Analytic Stacks - Lecture 16
Explore new foundations for analytic geometry, covering light condensed abelian groups, analytic rings, analytic stacks, and examples with Peter Scholze.
Nonnegative Ricci Curvature, Nilpotency, and Hausdorff Dimension
Explore nonnegative Ricci curvature, nilpotency, and Hausdorff dimension in relation to universal covers, minimal representing loops, and asymptotic cones of manifolds.
Stability of Llarull's Theorem in All Dimensions
Explore stability of Llarull's theorem in all dimensions using spin geometry, with results in intrinsic flat and C^0-convergence outside small sets.
Spaces with Ricci Curvature Lower Bounds
Explore recent findings on spaces with nonnegative Ricci curvature, including singular set dimensions, fractal-like Weyl's laws, and nonproper Busemann functions in manifolds.
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.
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.
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.
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.
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.
Positive Mass Theorem and Positive Scalar Curvature with Singularities
Explore recent developments in positive mass theorem and scalar curvature, focusing on singular metrics and isolated conical singularities in mathematical physics.
Different Notions of Tameness Revisited in Étale Morphisms
Explore different approaches to defining tameness in étale morphisms of schemes, focusing on valuation-theoretic methods and nonarchimedean geometry to overcome limitations of compactification-based approaches.