Mathematical Analysis Courses and Certifications

ICTP Mathematics

Global Regularity of Solutions to the 4-Species Quadratic Diffusion-Reaction System

Explore advanced mathematical concepts in nonlocal partial differential equations, focusing on global regularity solutions for a 4-species quadratic diffusion-reaction system across all spatial dimensions.

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

ICTP Mathematics

Regularity of the Boltzmann Equation in Bounded Domains - I

Explore the regularity of the Boltzmann equation in bounded domains, focusing on advanced mathematical concepts and applications in geometry, physics, and probability theory.

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

ICTP Mathematics

Dynamics, Symmetry and Asymmetry of Ancient Solutions to Mean Curvature Flow - Ancient Convex Solutions to MCF

Explore ancient convex solutions to Mean Curvature Flow, examining dynamics, symmetry, and asymmetry in this advanced mathematics lecture by Sigurd Angenent.

• YouTube
• 1 hour 15 minutes
• On-Demand
• Free Video

ICTP Mathematics

Standard and Less Standard Asymptotic Methods - Lecture 2

Explore advanced asymptotic methods in mathematics, delving into both standard and unconventional approaches to enhance problem-solving skills and theoretical understanding.

• YouTube
• 1 hour 35 minutes
• On-Demand
• Free Video

ICTP Mathematics

Young Towers for Geodesic Flows on Certain Non-Positively Curved Surfaces - ICTP 2021

Explore Young towers for geodesic flows on non-positively curved surfaces with Yakov Pesin. Gain insights into Sinai-Ruelle-Bowen measures and their applications in surface diffeomorphisms.

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

ICTP Mathematics

Reaction Diffusion Equations on Evolving Domains: Regularity and Global Existence

Explore regularity and global existence of reaction diffusion equations on evolving domains, focusing on mathematical analysis and advanced theoretical concepts.

• YouTube
• 1 hour 3 minutes
• On-Demand
• Free Video

ICTP Mathematics

On the Log-Local Principle for Refined Gromov-Witten Theory

Explore the log-local principle in Gromov-Witten theory, its applications, and recent developments in refined invariants with expert Andrea Brini from the University of Birmingham.

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

ICTP Mathematics

Heat and Schroedinger Evolution on Degenerate Riemannian Structures

Explore heat and Schrödinger evolution on degenerate Riemannian structures with expert Ugo Boscain. Gain insights into advanced mathematical concepts and their applications.

• YouTube
• 1 hour 6 minutes
• On-Demand
• Free Video

Hausdorff Center for Mathematics

The Weighted Energy Dissipation WED Principle for Gradient Flows

Explore advanced variational methods for gradient flows, focusing on the Weighted Energy Dissipation principle and its applications in metric spaces and optimal control problems.

• YouTube
• 1 hour 22 minutes
• On-Demand
• Free Video

Hausdorff Center for Mathematics

The Transfer Operator Method

Explore the Transfer Operator Method in dynamical systems, focusing on its applications in topology and number theory within the context of advanced mathematical research.

• YouTube
• 1 hour 2 minutes
• On-Demand
• Free Video

Hausdorff Center for Mathematics

Erik Palmgren: A Constructive Examination of a Russell Style Ramified Type Theory

Exploration of ramified type theory in Martin-Löf type theory, examining functional reducibility and its applications in constructive mathematical analysis. Introduces an intuitionistic ramified type theory.

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

ICTP Mathematics

Young Towers for Geodesic Flows on Certain Non-Positively Curved Surfaces - ICTP 2021

Explore geodesic flows on non-positively curved surfaces through Young towers, covering history, results, Jacobi fields, and hyperbolic maps with expert Carlos Matheus.

• YouTube
• 1 hour 2 minutes
• On-Demand
• Free Video

Hausdorff Center for Mathematics

Variational and Jump Inequalities

Explore variational and jump norms in mathematical analysis, covering applications in rough paths, singular integrals, and ergodic theory. Gain insights into endpoint results and their proofs.

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

Hausdorff Center for Mathematics

Quantitative Results on the Method of Averaged Projections

Quantitative analysis of averaged projections method in convex optimization, focusing on asymptotic regularity and weak convergence in CAT(0) spaces using proof mining techniques.

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

IMSA

Functional Inequalities and Improvements: Stability - Part 2

Explore functional inequalities, their optimal constants, and stability properties. Learn strategies for addressing these issues and recent developments in improved inequalities for non-optimizers.

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