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.
Characteristic Classes of Étale Local Systems
Explore characteristic classes of étale Z_p-local systems on algebraic varieties, their relation to Chern-Simons classes, and connections to Hodge filtration in p-adic settings.
Characteristic Cycle and Pushforward for L-adic Sheaves
Explore characteristic cycles for l-adic sheaves, their role in measuring ramification, and the compatibility of pushforward along proper morphism in this advanced mathematical lecture.
Positive Mass Theorem for Asymptotically Flat Manifolds with Isolated Conical Singularities
Explore recent advancements in positive mass theorem for asymptotically flat manifolds with isolated conical singularities, covering spin and non-spin settings, analysis techniques, and Geroch-type results.
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.
Finite Type Properties of Tame Fundamental Groups
Explore finite generation and presentation of fundamental groups in topology, including étale and tame cases, for various algebraic and analytic spaces.
A Stable Version of Gromov's Angle-Shrinking Problem and Its Index Theoretic Applications - Part 1
Explore Gromov's angle shrinking problem and its role in proving the dihedral extremality/rigidity conjecture through a new index theorem for manifolds with polyhedral boundary.
A Stable Version of Gromov's Angle-Shrinking Problem and Its Index Theoretic Applications - Lecture 2
Explore a stable algebraic version of Gromov's angle shrinking problem and its application to dihedral rigidity conjecture, focusing on Fredholm index computation.
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.
Analytic Stacks: New Foundations for Analytic Geometry
Explore new foundations for analytic geometry, covering light condensed abelian groups, analytic rings, analytic stacks, and examples.
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.
Motives and Ring Stacks
Explore advanced cohomology theories through ring stacks, examining their connection to 6-functor formalism and motivic theory. Gain insights into Tannaka duality and analytic geometry applications.
Analytic Stacks: New Foundations for Analytic Geometry - Lecture 22/24
Explore new foundations for analytic geometry, covering light condensed abelian groups, analytic rings, analytic stacks, and examples.
Analytic Stacks - Lecture 21
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
Explore new foundations for analytic geometry, covering light condensed abelian groups, analytic rings, analytic stacks, and examples.
Analytic Stacks - Lecture 19
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 18
Explore new foundations for analytic geometry, covering light condensed abelian groups, analytic rings, analytic stacks, and examples.
Analytic Stacks: New Foundations for Analytic Geometry - Lecture 17
Explore new foundations for analytic geometry, covering light condensed abelian groups, analytic rings, analytic stacks, and examples.
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.