Graph Theory Courses

Institute for Advanced Study

Fluid Equations - Regularity and Kolmogorov’s Turbulence Theory

Explore fluid dynamics, Navier-Stokes equations, and Kolmogorov's turbulence theory. Gain insights into regularity results and mathematical confirmations of phenomenological theories.

• YouTube
• 1 hour 5 minutes
• Self-Paced
• Free Video

Institute for Advanced Study

Gauge Theory and the Analytic Approach to Geometric Langlands - Edward Witten

Explore gauge theory's role in geometric Langlands correspondence, comparing categorical and analytic approaches through quantum states, operators, and gauge theory interpretations.

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

Institute for Advanced Study

Representation Theory & Combinatorics of the Symmetry Group and Related Structures - Monica Vazirani

Explore symmetry group representation theory and combinatorics, focusing on cycle notation, permutations, and linearization techniques for advanced mathematical analysis.

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

Institute for Advanced Study

Twisted Topological Tangles or- The Knot Theory of Knitting - Elisabetta Matsumoto

Explore the fascinating intersection of knot theory and knitting, delving into topological properties, elasticity, and mathematical models that unravel the complexities of fabric structure.

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

Institute for Advanced Study

N=2* SU(2) Supersymmetric Yang-Mills Theory and Four-Manifold Invariants - Gregory Moore

Explore supersymmetric Yang-Mills theory, four-manifold invariants, and their connections to topology and complex structures in this advanced theoretical physics seminar.

• YouTube
• 1 hour 14 minutes
• Self-Paced
• Free Video

Institute for Advanced Study

An Update on Exact WKB and Supersymmetric Field Theory - Andy Neitzke

Explore exact WKB methods and their applications in supersymmetric field theory, focusing on key concepts, challenges, and recent developments in this advanced physics topic.

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

Institute for Advanced Study

Statistical Learning Theory for Modern Machine Learning - John Shawe-Taylor

Explore statistical learning theory's role in modern machine learning, covering PAC-Bayes framework, risk measures, and deep network training experiments with John Shawe-Taylor.

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

Institute for Advanced Study

A Geometric View on Iwasawa Theory - Mladen Dimitrov

Explore a geometric perspective on Iwasawa theory, covering higher dimensions, periodic representations, and key concepts in number theory with Mladen Dimitrov from Université de Lille.

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

Institute for Advanced Study

Using Discrepancy Theory to Improve the Design of Randomized Controlled Trials - Daniel Spielman

Explore discrepancy theory's application in randomized controlled trials, enhancing experimental design and statistical analysis for more accurate and efficient research outcomes.

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

Institute for Advanced Study

Graph and Hypergraph Sparsification - Luca Trevisan

Explore graph and hypergraph sparsification techniques with Luca Trevisan, covering spectral definitions, irregular graphs, and unweighted graphs. Gain insights into advanced discrete mathematics concepts.

• YouTube
• 1 hour 34 minutes
• Self-Paced
• Free Video

Institute for Advanced Study

Lower Bounds in Complexity Theory, Communication Complexity, and Sunflowers - Toniann Pitassi

Explore lower bounds in complexity theory, communication complexity, and sunflowers. Delve into Boolean circuits, formulas, and key lemmas with expert insights from Toniann Pitassi.

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

Institute for Advanced Study

Proofs, Circuits, Communication, and Lower Bounds in Complexity Theory - Robert Robere

Explore advanced concepts in complexity theory, including proofs, circuits, and communication, with a focus on lower bounds and their implications for computational limits.

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

Institute for Advanced Study

Lie Algebras and Homotopy Theory - Jacob Lurie

Explore connections between Lie algebras and homotopy theory, covering fundamental groups, Whitehead brackets, and Quillen's theorem in this advanced mathematics seminar.

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

Institute for Advanced Study

Extremal Set Theory - Andrey Kupavskii

Explore extremal set theory with Andrey Kupavskii, covering shifting techniques, partial orders, and the Katniss Theorem. Gain insights into minimizing shadows and analyzing complex cases in discrete mathematics.

• YouTube
• 1 hour 52 minutes
• Self-Paced
• Free Video

Institute for Advanced Study

Representational Power of Graph Neural Networks - Stefanie Jegelka

Explore the representational power of Graph Neural Networks, focusing on message passing, aggregation operations, and their impact on network structure and reasoning tasks.

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