IMSA Courses

Partially Hyperbolic Dynamics - Introduction to Rigidity and Lyapunov Exponents

Delve into the fascinating world of partially hyperbolic dynamics, exploring key concepts from Smale and Anosov to modern developments in dynamical systems and their structural stability.

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

On the Signature of Unimodular Fans

Explore an elementary approach to Leung and Reiner's theorem on signatures of complete smooth toric varieties with specific fan properties and convexity hypotheses.

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

Complex and Symplectic Structures on Almost Abelian Lie Groups

Delve into the classification of left-invariant complex and symplectic structures on almost abelian Lie groups, exploring mathematical research developments in solvable Lie group geometry.

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

Existence Problem for Einstein Metrics on Compact Homogeneous Spaces

Explore the mathematical theory behind Einstein metrics on homogeneous spaces, examining existence conditions, properties, and the interplay between algebra, geometry, and topology.

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

Geometry of Hodge Bundles on Riemann Surfaces

Delve into the geometry of Hodge bundles, exploring G-Higgs bundles, C*-action scaling, and their connection to variations of Hodge structure, Toledo invariants, and Langlands duality.

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

N-dimensional Beaded Necklaces and Higher Dimensional Wild Knots Invariant by a Schottky Group

Explore the construction of n-dimensional wild knots using beaded necklaces and Schottky groups, examining their properties in higher dimensional spheres and branched coverings.

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

Frobenius and Differential Operators to Measure Singularities

Explore the mathematical theory behind using Frobenius maps and differential operators to classify and measure singularities in algebraic geometry, focusing on F-pure threshold applications.

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

New Look at Milnor Spheres - Geometric Topology and Complex Geometry

Explore advanced geometric topology concepts through Spherical T-duality, exotic spheres, and generalized log transform, examining their connections to complex geometry and higher-dimensional manifolds.

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

A Competitive Chemostat Model with Time-Dependent Delays

Explore mathematical modeling of competitive chemostat systems with time-dependent delays, examining extinction conditions and periodic solutions for microorganism populations.

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

Motivic Aspects of Generalized Logarithmic Transformations

Explore the algebraic geometry of logarithmic transformations and their motivic aspects through o-minimal geometry, focusing on elliptic surfaces and multiple fiber transformations.

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

Potentially Stably Rational Conic Bundle Over Non-Closed Field

Explore cohomological obstructions in conic bundles over non-closed fields, examining Galois group generators and their relationship to stable rationality conditions.

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

Remarks on Varieties of Essential CH0-Dimension at Most 2

Explore Voisin's concept of essential CH₀-dimension in varieties, examining conditions for trivial 0-cycles and the implications for Chow-theoretic diagonal decomposition.

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

Non-commutative Deformation of Moduli Space of Flat Connections on Riemann Surfaces

Explore the mathematical foundations of quantum mechanics through formal deformations of functions on manifolds, focusing on flat connections on Riemann surfaces and Kontsevich's revolutionary framework.

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

Atoms Meet Symbols - Theory of G-Equivariant Birational Geometry

Explore the intersection of atomic theory and symbolic mathematics in G-equivariant birational geometry, examining new Z-module applications and invariants in geometric information.

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

Smoothing Toric Fano 3-folds

Explore advanced mathematical concepts in toric Fano 3-folds and their deformation properties, focusing on terminal quotient singularities and optimal deformation criteria.

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