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.
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.
Orbit Counting Theorem for Cusped Hitchin Representations
Explore cusped Hitchin representations through orbit counting theorems, Bowen-Series coding, and Quint's Iwasawa cocycle. Gain insights into dynamics and potential applications.
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.
Thurston's Asymmetric Metrics for Anosov Representations
Explore Thurston's asymmetric metric and its generalization to Anosov representations, applying thermodynamical formalism to construct pressure metrics on representation spaces.
Dynamics Associated to Anosov Representations: Some Geometric Consequences - Lecture 2
Explore dynamical systems of Anosov representations, including Patterson-Sullivan theory, critical hypersurface, and directional-conicality. Examine dominated sequences and their impact on limit set regularity.
Dynamics Associated to Anosov Representations: Some Geometric Consequences - Lecture 1
Explore dynamical systems of Anosov representations, including Patterson-Sullivan theory, critical hypersurface, and directional-conicality. Examine dominated sequences and their impact on limit set regularity.
Anosov Representations - Lecture 3
Explore Anosov representations, their characterizations, domains of discontinuity, and connections to convex projective geometry. Discover recent developments and potential research directions.
Geometric Structures Associated to Anosov Representations
Explore geometric structures linked to Anosov representations, focusing on domains of discontinuity and their quotients as smooth fiber bundles over closed hyperbolic manifolds.
Anosov Representations - Lecture 2
Explore Anosov representations, their characterizations, domains of discontinuity, and connections to convex projective geometry in this advanced mathematical lecture.
Divisible Convex Sets with Properly Embedded Cones
Explore divisible convex sets, their theory, and new examples in projective geometry. Delve into connections with dynamical systems, geometric group theory, and Riemannian geometry.
Equidistribution of Periodic Tori
Explore equidistribution of periodic tori in higher rank Lie groups, extending Bowen and Margulis' work on closed geodesics in hyperbolic surfaces.
Introduction to Anosov Representations - Lecture 1
Explore Anosov representations, their characterizations, and applications in convex projective geometry. Gain insights into recent developments and potential research directions.
Regularising Manifolds Using Ricci Flow
Explore Ricci flow's applications in deforming and regularizing manifolds, including its use in identifying topology and proving geometric theorems.
Smoothing by Ricci-DeTurck Flow and Applications to Scalar Curvature
Explore Ricci-DeTurck flow's existence theory for non-smooth initial metrics and its applications to scalar curvature rigidity problems in geometry.
DT Invariants and Holomorphic Curves in Complex Integrable Systems
Explore the correspondence between Donaldson-Thomas invariants and holomorphic curves, focusing on mirror symmetry and applications in enumerative geometry.
Heegaard Branes and Exact Results for Non-perturbative Complex Chern-Simons Theory
Explore Heegaard branes in moduli spaces of Higgs bundles and their applications in mathematics, from geometric Langlands to low-dimensional topology and complex Chern-Simons theory.
On Resurgent Poisson Structures and Deformations
Explore Z-resurgent series algebra, alien derivations, and their applications in constructing Poisson structures and non-commutative deformations of algebraic products.
Holomorphic Floer Theory and Resurgence - Lecture 3
Explore holomorphic Floer theory and its connection to resurgence, examining the Riemann-Hilbert correspondence and its implications for perturbative expansions in mathematics and physics.
A Conjectural Reciprocity Law for Realizations of Motives
Explore a conjectural reciprocity law connecting realizations of motives, drawing parallels to classical number theory and expanding on Hodge theory's comparison isomorphisms.
Breaking a Large Square into Smaller Parts - Optimal Methods
Explore optimal methods for dividing large squares into smaller parts, enhancing problem-solving skills and geometric understanding.