Anosov Representations - Lecture 2
Explore Anosov representations, their characterizations, domains of discontinuity, and connections to convex projective geometry in this advanced mathematical lecture.
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.
Homology Cobordism and the Geometry of Hyperbolic Three-Manifolds
Explore the interaction between hyperbolic geometry and homology cobordism in low-dimensional topology using monopole Floer homology to study subgroups of the homology cobordism group.
Positivity, Representations, and Non-Commutative Hyperbolic Geometry
Explore total positivity in matrices, its generalization to split real Lie groups, and a new notion of positivity in flag varieties with applications to higher Teichmüller spaces.
A Finiteness Theorem for Gromov-Hyperbolic Groups
Explore a finiteness theorem for Gromov-hyperbolic groups, delving into δ-hyperbolic, torsion-free, non-cyclic marked groups with bounded entropy. Gain insights into the proof and key concepts.
From the Kauffman and Dubrovnik Polynomials to Cubic Skein Modules and Beyond
Explore the rich world of skein theory, from linear and quadratic modules to the untapped potential of cubic skein modules and their connections to various mathematical disciplines.
Twisted Ruelle Zeta Function on Locally Symmetric Spaces - Fried's Conjecture and Applications
Explore Twisted Ruelle zeta functions, Fried's conjecture, and applications in locally symmetric spaces. Gain insights into spectral geometry and refined analytic torsion.
Efficiently Chopping a Hyperbolic Surface in Two - Cheeger Constants and Spectral Geometry
Explore the Cheeger constant of hyperbolic surfaces, its relation to spectral gaps, and recent findings on its upper bound for large genus surfaces. Gain insights into cutting Riemannian manifolds efficiently.
Cluster Algebras and Hyperbolic Geometry
Explore the application of cluster algebra to 2D and 3D hyperbolic geometry, examining ideal triangulations, Teichmuller spaces, and knot volumes through mutations and cluster variables.
Finite Quotients of Fibered, Cusped 3-Manifold Groups
Explore finite quotients of 3-manifold groups, leveraging mapping class group properties to study profinite completions of fibered hyperbolic 3-manifold fundamental groups.
Geometrization and its Consequences in 3-Manifold Topology - Part I
Explore Thurston's geometric perspective on 3-manifolds, including Perelman's Geometrization Theorem, and its implications for topology, algorithms, and group theory in 3-dimensional spaces.
Geometrization and Its Consequences in 3-Manifold Topology - Part II
Explore Thurston's geometric perspective on 3-manifolds, Perelman's Geometrization Theorem, and their impact on topology. Discover algorithmic and group-theoretic applications in 3-manifold theory.
Geometric Approaches to Artin Groups
Explore geometric approaches to Artin groups, focusing on constructing group actions on spaces with CAT(0), hyperbolic, or systolic geometries. Gain insights into recent progress and parabolic subgroups.
The Markov Ordering of the Rationals
Explore hyperbolic geometry's role in characterizing monotonicity of rational number ordering on a modular torus, connecting to Diophantine approximation and number theory.
Banded Projections to Z-factor Graph - Lecture
Explore baneled projections to Z-factor graphs in subgroup geometry, delving into advanced mathematical concepts and their applications.
The Electrification of X Relative to Y is S^3 HYP
Explorez les concepts mathématiques avancés de l'électrification de X par rapport à Y et son lien avec S^3 HYP dans cette présentation approfondie.
Polyhedra with Vertices on a Quadric
Explore combinatorial types of polyhedra with vertices on quadrics, from Steiner's 1832 question to recent findings using ideal polyhedra in various geometries.
Dynamical Degrees - #ICBS2024
Explore dynamical degrees, comparing them to other dynamics concepts and delving into key findings using ideas from dynamics, Hodge theory, and geometries.
Ascending Chains of Free Groups in 3-Manifold Groups
Explore ascending chains of free groups in 3-manifold groups, examining proofs and techniques involving hyperbolic geometry, geometrization, and JSJ decompositions.
Dense Embeddings of Hyperbolic Manifold Groups
Explore dense embeddings of hyperbolic manifold groups, focusing on amalgamated products and linear Lie groups. Learn strategies to control properties of output embeddings.
Geometrization and its Consequences in 3-Manifold Topology - Lecture 4
Explore hyperbolic geometry's role in 3-manifold topology, including Thurston's viewpoint and Perelman's theorem. Discover algorithmic and group-theoretic applications in computational experiments.