Profinite Properties of Finite-Volume Hyperbolic 3-Manifold Groups
Explore profinite rigidity of finite-volume hyperbolic 3-manifold groups, examining volume, invariant trace fields, and arithmeticity as profinite invariants in geometric topology.
3-Manifold Groups and Fundamental Group Conjectures - Part II
Explorez les conditions conjecturales impliquant qu'un groupe est le groupe fondamental d'une 3-variété compacte, en examinant les conjectures de Cannon et Wall et leurs interconnexions.
Notions of Nonpositive Curvature and Groups - Lecture 2
Explorez les théories de petite simplification et leurs liens avec les complexes systoliques et quadriques. Découvrez comment ces espaces combinatoires à courbure non positive s'appliquent à l'étude des groupes.
Virtually Free-by-Cyclic Groups
Explore recognition methods for virtually free-by-cyclic groups within hyperbolic compact special groups using homology techniques.
Subgroup Separability of 3-Manifold Groups and Its Applications
Explore subgroup separability in 3-manifold groups, its characterization via torus decomposition, and applications to subgroup distortion and Grothendieck rigidity. Joint work with Hoang Thanh Nguye.
Division, Group Rings, and Negative Curvature in Low-Dimensional Topology
Explore low-dimensional topology through group rings and division algorithms, focusing on 2-complexes and hyperbolic manifolds. Gain insights into fundamental group structures and cell-decomposition complexity.
CAT(0) Cube Complexes - Lecture 2
Explore advanced concepts of CAT(0) cube complexes, building on fundamental principles to deepen understanding of geometric and combinatorial properties.
Profinite Rigidity, Triangle Groups, and Seifert Fibred Spaces
Explore profinite rigidity in 3-manifold groups, examining unique determination by finite images and distinctions between finitely presented and generated groups.
CAT(0) Cube Complexes - Lecture 1
Explore CAT(0) cube complexes in this introductory minicourse, delving into fundamental concepts and applications in geometric group theory.
3-Manifold Groups and Fundamental Group Conjectures - Lecture 3
Explorez les conditions conjecturales impliquant qu'un groupe est le groupe fondamental d'une 3-variété compacte, en examinant les conjectures de Cannon et Wall ainsi que leurs interconnexions.
Arithmeticity and FC-Subspaces of Hyperbolic Manifolds
Explore connections between geometry and arithmeticity of hyperbolic orbifolds using fc-subspaces. Learn about new arithmeticity criteria and applications to reflection groups and hyperbolic link complements.
Homological Aspects of Branching Laws in p-adic Groups
Explore homological aspects of branching laws for p-adic group representations, focusing on restriction to subgroups and projective representations in Bernstein blocks.
Growth in Tensor Powers
Explore tensor power decomposition in group representations, focusing on asymptotic behavior and non-negligible summands using symmetric tensor category theory.
Asymptotic Orthogonality Relation for GL(n,R) - ICBS 2024
Explore generalized Dirichlet character orthogonality for GL(n,R), extending classical number theory to higher dimensions with applications.
The Combinatorics of Finite Simple Groups - ICBS 2024
Explore the interplay between finite simple groups, combinatorics, and group theory, examining recent developments and introducing algebraic tools for geometric structures.
Countable Amenable Groups, Tilings, Multiorders and Orbit Equivalence of Measure-Theoretic Actions with Z-Actions
Explore countable amenable groups, tilings, multiorders, and orbit equivalence in measure-theoretic actions, comparing them with Z-actions.
A Beautiful World Beyond Hyperbolic Geometry - Anosov Representations and Higher Teichmüller Spaces
Explore advanced geometric concepts beyond hyperbolic geometry, delving into Anosov representations and higher Teichmüller spaces.
Spectral Multipliers and Wave Equation for Sub-Laplacians - Part 4
Explore advanced concepts in spectral analysis and wave equations for sub-Laplacians, focusing on multipliers and their applications in mathematical physics.
Spectral Multipliers and Wave Equation for Sub-Laplacians - Part 2
Explore advanced concepts in spectral multipliers and wave equations for sub-Laplacians, building on previous knowledge and delving into complex mathematical theories.
Thurston's Asymmetric Metric on Teichmüller Space Revisited
Explore Thurston's asymmetric metric on Teichmüller space and its generalizations to higher-rank Lie groups, examining geometric and dynamical invariants of hyperbolic structures.
Subgroup Tests and the Aldous-Lyons Conjecture
Explore the refutation of the Aldous-Lyons conjecture through novel interactive proof systems and subgroup tests, connecting complexity theory to probability theory and group theory.