Curvature Courses and Certifications

Institute for Advanced Study

Relationships Between Nilpotency and Curvature in Riemannian Geometry

Explore the fascinating connection between nilpotency and Riemannian geometry, from Gromov's almost flat theorem to Fukaya-Yamaguchi's work, with concrete examples and minimal prerequisites.

• YouTube
• 58 minutes
• On-Demand
• Free Video

Discover AI

AI Learns in Low-Curvature Subspaces - RLVR

Uncover how reinforcement learning fine-tuning achieves dramatic reasoning gains through geometric optimization bias, revealing the "Three-Gate Theory" behind sparse parameter updates.

• YouTube
• 34 minutes
• On-Demand
• Free Video

Banach Center

Distance, Curvature and Symmetry - A Haphazard Tour Through Metric Geometry

Explore metric geometry through distance, curvature, and symmetry concepts, gaining insights into fundamental mathematical principles and their applications in spatial analysis.

• YouTube
• 1 hour 12 minutes
• On-Demand
• Free Video

Banach Center

Curvature and Noncommutative Probability

Explore connections between curvature and noncommutative probability, delving into advanced mathematical concepts and their applications in probability theory.

• YouTube
• 1 hour 18 minutes
• On-Demand
• Free Video

Institut des Hautes Etudes Scientifiques (IHES)

Positive Scalar Curvature with Point Singularities

Explore topological construction of positive scalar curvature metrics with Euclidean point singularities, challenging Schoen's conjecture and geometric flow limitations.

• YouTube
• 1 hour 21 minutes
• On-Demand
• Free Video

BIMSA

Positive Scalar Curvature on Manifolds and Foliations - ICBS 2024

Explore recent advances in positive scalar curvature metrics on manifolds and foliations, a key topic in differential geometry.

• YouTube
• 48 minutes
• On-Demand
• Free Video

BIMSA

Curvature Positivity and $\bar\partial$ Equation with Optimal $L^2$ Estimate - ICBS 2024

Explore recent advancements in multiplier ideal sheaves, multiplier submodule sheaves, and converse L^2 theory. Gain insights into Nakano semipositivity criteria and solutions to Lempert's problem.

• YouTube
• 48 minutes
• On-Demand
• Free Video

Centre de recherches mathématiques - CRM

Curvature Contribution to the Essential Spectrum of Dirac Operators with Critical Shell Interactions

Explore the essential spectrum of 3D Dirac operators with critical shell interactions, examining how surface geometry influences spectral properties in quantum mechanics.

• YouTube
• 55 minutes
• On-Demand
• Free Video

Schmid College, Chapman University

Comparing Oresme's Curvitas with Riemann's Curvature

Explore the historical evolution of curvature concepts from Oresme's 14th-century insights to Riemann's geometric definitions, examining their mathematical and philosophical implications.

• YouTube
• 1 hour 55 minutes
• On-Demand
• Free Video

Galileo Galilei Institute

Basic Curvature, the Atiyah Cocycle and BV

Explore advanced mathematical concepts including curvature, Atiyah cocycle, and BV formalism in this in-depth lecture by Athanasios Chatzistavrakidis.

• YouTube
• 1 hour 7 minutes
• On-Demand
• Free Video

Centrum Fizyki Teoretycznej PAN

Christoffel Symbols, Curvature, and Riemann Tensor - Lecture 8

Zgłęb zaawansowane koncepcje geometrii różniczkowej, w tym symbole Christoffela, krzywiznę i tensor Riemanna. Poznaj ich właściwości algebraiczne i zastosowania w fizyce teoretycznej.

• YouTube
• 1 hour 47 minutes
• On-Demand
• Free Video

Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Geometric Inequalities in Space of Nonpositive Curvature - Part I

Explore geometric inequalities in spaces of nonpositive curvature, focusing on advanced mathematical concepts and their applications.

• YouTube
• 54 minutes
• On-Demand
• Free Video

Hausdorff Center for Mathematics

Entropy and Curvature of Markov Chains on Metric Spaces

Explore Markov chains, Wasserstein distance contraction, and relative entropy in metric spaces. Gain insights into the Peres-Tetali conjecture and its applications.

• YouTube
• 57 minutes
• On-Demand
• Free Video

NCCR SwissMAP

Lorentzian Calderón Problem Under Curvature Bounds

Explore analytic techniques in dynamics and geometry, focusing on the Lorentzian Calderón problem with curvature bounds. Gain insights from expert L. Oksanen of the University of Helsinki.

• YouTube
• 1 hour
• On-Demand
• Free Video

IAS | PCMI Park City Mathematics Institute

Mathematics and Physics in Creative Crafts - From Curvature to Knot Theory

Explore the fascinating intersection of mathematics and crafting, discovering how physics, geometry, and knot theory connect with crochet, quilting, and textile manufacturing patterns.

• YouTube
• 50 minutes
• On-Demand
• Free Video