Low Dimensional Topology and Circle-valued Morse Functions
Explore representations in Homeo_+(S^1) and their role in verifying left-orderability of 3-manifold groups, with applications to the L-space conjecture and taut foliations in various topological settings.
Low Dimensional Topology and Circle-valued Morse Functions
Explore taut foliations in 3-manifolds with Heegaard genus two, examining the connection between left-orderable fundamental groups and co-orientable taut foliations in closed, orientable, irreducible 3-manifolds.
Low Dimensional Topology and Circle-valued Morse Functions
Explore the Margulis constant in hyperbolic geometry, its significance, and ongoing research to determine its precise value through computational methods and theoretical analysis.
Low Dimensional Topology and Circle-Valued Morse Functions
Exploración de límites en el número de asas de variedades suturadas, utilizando argumentos geométricos y desarrollando una función de número de asas en homología de segundo grado.
Low Dimensional Topology and Circle-valued Morse Functions
Explore applications of guts in 3-manifolds, including minimal volumes of hyperbolic manifolds and Euler characteristic control in Dehn fillings. Gain insights into advanced topological concepts and their implications.
Low Dimensional Topology and Circle-Valued Morse Functions
Explore knot complements, Seifert surfaces, and sutured manifolds in low-dimensional topology. Discover unique decompositions and their implications for the Kakimizu complex and Thurston norm.
Low Dimensional Topology and Circle-valued Morse Functions
Explore forbidden minor multibranched surfaces and critical complexes in 3-sphere embeddings. Analyze K5 × S1 and K3,3 × S1 families, critical complexes, and their properties in low-dimensional topology.
Low Dimensional Topology and Circle-valued Morse Functions
Explores non almost-fibered knots in 3-sphere, analyzing circular thin positions and Seifert surfaces. Focuses on hyperbolic genus one knots with multiple disjoint Seifert surfaces, demonstrating their complex circular thin positions.
Low Dimensional Topology and Circle-valued Morse Functions
Explore instanton Floer homology's surgery formula, its applications in computing 3-manifold invariants, and connections to SU(2)-representations of fundamental groups.
Low Dimensional Topology and Circle-valued Morse Functions
Explore singular fibrations in knot exteriors and their extensions over handlebodies, connecting handle-ribbon knots to circular Morse functions in low-dimensional topology.
Symmetry Defects - Affine Invariants of Curves and Surfaces
Explore symmetry defects and affine invariants in curves and surfaces with Director Stanislaw Janeczko's insightful presentation from the WIMSA Inaugural Conference.
The Geometry of Creativity - Five Creative Principles
Kurt Wenner explores five creative principles linking math, art, and nature, offering innovative problem-solving tools and insights into the fundamental connection between geometry and creativity.
The Mathematician Who Cracked Wall Street
Explore how mathematician Jim Simons applied complex math to finance, revolutionizing Wall Street and using his success to support math education and scientific research.
The Kakeya Needle Problem for Rectifiable Sets
Explore the Kakeya needle problem for rectifiable sets, covering basic theorems, discrete sets, differential structures, and dimensions, with insights from mathematician Marianna Csőrnyei.
Euclidean Lines on Hyperbolic Manifolds
Explore Euclidean lines on hyperbolic manifolds, from basic models to complex surfaces, with insights on rigidity theorems and dynamical systems in this advanced mathematics lecture.
Mixing Surfaces, Algebra, and Geometry
Explore the interplay of surfaces, algebra, and geometry through Mirzakhani's theorem, taffy pullers, and mapping class groups in this engaging mathematical journey.
Groups with Bounded Geometry
Explore geometric groups, their properties, and connections to topology and transformation groups in this advanced mathematics lecture on groups with bounded geometry.
Khovanov Homology and Surfaces in Four-Manifolds
Explore Khovanov homology, exotic smooth structures, and surfaces in four-manifolds. Discover applications in gauge theory and new approaches to longstanding mathematical problems.
Smooth Invariants of Four-dimensional Manifolds and Quantum Field Theory
Explore the intersection of smooth 4D manifold invariants and quantum field theory, focusing on Yang-Mills theory, instantons, and topological invariants in this advanced mathematics lecture.
Packing Points in Projective Spaces
Explore optimal point arrangements in projective spaces, surveying current research and open problems in this fundamental area of metric geometry with applications in digital communication.
Metric Representations - Algorithms and Geometry
Explore metric representations, algorithms, and geometry in this lecture covering multidimensional scaling, metric repair, optimization techniques, and dimensionality reduction.