IMSA Courses

Topological Recursion: From A to Z

Comprehensive exploration of topological recursion, covering fundamental concepts to advanced applications in mathematics and physics.

• YouTube
• 1 hour 4 minutes
• On-Demand
• Free Video

From Ribbon Graphs to CohFT

Explore the mathematical connection between ribbon graphs and Cohomological Field Theories (CohFT) in this advanced topology lecture by Olivia Dumitrescu from Central Michigan University.

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

Asymptotics and Resurgence in Weil-Petersson Volumes

Explore non-perturbative properties of 2D gravity models using Resurgence, uncovering insights into Weil-Petersson volume asymptotics and topological gravity instanton contributions.

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

Geometric Recursion for Combinatorial Teichmüller Spaces and Applications

Explores geometric recursion in combinatorial Teichmüller spaces, covering Mirzakhani-McShane identity, Topological Recursion, and discrete versions, with applications to Witten-Kontsevich theorem and Norbury's polynomials.

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

On the Kontsevich Geometry of the Combinatorial Teichmüller Space

Explore combinatorial Teichmüller space, global Fenchel-Nielsen coordinates, and Kontsevich symplectic form. Learn about integrating geometric functions over combinatorial moduli spaces in this advanced mathematics lecture.

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

Polynomials for Quivers and Topological Recursion

Explore A-polynomials for quivers and their connection to topological recursion in this advanced mathematics lecture by Piotr Sułkowski from the University of Warsaw.

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

BPS States and 3d TQFTs

Explore the connection between BPS state counting in string theory and new 3-manifold invariants, examining recent progress and relationships with familiar topological quantum field theories.

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

Quantum Spectrum and Stirling Formula

Explore quantum spectrum analysis and the Stirling formula with expert Maxim Kontsevich, delving into advanced mathematical concepts and their applications in quantum physics.

• YouTube
• 1 hour 9 minutes
• On-Demand
• Free Video

Topological Recursion for Hurwitz Theory and Intersection Theory of Moduli Spaces of Curves

Explore topological recursion in Hurwitz theory and its connections to moduli spaces of curves. Discover ELSV-type formulae and their impact on understanding ramifications and cohomological field theories.

• YouTube
• 1 hour 4 minutes
• On-Demand
• Free Video

Prequels and Possible Sequels to Topological Recursion

Exploration of topological recursion's origins, connections to Hopf algebras, and potential future developments, bridging discrete data and moduli spaces through cubical complexes.

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

Resurgence of Faddeev's Quantum Dilogarithm Function

Explore the mathematical proof linking Borel resummation of formal power series to Faddeev's quantum dilogarithm in linear difference equations.

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

Open-Relative Correspondence and Topological Recursion

Explore the connection between open Gromov-Witten invariants and relative Gromov-Witten invariants in symplectic geometry, and their relation to topological recursion.

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

Topological Recursion, Virasoro-W-Algebra Constraints, and Kontsevich-Soibelman

Explore Virasoro and W-algebra constraints in topological recursion, Kontsevich-Soibelman operators, and their connection to Conformal Field Theory in this advanced mathematics lecture.

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

Exceptional Collections and Rationality

Explore the relationship between exceptional collections and rationality in algebraic geometry, focusing on non-closed fields and toric varieties. Gain insights into recent developments and open questions in this area.

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

Functoriality in Gromov Witten Theory

Explore advanced concepts in Gromov-Witten theory, including quantum Lefschetz, quantum Leray-Hirsch, and functoriality in birational transformations, presented by Yuan-Pin Lee from the University of Utah.

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