Analytic Stacks: New Foundations for Analytic Geometry - Lecture 15
Explore new foundations for analytic geometry, covering light condensed abelian groups, analytic rings, analytic stacks, and examples.
Analytic Stacks - Lecture 14
Explore new foundations for analytic geometry, covering light condensed abelian groups, analytic rings, analytic stacks, and examples with Peter Scholze.
Ricci Curvature, Fundamental Group and the Milnor Conjecture - Part 2
Explore advanced concepts in topology and geometry, focusing on counterexamples to the Milnor conjecture and their construction using mapping class groups and asymptotic cones.
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.
Index Theory and Applications to Scalar Curvature
Explore index theorems for compact manifolds with boundary and their applications to scalar curvature geometry, focusing on Dirac operators and boundary value problems.
Gromov's Rigidity Theorem for Polytopes with Acute Angles
Explore recent developments in dihedral rigidity, focusing on Gromov's conjecture and Brendle-Wang's alternative smoothing construction for polytopes with acute angles.
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.
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.