Differential Geometry
Explore local curve theory, curvature, Frenet-Serret formulas, and the Fundamental Theorem of Curves in this comprehensive introduction to differential geometry.
Differential Forms
Explora las formas diferenciales, sus propiedades algebraicas, integración y aplicaciones en cálculo vectorial y ecuaciones de Maxwell.
Sloppy Models, Differential Geometry, and Why Science Works
Explore how complex systems can be modeled despite parameter uncertainties, using differential geometry to understand 'sloppiness' and its implications for scientific comprehension and prediction.
Topology Shapes Dynamics of Higher-order Networks
Exploring how higher-order network interactions influence non-linear dynamics, synchronization, and percolation in complex systems like brain networks and climate patterns.
Multidimensional Analysis and Geometry - Introduction to the Derivative in Higher Dimensions - Lecture 1
Explore the derivative in higher dimensions, extending single-variable concepts to multidimensional functions and introducing the derivative as a linear map for best approximation.
Superabundance and Unobstructedness in Lagrangian Torus Fibrations - Lecture
Explore the concept of Lagrangian realization in tropical geometry through this M-Seminar talk by Jeff Hicks from the University of Edinburgh. Delve into the relationship between tropical curves in the base of a Lagrangian torus fibration and their corre…
Floer Homology with DG Coefficients - Applications to Cotangent Bundles
Explore Floer homology with DG coefficients and its applications to cotangent bundles. Gain insights into symplectic geometry and dynamical systems through advanced mathematical concepts.
Spectral Analysis of Dirac Operators with a Purely Imaginary Dislocation
Explore spectral analysis of Dirac operators with imaginary dislocation, covering Green functions, pseudospectra, and effects of matrix potentials on essential and discrete spectra.
A Panorama of Singular Sub-Laplacians and Their Spectra
Explore exotic properties of Laplace-Beltrami operators on rank-varying sub-Riemannian structures. Delve into self-adjointness, spectral properties, and sub-Riemannian Weyl laws. Discover open questions in this fascinating field.
The Moduli Space of Twisted Laplacians and Random Matrix Theory
Explore the convergence of spectral number variance for twisted Laplacians to random matrix theory ensembles, extending Rudnick's work to break time-reversal symmetry and include Dirac operators.
Equivariant Symplectic Homology - Ekeland-Hofer Capacities and Gutt-Hutchings Capacities
Explore the connection between Ekeland-Hofer and Gutt-Hutchings capacities in star-shaped domains, unraveling their equivalence through equivariant symplectic homology.
Derived Moduli Spaces of Hermitian-Einstein Connections
Explore advanced concepts in geometry and physics, focusing on derived moduli spaces of Hermitian-Einstein connections in this seminar by Dennis Borisov.
Symmetries of Manifolds - Lecture 3
Explore symmetries of manifolds in topology and geometry. Delve into classical and recent results, methods, and emerging conjectures about symmetry spaces of simple manifolds like spheres and discs.
Symmetries of Manifolds - Lecture 2
Delve into symmetries of manifolds, exploring classical and recent results on spaces of symmetries for simple manifolds like spheres and discs, with insights into emerging conjectural perspectives.
Symmetries of Manifolds - Lecture 1
Explore symmetries of manifolds in topology and geometry. Delve into classical and recent results, methods, and emerging conjectures about symmetry spaces of simple manifolds like spheres and discs.
Generalizations of the Bernstein Problem
Dive into Otis Chodosh's exploration of the Bernstein Problem's generalizations, examining minimal surface equations and their connections to higher dimensions.
Nonlinear Harmonic Maps and the Energy Identity
Dive into nonlinear harmonic maps, exploring singularity formation and defect measures. Gain insights into the Energy Identity conjecture and its recent proof in this advanced mathematics lecture.
Poisson Algebra, Combinatorics and Representations of Surface Groups
Dive into Poisson algebras, combinatorics, and surface group representations. Explore Goldman's Lie algebra construction and its applications to character varieties and Anosov representations.
Growth of Laplacian Eigenfunctions
Delve into the growth patterns of Laplacian eigenfunctions on compact manifolds, exploring concentration phenomena and the intriguing 'spooky action at a distance' in mathematical contexts.
Counting Closed Geodesics and Improving Weyl's Law for Predominant Sets of Metrics
Dive into the behavior of closed geodesics and Weyl's law on compact manifolds. Explore predominance in Riemannian metrics and its implications for quantitative bounds in geometry.
Courant, Bezout, and Persistence - Lecture 2
Explore spectral geometry through persistence modules and barcodes, examining oscillation of functions and applications to Courant's nodal domain theorem and Bezout's theorem in eigenfunctions.