IMSA Courses

PL-Surfaces in Homology 4-Balls

Exploration of PL-surfaces in homology 4-balls, discussing minimum genus of PL surfaces and their bounds in homology balls using Heegaard Floer homology. Joint research findings presented.

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

Equivariant Rokhlin, Eta, and Kappa Invariants of Seifert-Fibered Homology Spheres

Explore equivariant Rokhlin, eta, and kappa invariants of Seifert-fibered homology spheres in this advanced topology talk, delving into gauge theory applications and low-dimensional manifold properties.

• YouTube
• 1 hour 4 minutes
• Self-Paced
• Free Video

An Exact Triangle in Monopole Floer Spectra

Explore an exact triangle for monopole Floer spectra, its application to almost-rational plumbings, and potential future calculations in this advanced topology conference talk.

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

Characterizing Slopes for Alternating Knots

Exploration des pentes caractérisantes pour les nœuds alternés, examinant leur unicité lors de chirurgies rationnelles et discutant des progrès récents dans ce domaine de la topologie.

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

Four-Genus Bounds from the 10/8+4 Theorem

Explore knot slicing obstructions and four-ball genus bounds using the 10/8+4 theorem. Learn about advanced techniques in gauge theory and low-dimensional topology.

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

Nearly Parallel G2-Structures on 7-Manifolds - Associative 3-Folds in Aloff-Wallach Spaces

Explore nearly parallel G2-structures on 7-manifolds, focusing on Aloff-Wallach spaces and Sasaki-Einstein manifolds. Learn about associative 3-folds and their construction in these spaces.

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

Coassociative Fibrations in G2 Geometry

Explore G2 geometry in 7D spaces, focusing on coassociative submanifolds. Learn about their properties, deformation theory, and constructions forming fibrations with singular fibers in 7-manifolds.

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

Tight Contact Structures on Hyperbolic 3-Manifolds - IMSA Topology Seminar

Exploring tight contact structures on hyperbolic 3-manifolds via Dehn surgery on genus one fibered knots in lens spaces, with insights on classification and Stein fillability.

• YouTube
• 1 hour 3 minutes
• Self-Paced
• Free Video

Quasipositive Surfaces and Decomposable Lagrangians in Topology - IMSA Seminar

Explore Legendrian links, knot Floer homology, and Lagrangian link cobordisms in topology. Learn about braiding techniques and the comultiplication property in this advanced mathematical seminar.

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

Linearized Instability for Neutral Functional Differential Equations with State-Dependent Delays

Lecture on linearized instability for neutral functional differential equations with state-dependent delays, presenting recent research findings in advanced mathematics.

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

An Introduction to Delay Differential Equations - Motivation and Applications

Explore delay differential equations, their applications, and open problems in this insightful lecture by Jacqueline Godoy Mesquita, offering a comprehensive introduction to this mathematical field.

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

Andras Szenes- Intersection Cohomology of the Moduli Spaces of Stable Bundle II

Exploration of intersection cohomology in moduli spaces of semistable bundles on Riemann surfaces, featuring new formulas for intersection Betti numbers and geometric insights.

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

Intersection Cohomology of the Moduli Spaces of Stable Bundle I

Explore intersection cohomology of semistable bundle moduli spaces on Riemann surfaces, including Decomposition Theorem analysis and new formula for intersection Betti numbers.

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

Symmetric Unions and Ribbon Knots

Explore symmetric unions in knot theory, focusing on ribbon knots. Learn about classification, composite types, and infinite families of ribbon knots that defy simple symmetric union diagrams.

• YouTube
• 1 hour 2 minutes
• Self-Paced
• Free Video

Generalized Calabi-Yau Problem

Explore advanced concepts in generalized complex geometry, focusing on holomorphically trivial generalized canonical bundles, Calabi-Yau structures, and the current status of the Calabi-Yau problem.

• YouTube
• 1 hour 16 minutes
• Self-Paced
• Free Video