Cluster Duality and Non-Holomorphic Spectral Curves
Explore cluster duality, geometric interpretations of tropical points, and their connections to local systems on curves through graphs, Lagrangian coverings, and affine group-valued local systems.
Kontsevich's Star-Product up to Order Seven for Affine Poisson Brackets
Explore Kontsevich's star-product formula for affine Poisson brackets, examining its expansion up to seventh order and investigating the mechanism of associativity in higher orders.
Reddening Sequences for Cluster Algebras
Explore reddening sequences in cluster algebras, their implications, and known cases, delving into finite dimensionality, invariants, and canonical bases.
Introduction to Resurgence via Wall-crossing Structures - Lecture 2
Explore an alternative approach to Borel-Écalle resummation using analytic wall-crossing structures. Delve into holomorphic bundles, gauge transformations, and geometric interpretations with practical examples.
Introduction to Resurgence via Wall-crossing Structures - Lecture 1
Explore an alternative approach to Borel-Écalle resummation using analytic wall-crossing structures. Delve into holomorphic bundles, gauge transformations, and geometric interpretations with practical examples.
Number Theory over Function Fields - Lecture 6
Explore recent progress in number theory using polynomial analogues over finite fields, connecting to topology, probability, and geometric Langlands theory.
Number Theory over Function Fields - Lecture 5
Explore recent progress in number theory using polynomial analogues over finite fields, connecting to topology, probability, and geometric Langlands theory.
Number Theory over Function Fields - Lecture 4
Explore recent progress in number theory using polynomial analogues over finite fields, connecting geometric perspectives to topology, probability, and automorphic forms.
Number Theory over Function Fields - Lecture 3
Explore recent progress in number theory using polynomial analogues over finite fields, connecting to topology, probability, and geometric Langlands theory.
Number Theory over Function Fields - Lecture 2
Explore recent progress in number theory using polynomial analogues over finite fields, connecting to topology, probability, and geometric Langlands theory.
Number Theory over Function Fields - Lecture 1
Explore recent progress in number theory using polynomial analogues over finite fields, connecting to topology, probability, and geometric Langlands theory.
Twisted K-theory in Motivic Homotopy Theory
Explore algebraic K-theory of vector bundles twisted by Brauer class, its role in motivic homotopy theory, and a new approach to the motivic spectral sequence for twisted K-theory.
Prismatic Cohomology Relative Delta-Rings
Explore prismatic cohomology's evolution, comparing absolute and relative variants, and delve into a new generalization bridging the two approaches.
Motivic Cohomology of Schemes - Lecture 3
Explore advanced motivic cohomology theory for equicharacteristic schemes, covering cdh topology, K-theory filtration, and applications to algebraic geometry and zero cycles.
Prismatic Cohomology of Commutative Ring Spectra
Explore motivic filtrations on trace invariants of commutative ring spectra and their extension to prismatic cohomology, as presented by Arpon Raksit from MIT.
Introduction to Prismatic Cohomology - Lecture 4
Explore prismatic cohomology, focusing on prismatization and the prismatic logarithm in advanced algebraic geometry and number theory.
Introduction to Prismatic Cohomology - Lecture 3
Explore prismatic cohomology, covering general results, prismatization, and the prismatic logarithm in this advanced mathematics lecture by Johannes Anschütz.
Introduction to Prismatic Cohomology - Lecture 2
Explore prismatic cohomology, focusing on general results and derived concepts. Delve into prismatization as a tool for understanding this advanced mathematical theory.
A Homotopical Approach to Crystalline Cohomology
Explore a homotopical approach to crystalline cohomology, focusing on higher homotopies for canonical lifts and easier global definition through gluing.
Introduction to Prismatic Cohomology - Lecture 1
Explore prismatic cohomology's foundations, including its applications in characteristic 0 and p, general results, prismatization, and the prismatic logarithm.
Ghost Polygons, Poisson Bracket and Convexity in Anosov Representations
Explore Anosov representations, length functions, and Poisson brackets in moduli spaces. Discover combinatorial techniques and their applications to convexity in character varieties.