Birational Invariants from Gromov-Witten Theory - Lecture 3
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 - Foundations for Analytic Geometry
Explore new foundations for analytic geometry, covering light condensed abelian groups, analytic rings, analytic stacks, and examples with Peter Scholze.
Counting Partitions by Genus
Explore set partition counting by genus, focusing on primitive partitions and functional equations to reconstruct all partitions, with emphasis on genus 0-2 cases.
Three Problems in the Mathematics of Deep Learning
Explore mathematical concepts behind aligning neural networks with classical programs, including polynomial functors, cohomology, and higher categories.
Integrality of the Betti Moduli Space
Explore the integrality of Betti moduli spaces for smooth projective varieties, examining representations of fundamental groups and their implications for algebraic geometry.
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.
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.