IMSA Courses

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

Positivity and Higher Teichmüller Spaces

Explore positivity in Lie groups, positive representations, and their connected components. Delve into Hitchin's Teichmüller components and related open questions in higher Teichmüller theory.

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

Twistor Spaces and Compact Manifolds Admitting Kähler and Non-Kähler Structures

Explore twistor spaces and compact manifolds with dual Kähler and non-Kähler structures. Discover historical examples and new findings in higher dimensions using quaternion twistor spaces of hyperkähler manifolds.

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

Double Groupoids and Generalized Kahler Structures

Explore double groupoids and generalized Kahler structures, focusing on holomorphic symplectic groupoids and their role in describing generalized Kahler metrics using a single real scalar function.

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

Future of Hitchin Mathematics - Round Table Discussion

Experts discuss advancements and future directions in Hitchin mathematics, exploring its impact on various mathematical fields and potential applications.

• YouTube
• 1 hour 24 minutes
• On-Demand
• Free Video

Motives in Generalized Geometry

Explore generalized geometry and motives in this insightful conference talk, delving into advanced mathematical concepts and their applications in contemporary research.

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

Homological Mirror Symmetry: Recent Developments and Future Directions

Explore recent advancements in Homological Mirror Symmetry, surveying new results and opening avenues for future development and collaboration in mathematics.

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