Dimension Theory Courses and Certifications

NPTEL-NOC IITM

Noether Normalization Lemma and Important Results in Dimension Theory - Tutorial 2

Explore the Noether Normalization Lemma and key results in dimension theory through detailed mathematical proofs and applications.

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

Simons Semester on Dynamics

Dimension of Stationary Measures - Lecture 4

Delve into the dimension of stationary measures in random walks on matrix groups, exploring flag spaces, Oseledets measures, and configuration space dynamics.

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

Simons Semester on Dynamics

Dimension of Stationary Measures - Lecture 3

Delve into the dimension of stationary measures in random walks on matrix groups, exploring flag spaces, Oseledets measures, and configuration space dynamics. Gain insights into entropy and dimension addition.

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

IMSA

Blow Up Formulae and Invariants II - Dimension Theory

Explore numerical invariants in meromorphic connections, their relation to singularity theory, and applications to non-rationality criteria for Fano varieties.

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

Simons Semester on Dynamics

Recent Progress on Dimension Drop Conjecture

Delve into recent advances in dimension drop conjecture, exploring self-similar sets, Hochman's theorem, and exponential separation in fractal geometry with applications to algebraic parameters.

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

Kavli Institute for Theoretical Physics

Mean String Field Theory and the Lower Critical Dimension - John McGreevy

Explores mean string field theory and lower critical dimension in color confinement, focusing on non-Abelian gauge theories, flux tubes, and large N methods in fundamental physics.

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

Hausdorff Center for Mathematics

Dimension, Complexity and K Theory

Explore connections between dimension theory, complexity, and K-theory in mathematics, focusing on applications in topology and geometry. Gain insights into cutting-edge research in these interconnected fields.

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

Centre de recherches mathématiques - CRM

Orbit Equivalence Theory, Cost, Ergodic Dimension and L2 Betti Numbers - Lecture 3

Explore orbit equivalence theory, cost, ergodic dimension, and L2 Betti numbers in measured group theory. Gain insights into foundational concepts and invariants through examples and exercises.

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

Centre de recherches mathématiques - CRM

Orbit Equivalence Theory, Cost, Ergodic Dimension and L2 Betti Numbers - Lecture 2

Explore orbit equivalence theory, cost, ergodic dimension, and L2 Betti numbers in measured group theory. Delve into advanced mathematical concepts with examples and exercises.

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

Centre de recherches mathématiques - CRM

Orbit Equivalence Theory: Cost, Ergodic Dimension, and L2 Betti Numbers - Part I

Explore orbit equivalence theory, cost, ergodic dimension, and L2 Betti numbers in measured group theory. Gain insights into foundational concepts and invariants through examples and exercises.

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

Simons Semester on Dynamics

Self-affine Systems and Hausdorff Dimension Theory - Lecture 2A

Delve into the dimension theory of self-affine systems, exploring Hausdorff dimensions, Falconer's results, and recent developments in non-conformal transformations and planar self-affine sets.

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

Simons Semester on Dynamics

Self-affine Systems and Hausdorff Dimension Theory - Lecture 2B

Delve into the dimension theory of self-affine systems, exploring Hausdorff dimensions, Falconer's results, and recent developments in non-conformal transformations and planar self-affine sets.

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

Simons Semester on Dynamics

Self-affine Systems and Hausdorff Dimension Theory - Lecture 1B

Delve into the dimension theory of self-affine systems, exploring Falconer's foundational work and recent advances in calculating Hausdorff dimensions of planar self-affine sets.

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

INI Seminar Room 2

Dispersionless Integrability and Twistor Theory Above Dimension 4

Delve into advanced mathematical concepts of dispersionless integrability and its relationship with twistor theory, exploring theoretical frameworks beyond four-dimensional space with Professor Kruglikov.

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

Squid: Schools for Quantum Information Development

Quantum Theory in Finite Dimension Cannot Explain Every General Process

Explore groundbreaking research demonstrating how certain finite-dimensional processes in quantum theory require explanations beyond classical probability and quantum mechanics frameworks.

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