Banach Center Courses

Probabilistic Methods in Geometry and Topology

Discover how probabilistic methods prove existence of geometric and topological structures without explicit construction, from combinatorics to cutting-edge applications in algebra and Riemannian geometry.

• YouTube
• 1 hour 7 minutes
• Self-Paced
• Free Video

Differential Calculus on Quantum Principal Bundles over Projective Base

Explore quantum deformation of algebraic group quotients using sheaf-theoretic methods, focusing on principal bundles and differential calculi over projective bases.

• YouTube
• 1 hour 11 minutes
• Self-Paced
• Free Video

How Much, How Often, in What Sequence? Optimal Control Approach to Protocols for Cancer Therapies

Explore optimal control theory to design cancer treatment protocols, balancing drug dosing, timing, and sequencing for maximum effectiveness while minimizing toxicity in combination therapies.

• YouTube
• 1 hour 26 minutes
• Self-Paced
• Free Video

What is Non-Commutative Geometry?

Explore how quantum physics ideas merge with ordinary geometry to create non-commutative geometry, including quantum compact metric spaces and practical examples.

• YouTube
• 1 hour 27 minutes
• Self-Paced
• Free Video

Dissipative Aw-Rascle System - Analysis and Open Problems

Explore the dissipative Aw-Rascle model for vehicular traffic, covering derivation, solution existence, uniqueness, asymptotic limits, and open research problems in this advanced mathematical analysis.

• YouTube
• 1 hour 12 minutes
• Self-Paced
• Free Video

Holonomy as a Key Concept of Differential Geometry

Discover how holonomy generalizes triangle angle sums into a powerful differential geometry concept, exploring Berger's theorem, curvature relationships, and connections to physics.

• YouTube
• 1 hour 23 minutes
• Self-Paced
• Free Video

Sampling and ML Testing vs. Verification - Gradient Flow Methodology

Explore gradient flow methodology for sampling and machine learning testing versus verification techniques in mathematical analysis.

• YouTube
• 1 hour 8 minutes
• Self-Paced
• Free Video

Spectral Triples for Inductive Limits with Applications to Noncommutative Solenoids

Explore spectral triples in inductive limits and their applications to noncommutative solenoids with expert insights from University of Oslo research.

• YouTube
• 1 hour 12 minutes
• Self-Paced
• Free Video

Some Old and New Problems and Results in Ergodic Ramsey Theory

Explore the intersection of ergodic theory and combinatorics through classic and contemporary problems in Ergodic Ramsey Theory with insights from advanced mathematical research.

• YouTube
• 1 hour 22 minutes
• Self-Paced
• Free Video

Nonpositive Curvature in Geometric Group Theory

Explore how nonpositive curvature concepts from differential geometry apply to understanding group structures and their geometric properties in modern mathematics.

• YouTube
• 1 hour 19 minutes
• Self-Paced
• Free Video

On Dynamical Systems Associated with Multiplicative Functions in Number Theory

Explore the deep connections between dynamical systems theory and multiplicative functions, uncovering how these mathematical structures interact in number theory.

• YouTube
• 1 hour 18 minutes
• Self-Paced
• Free Video

Complex Interpolation Theory and Sobolev Spaces

Explore advanced mathematical concepts connecting complex interpolation methods with Sobolev space theory in functional analysis.

• YouTube
• 59 minutes
• Self-Paced
• Free Video

Fraïssé Theory and Topological Dynamics

Explore the intersection of Fraı̈ssé theory and topological dynamics through advanced mathematical concepts and their applications in modern analysis.

• YouTube
• 1 hour 10 minutes
• Self-Paced
• Free Video

Matematyka Ryzyka - Pomiar i Zarządzanie Ryzykiem w Finansach i Ubezpieczeniach

Poznaj metody pomiaru i zarządzania ryzykiem w finansach i ubezpieczeniach. Odkryj zastosowania matematyki finansowej i teorii sterowania stochastycznego w popularnym ujęciu.

• YouTube
• 1 hour 20 minutes
• Self-Paced
• Free Video

The 1950s: A Golden Age of Harmonic Analysis - Connections with Calderón-Zygmund Theory - Part 4

Explore connections between harmonic analysis and Calderón-Zygmund theory in the 1950s, focusing on groundbreaking developments and their lasting impact.

• YouTube
• 1 hour
• Self-Paced
• Free Video