zilber-Pink Conjecture - Lecture 1
Explore the Zilber-Pink conjecture, its relation to classical conjectures, and point-counting strategies for proving cases, focusing on curves in modular curve powers.
Analytic Stacks: New Foundations for Analytic Geometry - Lecture 24
Explore new foundations for analytic geometry, covering light condensed abelian groups, analytic rings, analytic stacks, and examples with Peter Scholze.
Generic Regularity in Obstacle Problems
Explore the classical obstacle problem, its free boundary, and recent developments in regularity theory with insights from renowned mathematician Alessio Figalli.
Modularity of Abelian Surfaces
Explorez la preuve de la modularité d'une proportion positive de surfaces abéliennes sur les rationnels dans cette conférence mathématique avancée.
Stable Homotopy Groups, Higher Algebra, and the Telescope Conjecture
Explore stable homotopy groups, spectra, and their applications in topology and geometry. Gain insights into fundamental concepts shaping modern algebraic topology and related fields.
Period Relations for Arithmetic Automorphic Periods on Unitary Groups
Explore period relations for arithmetic automorphic periods on unitary groups, focusing on Petersson inner products and connections to L-function special values.
Shimurian Generalizations of Truncated Barsotti-Tate Groups - After V. Drinfeld
Explore Drinfeld's Shimurian analogs of truncated Barsotti-Tate groups, prismatic F-gauges, and their algebraicity in this advanced mathematical lecture.
On the Cohomology of Shimura Varieties with Torsion Coefficients
Explore recent advances in Shimura varieties' cohomology with torsion coefficients, including Hodge-Tate period morphism geometry and local-global compatibility insights.
Conjectures on L-functions for Varieties over Function Fields and Their Relations
Explore conjectures on L-functions for varieties over function fields, focusing on abelian varieties and the BSD-rank conjecture. Examine relationships using rigid cohomology.
Sato-Tate Conjecture for Bianchi Modular Forms
Explore potential automorphy results for Ramanujan and Sato-Tate conjectures in GL(2) over imaginary quadratic fields, extending previous work and introducing new mathematical concepts.
Eigenvarieties and Completed Cohomology in p-adic Automorphic Forms
Explore connections between eigenvarieties and p-adic cohomology representation theory, focusing on p-adic families of finite slope automorphic eigenforms.
Kummer Extensions: Applications to Generalized Cross-Ratios and Functions on Hilbert Schemes
Explore Kummer extensions in geometry and arithmetic, including generalized cross-ratios and functions on Hilbert schemes. Gain insights into advanced algebraic geometry concepts.
Plectic Cohomology of Mixed Shimura Varieties and Stacks
Explore joint work on plectic cohomology of mixed Shimura varieties and stacks with Tony Scholl from the University of Cambridge.
Uniform Bounds for Chow Groups in Codimension Two Cycles
Explorez les limites uniformes pour les sous-groupes de torsion dans le groupe de Chow des cycles de codimension deux pour les familles de variétés sur les corps de nombres.
Finiteness Questions for Étale Coverings with Bounded Wild Ramification
Explorez les coverings étales des variétés en caractéristique positive, leurs ramifications et les problèmes ouverts associés dans cette présentation mathématique avancée.