IMSA Courses

Homological Mirror Symmetry: Recent Developments and Future Directions

Explore recent advancements in Homological Mirror Symmetry and their impact on Mathematics. Join experts to survey new results and discover collaborative opportunities in this field.

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

Discrete Group Actions on the Complex Projective Plane CP^2

Explore discrete group actions on CP^2, extending classical Kleinian group theory to higher dimensions. Gain insights into complex geometry and holomorphic dynamics.

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

Instanton Sheaves - The Next Frontier in 3D Varieties

Explore the evolution of instanton sheaves on 3D varieties, from Atiyah-Ward correspondence to recent Bridgeland stability conditions, based on collaborative research.

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

Geometric Quantization of General Kähler Manifolds

Explore geometric quantization on Kähler manifolds, examining compatible constructions of function quantization, Hilbert space structure, and Kähler structure dependence in symplectic manifolds.

• YouTube
• 1 hour 10 minutes
• On-Demand
• Free Video

Best Lipschitz Maps and Transverse Measures - Lecture 1

Exploration of best Lipschitz maps between hyperbolic surfaces, infinity harmonic maps, and transverse measures. Discusses approximation methods, geodesic laminations, and connections to Teichmüller theory and geometric topology.

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

Mirror Symmetry and Big Algebras in the Hitchin System

Explore mirror symmetry, Hitchin systems, and algebraic structures in representation theory. Discover connections between equivariant cohomology, Kirillov algebras, and affine Schubert varieties.

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

Generalized Hitchin Systems - New Geometric Structures

Explore generalized Hitchin systems with Bảo Châu Ngô, delving into new geometric structures and celebrating Hitchin's mathematical legacy in this insightful conference talk.

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

Parabolic Higgs Bundles in Geometric Langlands Program

Explore parabolic Higgs bundles in geometric Langlands program, focusing on rank 2 local systems on genus 2 curves and associated rank 8 local systems on moduli stacks.

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

ALE Metrics and Nodal Curves - Kronheimer's Construction and Alternative Approaches

Explore asymptotically locally Euclidean metrics on Kleinian singularity resolutions, examining algebraic geometry of twistor spaces and nodal curves in rational surfaces.

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

T-Duality with Fixed Points - A Differential Geometric Approach

Explore T-duality's mathematical history, successes, and challenges, focusing on a new differential geometric approach to log-geometry for handling fixed points in torus actions.

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

Asymptotics in Hitchin's Moduli Space

Explores asymptotic behavior in Hitchin's moduli space, comparing different notions of ideal points at infinity and examining the extension of the nonabelian Hodge correspondence between partial compactifications.

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

Components of Higgs Bundle Moduli Spaces - A Legacy of Hitchin's Ideas

Explore Higgs bundle moduli spaces, their components, and the lasting impact of Hitchin's groundbreaking ideas in this mathematical lecture by Steven Bradlow.

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

Higgs Bundles, Convex Cocompact Subgroups of SU(1,n), and Slodowy Slices

Explore Higgs bundles, SU(1,n) subgroups, and Slodowy slices. Discover connections between stable Higgs bundles and holonomy groups, focusing on SU(1,n) representations and complex hyperbolic manifolds.

• YouTube
• 1 hour 8 minutes
• On-Demand
• Free Video

Variations on a Theme of Hitchin's System

Explores recent developments in Hitchin's system, including connections to SCFTs, extensions to integrable systems, geometry of the base, and links to the Deligne-Simpson problem.

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

Hodge Numbers in Quantum Toric Geometry

Explore Quantum Toric Geometry and its impact on Hodge numbers in non-algebraic complex manifolds. Discover enriched perspectives in this collaborative research presentation.

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