Log Symplectic Pairs and Mixed Hodge Structures
Explores log symplectic pairs, their connection to hyperkaehler variety degenerations, and classification of pure weight pairs. Discusses analogies with log Calabi-Yau surfaces and implications for mixed Hodge structures.
Nonrational Toric Geometry I - Symplectic Toric Quasifolds Minicourse
Explore symplectic toric quasifolds, generalizing toric varieties to non-rational polytopes. Learn about quasilattices, quasirationality, and quasitori through examples like quasispheres and Penrose tilings.
Nonrational Toric Geometry II - Quasifolds, Foliations, Combinatorics and One-parameter Families
Explore complex toric quasifolds, their structure, and relation to rational toric varieties. Learn about extending constructions to nonsimple convex polytopes in symplectic and complex settings.
The Pushforward Theorem and Applications
Explore relative shifted symplectic structures, their pushforward theorem, and applications to Poisson structures on derived moduli of Stokes data, with insights on symplectic leaves and irregular types.
Homological Mirror Symmetry - Lagrangian SYZ Fibrations
Explore Lagrangian SYZ fibrations in symplectic geometry, focusing on integral affine manifolds with singularities and the construction of local models and gluing techniques.
Moduli Spaces on K3 Categories Are Irreducible Symplectic Varieties
Explore irreducible symplectic varieties as building blocks in singular projective varieties, focusing on moduli spaces of Bridgeland stable objects in Kuznetsov components of specific fourfolds.
Real Gromov-Witten Theory
Survey of recent developments in real Gromov-Witten theory, covering construction challenges, structural results, and connections to physics. Explores moduli spaces, invariants, and enumerative geometry.
Cyclotomic KLR Algebras - Part 1 of 4
Exploring cyclotomic KLR algebras, their connection to quantum groups, and their role in categorifying highest weight representations, with a focus on type A and the Ariki–Brundan–Kleshchev theorem.
Introduction to Fukaya Categories - James Pascaleff
Explore symplectic geometry fundamentals for Fukaya categories, covering symplectic manifolds, Lagrangian submanifolds, exactness conditions, and more in this comprehensive lecture.
Introduction to Contact Geometry by Dheeraj Kulkarni
Explore contact geometry fundamentals, including Frobenius theorem, contactomorphisms, and Gray stability theorem. Learn about symplectic structures and their relation to contact manifolds.
Gromov-Hausdorff Convergence of Filtered A Infinity Categories
Explore Floer homology's dependence on Hamiltonian isotopy, its multiplicative structure, and connections to homological Mirror symmetry in formal deformation theory.
Stability Structures in Holomorphic Morse-Novikov Theory
Explore complex symplectic manifolds, Floer theory, and Morse-Novikov theory. Delve into analytic questions of convergence and generalization to almost-complex cases in this advanced mathematical lecture.
Basic Remarks on Lagrangian Submanifolds of Hyper-Kähler Manifolds
Explore properties of Lagrangian subvarieties in hyper-Kähler manifolds, focusing on their interaction with Lagrangian fibrations and albanese dimension of Lagrangian surfaces.
Mirror Symmetry and Cluster Varieties
Explore symplectic geometry of cluster varieties and their applications to mirror symmetry, including homological mirror symmetry for Gross-Hacking-Keel cluster varieties.
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.
Toward Homological Mirror Symmetry for Intrinsic Mirror Pairs
Exploration of homological mirror symmetry for intrinsic mirror pairs, comparing algebraic-geometric and symplectic approaches using quantum cohomology and VFC machinery.
Mirrors of Curves and Their Fukaya Categories II
Exploración avanzada de la simetría especular homológica para curvas, enfocándose en la geometría simpléctica de sus espejos y las categorías de Fukaya. Incluye discusiones sobre modelos de Landau-Ginzburg y geometría tropical.
Mirrors of Curves and Their Fukaya Categories I
Explores homological mirror symmetry for curves, focusing on symplectic geometry of mirrors and comparing coherent sheaves to Fukaya categories. Discusses Landau-Ginzburg models and fiberwise wrapped Fukaya categories.
Homological Mirror Symmetry - Homological Link Invariants from Floer Theory
Explore a groundbreaking connection between homological mirror symmetry and representation theory, solving the knot categorification problem and generalizing Heegard-Floer theory to simple Lie superalgebras.
Homological Mirror Symmetry - Functorial Mirror Symmetry for Very Affine Hypersurfaces
Explore functorial mirror symmetry for very affine hypersurfaces, examining Auroux's conjectures and their modifications to account for derived structures in complement mirrors.
Homological Mirror Symmetry - Mohammed Abouzaid - Floer Homotopy Theory Pt. II
Explore recent advancements in Floer generalized homology groups, their applications, and ongoing research on curvature in this context with Mohammed Abouzaid.