Courant, Bezout, and Persistence in Spectral Geometry - Lecture 1
Explore spectral geometry and topological persistence, focusing on oscillation of functions, Courant's nodal domain theorem, and Bezout's theorem in the context of eigenfunctions.
Renormalization in Dimension Two - Lecture 1
Explore renormalization theory in two-dimensional dynamical systems, extending techniques from one-dimensional cases to higher dimensions using non-uniformly partially hyperbolic systems.
Chain Recurrence Classes of Generic Diffeomorphisms - Lecture 1
Dive into chain recurrence classes of generic diffeomorphisms, exploring advanced concepts in dynamical systems and topology.
Strong Positive Recurrence for Diffeomorphisms
Explore strong positive recurrence in diffeomorphisms, its implications for entropy-maximizing measures, and its equivalence to Lyapunov exponent continuity. Gain insights into smooth diffeomorphisms on compact surfaces.
On the Algebraic Structure of Groups of Area-Preserving Homeomorphisms - Lecture 2
Explore the algebraic structure of area-preserving homeomorphism groups, focusing on Fathi's question and the simplicity conjecture for compact surfaces. Discover link spectral invariants and their role in solving this problem.
Physics
Explora las ecuaciones de Maxwell a través de formas diferenciales y observa a un profesor de matemáticas enfrentarse a un desafío de la Olimpiada de Física.
Geometry of 2-Dimensional Riemannian Disks and Spheres - Regina Rotman
Explore 2D Riemannian geometry, focusing on disks and spheres. Learn about geodesics, sweep-outs, and curve shortening through examples and problem-solving.
Bounds in Renormalized Volume for Hyperbolic 3-Manifolds - Franco Vargas Pallete
Explore advanced geometric concepts in hyperbolic 3-manifolds, focusing on renormalized volume bounds, mean curvature, and variation formulas through rigorous mathematical analysis.
Notions of Scalar Curvature - Mikhail Gromov
Explore scalar curvature concepts, spin bundles, and rich curves with renowned mathematician Mikhail Gromov in this advanced topology lecture from the Institute for Advanced Study.
Existence Theory of Minimal Hypersurfaces - Fernando Marquez
Explore the existence theory of minimal hypersurfaces, covering minimax theorems, space of cycles, and volume spectrum. Gain insights into Ricci curvature and generic metrics.
How Hard is the Theorem of Stolz - Metrics and Scalar Curvature in Spin Manifolds
Delve into the complexity of Stolz's theorem on positive scalar curvature metrics, exploring metric deformations and manifold transformations through groundbreaking mathematical research findings.
Current Algebra and Generalised Cartan Geometry
Dive into advanced mathematical concepts exploring current algebra and generalized Cartan geometry, examining their interconnections and applications in mathematical physics.
Collapsed Anosov Flows: Characterizations and Proofs - Lecture 2
Delve into equivalent characterizations of collapsed Anosov flows and their strong variants, exploring key mathematical proofs and theoretical foundations in dynamical systems.
Análise em Variedades - Aula 18
Explore advanced concepts in differential geometry, including manifolds, tangent bundles, and differential forms. Delve into the Whitney embedding theorem and De Rham cohomology.
Análise em Variedades - Aula 17
Aprofunde-se em análise em variedades, explorando tópicos avançados como variedades diferenciáveis, fibrados, formas diferenciais e o Teorema de Stokes. Desenvolva habilidades essenciais para pesquisa matemática.
Análise em Variedades - Aula 16
Assista à décima sexta aula do curso de mestrado em Análise em Variedades, ministrada pelo Professor Vinicius Ramos no Instituto de Matemática Pura e Aplicada. Explore conceitos avançados como variedades diferenciáveis, variedades com bordo, variedades o…
Análise em Variedades - Aula 19
Explore conceitos avançados de análise em variedades, incluindo formas diferenciais, teorema de Stokes, cohomologia de De Rham e aplicações em geometria diferencial.
Optimal Transportation, Monge-Ampère Equations and Riemannian Ricci Bounds - Lecture 3
Explore geometric measure theory and optimal transport with a focus on Monge-Ampère equations and Riemannian Ricci bounds in this advanced mathematics lecture by L. Ambrosio.
The Calabi Problem from a Birational Geometer's Viewpoint - Part 2
Explore the Calabi problem in Fano manifolds, focusing on recent developments in birational geometry and K-polystability. Gain insights from a renowned algebraic geometer.
The Calabi Problem from a Birational Geometer's Viewpoint - Part 1
Explore the Calabi problem in complex geometry, focusing on Kähler-Einstein metrics and recent developments in birational geometry. Learn from renowned algebraic geometer Carolina Araujo.
Canonical Weierstrass Representation of Minimal Lorentz Surfaces in Pseudo-Euclidean 4-Space with Neutral Metric
Explore canonical Weierstrass representation of minimal Lorentz surfaces in pseudo-Euclidean 4-space, including isothermal parameters, PDEs, and explicit solutions.