Homogeneous Dynamics and u-Gibbs States
Explore orbit closure and measure classification in homogeneous dynamics, with insights on extending results to non-homogeneous settings using robust approaches.
Discrete Subgroups with Finite Bowen-Margulis-Sullivan Measure in Higher Rank - Part 1
Explore discrete subgroups with finite Bowen-Margulis-Sullivan measure in higher rank semisimple real algebraic groups, including classification and applications to L^2 spectrum.
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.
The Bottom of the L^2 Spectrum of Higher-rank Locally Symmetric Spaces
Explore the $L^2$ spectrum of higher-rank locally symmetric spaces, examining connections between Laplace eigenfunctions and Patterson-Sullivan measures.
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.
Local Mixing of Diagonal Flows on Anosov Homogeneous Spaces
Explore local mixing of diagonal flows on Anosov homogeneous spaces, generalizing Winter's result and discussing applications in equidistribution and matrix coefficients.
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.
q-series, Resurgence and Modularity
Explore q-series, resurgence, and modularity in quantum modular forms, focusing on Ramanujan's σ(q) series and its connections to other mathematical structures.
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.
Introduction to Resurgence via Wall-crossing Structures - Lecture 4
Explore alternative approach to Borel-Écalle resummation using analytic wall-crossing structures. Delve into holomorphic bundles, gauge transformations, and geometric interpretations with practical examples.
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.
Introduction to Resurgence via Wall-crossing Structures - Lecture 3
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.
A Higher Dimensional Generalization of the Birkhoff Attractor
Explore higher-dimensional generalizations of the Birkhoff attractor using spectral metrics for conformal symplectic maps and damped Hamiltonian systems.