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.
Quantum Spectrum in Algebraic Geometry I
Explore quantum spectrum in algebraic geometry, focusing on quantum blow-up formula and its applications in birational geometry, motivic measures, and singularity resolution.
Homological Mirror Symmetry - Moduli Space of Non-Archimedean Holomorphic Disks
Explore non-archimedean holomorphic disks in affine log Calabi-Yau varieties, covering boundary conditions, smoothness, dimension, and properness in the context of mirror symmetry.
Homological Mirror Symmetry - DT Invariants & Holomorphic Curves
Explore the correspondence between Donaldson-Thomas invariants and holomorphic curves, with applications in enumerative geometry and insights from quantum field theories.
Homological Mirror Symmetry - Coulomb Branches & Rozansky-Witten Theory Pt. II
Explore Rozansky-Witten theory and its connection to homological mirror symmetry, from basics to modern developments involving non-compact and infinite-dimensional target spaces.
Homological Mirror Symmetry - Quivers & Curves in Higher Dimensions
Explore the connection between quiver mutations, Poisson X-cluster varieties, and Calabi-Yau categories, leading to a correspondence between Donaldson-Thomas invariants and rational curve counts in higher dimensions.
Homological Mirror Symmetry - Coulomb Branches and Rozansky-Witten Theory
Explore Rozansky-Witten theory and its connection to homological mirror symmetry, from basics to modern developments involving non-compact spaces and ongoing research.
Homological Mirror Symmetry - Twisted Shklyarov Pairing & Applications
Explore twisted Shklyarov pairing in Hochschild homology, its applications to Lefschetz fibrations, mirror symmetry, and classical problems. Joint work with Paul Seidel presented.
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- Non-Holomorphic Deformations of Landau-Ginzburg Models
Explore non-holomorphic deformations of Landau-Ginzburg models, examining derived moduli spaces, Frobenius manifold structures, and Gromov-Witten invariants in symplectic geometry.
Fundamentals of Lie Groupoids and Algebroids - Lecture Series
Introducción a la teoría de Lie de grupoides y algebroides, explorando sus definiciones, propiedades y aplicaciones en diversas estructuras geométricas.
Homological Mirror Symmetry for Theta Divisors
Explore complex moduli of theta divisors in abelian varieties and their mirror Landau-Ginzburg models, focusing on global homological mirror symmetry across the entire moduli space.
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 - Yan Soibelman
Explore holomorphic Floer theory, wall-crossing structures, and their connections to Chern-Simons theory. Discover the interplay between complex symplectic geometry and quantum field theory in this advanced mathematics lecture.
Homological Mirror Symmetry - Introduction to 3D Mirror Symmetry
Explore 3d mirror symmetry's duality between holomorphic symplectic manifolds, focusing on a new 2-categorical formulation that extends homological mirror symmetry concepts.
Khajuraho's Magic Square and Hypercube Symmetries - General Seminar
Explore the symmetries of Khajuraho's Magic Square, its connection to hypercube movements, and broader implications for magic structures in this intriguing mathematical lecture.
Surface Quotient Singularities and Big Cotangent Bundle
Explore hyperbolic properties of surfaces with big cotangent bundle, including the Green-Griffiths-Lang conjecture and a new bigness criterion for orbifold surface resolutions.
Donaldson-Thomas and Gromov-Witten Theories - Part 18
Explore moduli spaces of algebraic curves and coherent sheaves, focusing on Gromov-Witten and Donaldson-Thomas invariants in complex algebraic varieties, with applications to superstring theory.
Donaldson-Thomas and Gromov-Witten Invariants - Part 17
Explore moduli spaces of algebraic curves and coherent sheaves, focusing on Gromov-Witten and Donaldson-Thomas invariants in complex algebraic varieties and their relevance to superstring theory.
Donaldson-Thomas and Gromov-Witten Invariants - Part 16
Explore moduli spaces of algebraic curves and coherent sheaves, focusing on Gromov-Witten and Donaldson-Thomas invariants in complex algebraic varieties and their relevance to superstring theory.
Donaldson-Thomas and Gromov-Witten Theories - Part 15
Explore moduli spaces of algebraic curves and coherent sheaves, focusing on Gromov-Witten and Donaldson-Thomas invariants in complex algebraic varieties and their connections to superstring theory.