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.
A Combinatorial Characterization of Geometric 3-Manifolds - Lecture
Explore geometric 3-manifolds through combinatorial characterization, focusing on Thurston geometries and their local combinatorial definitions. Learn about new algorithms for geometric decomposition.
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.
Geometrization and its Consequences in 3-Manifold Topology - Lecture 3
Explore Thurston's geometric perspective on 3-manifolds, Perelman's Geometrization Theorem, and their impact on topology, algorithms, and group theory in 3D geometry.
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.
An Approach to Simon's Conjecture
Explore fundamental group epimorphisms between 3-manifolds and their implications for knot genera. Investigate conjectures related to Simon's conjecture in knot theory.
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.
The Dry Ten Martini Problem for Sturmian Schrodinger Operators
Explore the Dry Ten Martini Problem for Sturmian Schrodinger operators, examining spectral gaps and integrated density of states. Delve into recent solutions and advancements in this mathematical challenge.
Exponentially Many Graphs Are Determined by Their Spectrum
Explore discrete analogues of Kac's question on "hearing the shape of a drum" and learn about graphs determined by their spectrum in this mathematical seminar.
Why p-adic Numbers Are Better Than Real for Representation Theory
Explore p-adic numbers and their application in representation theory, focusing on SL(2) group and nilpotent orbits in Lie algebra.
Dirac Eigenvalue Optimization and Harmonic Maps
Explore Dirac eigenvalue optimization, comparing it to Laplace eigenvalues and examining critical metrics' correspondence with harmonic maps to complex projective spaces.
Learning Causal Models via Algebraic Constraints
Explorez les modèles causaux linéaires et leurs graphes dirigés. Découvrez des méthodes algébriques pour identifier les relations causales à partir de données observationnelles, même avec des cycles ou variables cachées.
Combinatorial Testing Problems - Lecture 1
Explore combinatorial testing problems, including hidden clique and high-dimensional random geometric graphs, with insights on statistical challenges and estimation techniques.
Mean Estimation: Median of Means Tournaments - Lecture 2
Explore mean estimation techniques using median of means tournaments in this advanced statistical lecture by Gabor Lugosi from Pompeu Fabra University.