Geometry and Topology of Surfaces - Lecture 1
Introductory lecture on geometry and topology of surfaces, covering polyhedrons, Euler numbers, and the Gauss-Bonnet theorem. Includes exercises and Q&A for university lecturers.
Variations on the Wire Problem - Optimization in Geometry for Math Teachers
Explore optimization through hands-on activities, addressing Common Core Standards. Learn to cut and bend wire into polygons for minimum or maximum enclosed area, enhancing high school math instruction.
Optimization and Modeling in AP Calculus
Learn techniques for solving optimization and modeling problems in calculus, including practical applications and step-by-step solutions for various real-world scenarios.
Related Rate Problems in AP Calculus
Learn strategies for solving related rate problems, including soap bubbles, cylindrical tanks, right triangles, conical tanks, and street light scenarios using similar triangles.
Formal Mathematics for Mathematicians and Mathematics Students - IPAM at UCLA
Explore formal mathematics' potential to revolutionize mathematical exposition, focusing on benefits beyond proof verification and its impact on mathematicians and students.
Floer Cohomology and Birational Geometry
Explore Floer cohomology applications in birational geometry, including McKay correspondence and quantum cohomology of Calabi-Yau manifolds.
Self-Similar Sets and Measures on the Line
Explore fractal geometry through self-similar sets and measures, focusing on recent developments in determining their dimensions. Gain insights into classical fractals and cutting-edge research.
The Positive Grassmannian, the Amplituhedron, and Cluster Algebras
Explore the positive Grassmannian and amplituhedron, delving into their combinatorial structures and connections to physics, integrable systems, and scattering amplitudes using oriented matroids, tropical geometry, and cluster algebras.
Canonical Kaehler Metrics and Stability of Algebraic Varieties
Explore canonical Kähler metrics, algebraic variety stability, and the Yau-Tian-Donaldson conjecture in complex geometry. Delve into Kähler manifolds, curvature, and pluripotential theory with recent progress and applications.
Greg Malen - Collapsibility of Random Clique Complexes
Explore k-collapsibility in random clique complexes, examining dimensional faces, strong connectivity, and homology implications for topological data analysis.
Category Weight Estimates of Minimal Triangulations
Explore LS-category methods for estimating minimal triangulations of manifolds and polyhedra, focusing on lower bounds for vertex counts in space triangulations.
Decomposing Simplicial Complexes - Without Losing Pieces
Explore simplicial complex decomposition, its impact on homotopy type, and applications in Vietoris-Rips complexes. Learn about obstruction complexes and their role in understanding topological changes.
Tropical Geometry of Phylogenetic Tree Spaces
Explore tropical geometry's application to phylogenetic tree spaces, examining BHV space, tropical Grassmannians, and their implications for computational biology and statistics.
Intrinsic Topological Transforms via the Distance Kernel Embedding
Explore topological transforms for abstract metric spaces using distance kernel embedding, combining persistent homology with Euclidean embeddings for enhanced shape analysis and discrimination.
Thomas Nikolaus: Frobenius Homomorphisms in Higher Algebra
Explore algebraic K theory, higher algebra, and Frobenius homomorphisms in topology and K theory with insights from Thomas Nikolaus.
Jennifer Hom: Homology Cobordism and Heegaard Floer Homology
Explore homology cobordism and Heegaard Floer homology, delving into manifolds, theorems, and chain complexes in this advanced mathematical lecture.
Kathryn Mann- Groups Acting at Infinity
Explore rigidity in group actions, lattices, and infinity, with applications to surface groups, boundaries, and Anosov flows. Gain insights into mathematical concepts and their interconnections.
Aaron Brown- Lattice Subgroups Acting on Manifolds
Explore lattice subgroups' actions on manifolds, covering definitions, theorems, and Zimmer's conjecture. Gain insights into isometric and projective actions, standard modifications, and ongoing research.
Isabella Novik - Face Numbers - The Upper Bound Side of the Story
Explore face numbers in simplicial polytopes and sphere triangulations, examining upper bounds, maximizers, and central symmetry implications. Recent developments and open problems are discussed.
Stable Homotopy Groups of Spheres and Motivic Homotopy Theory
Survey of stable homotopy groups of spheres computation, covering classical methods, Mahowald's Uncertainty Principles, and new techniques using motivic homotopy theory. Includes recent computations and future research directions.
Tamas Hausel - Enhanced Mirror Symmetry for Langlands Dual Hitchin Systems
Explore enhanced mirror symmetry for Langlands dual Hitchin systems, covering topics from SYZ mirror symmetry to equivariant cohomology and Kirillov algebras.