Analytic Stacks - Lecture 14
Explore new foundations for analytic geometry, covering light condensed abelian groups, analytic rings, analytic stacks, and examples with Peter Scholze.
Analytic Stacks: New Foundations for Analytic Geometry - Lecture 7/24
Explore new foundations for analytic geometry, covering light condensed abelian groups, analytic rings, analytic stacks, and examples.
Birational Invariants from Gromov-Witten Theory - Lecture 2
Explore birational invariants derived from Gromov-Witten theory, focusing on Iritani's theorem and its applications to proving non-rationality of algebraic varieties.
Analytic Stacks - Lecture 6
Explore new foundations for analytic geometry, covering light condensed abelian groups, analytic rings, analytic stacks, and examples with renowned mathematician Peter Scholze.
Analytic Stacks - Lecture 5
Explore new foundations for analytic geometry, covering light condensed abelian groups, analytic rings, analytic stacks, and examples with renowned mathematician Peter Scholze.
Birational Invariants from Gromov-Witten Theory - Lecture 1
Explore birational invariants derived from Gromov-Witten theory, focusing on Iritani's theorem and its applications to proving non-rationality of geometric objects like cubic 4-folds.
Analytic Stacks - Lecture 3
Explore new foundations for analytic geometry, covering light condensed abelian groups, analytic rings, analytic stacks, and examples with Peter Scholze.
Analytic Stacks - Lecture 2
Explore new foundations for analytic geometry, covering light condensed abelian groups, analytic rings, analytic stacks, and examples with renowned mathematician Peter Scholze.
Analytic Stacks - Lecture 1/24
Explore new foundations for analytic geometry, covering light condensed abelian groups, analytic rings, analytic stacks, and examples.
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.
De Rham Cohomology in Characteristic p - Advanced Topics
Explore advanced topics in de Rham cohomology of algebraic varieties in characteristic p, including stacky approaches and Steenrod operations' implications on spectral sequences.
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.
On Geometric Construction of Artin Representation
Explore Serre's conjecture on integer-valued functions and Q_l-rational representations of finite groups acting on regular local rings.
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.
The Galois Group of the Category of Mixed Hodge-Tate Structures
Explore the Galois group of mixed Hodge-Tate structures, examining its Hopf algebra structure, derived category models, and applications to period theory in complex and p-adic settings.
Variants of Lojasiewicz's Gradient Inequality
Explore Lojasiewicz's gradient inequality, its extensions, and implications for gradient trajectories. Gain insights into a new variant for vector-valued maps and its geometric consequences.