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.
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.
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.
Minimal Surfaces and the Allen-Cahn Equation on 3-Manifolds
Explore minimal surfaces and the Allen–Cahn equation on 3-manifolds, focusing on recent results and the multiplicity-one theorem in three dimensions.
Analytic and Reidemeister Torsions of Digraphs and Path Complexes
Explore Reidemeister and analytic torsions on finite digraphs using path homology theory. Learn about Hodge Laplace operators, torsion identities, and formulas for Cartesian products and joins.
Symplectomorphism Invariants of Open Domains
Explore symplectomorphism invariants of open domains, focusing on zeta functions, Reeb dynamics, and equivariant symplectic homology to distinguish toric domains.
Hausdorff Dimension of Three-Dimensional Kakeya Sets
Explore groundbreaking research on Kakeya sets in R^3, uncovering a new lower bound for Hausdorff dimension and its implications in geometric measure theory.
Pseudo-Isotopy and Diffeomorphisms of 4-Manifolds
Explore recent advancements in pseudo-isotopy theory and its applications to studying diffeomorphisms of 4-manifolds with David Gabai.
The Ricci Flow - Lecture by Richard Hamilton
Explore the Ricci flow equation, its applications in geometry, and its role in understanding manifold curvature evolution. Gain insights into singularities and geometric analysis.
Rectifiable-Reifenberg and the Regularity of Stationary and Minimizing Harmonic Maps
Explore sharp rectifiability results for singular sets of minimizing harmonic maps, with uniform Minkowski bounds and integrability. Analyze quantitative stratification and dimension-reduction techniques.
Derived Approach to Highest Weight Categories
Explore highest weight categories in Representation Theory, examining their interpretation through exact categories, abelian envelops, and exceptional collections in derived categories.