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 - 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.
Homological Mirror Symmetry for Hypersurface Singularities II
Explores graded matrix factorizations of invertible polynomials and stability conditions in homological mirror symmetry for singularities, continuing from a previous lecture.
Semi-Affineness of Wrapped Invariants on Affine Log Calabi-Yau Varieties
Explore mirror symmetry in affine log Calabi-Yau varieties, examining finiteness properties of Floer theoretic invariants and their implications for categorical crepant resolutions.
Deformations of Cusp Singularities of Algebraic Surfaces and Mirror Symmetry
Explore cusp singularities in algebraic surfaces, their deformations, and connections to mirror symmetry. Delve into Milnor fibers, log Calabi-Yau surfaces, and Kähler cones.
On the P=W Conjecture I
Exploration of the P=W conjecture for character varieties, its mirror version in Fano mirror symmetry, and applications to Hodge theory of Landau-Ginzburg models. Discusses recent developments and ongoing research in the field.
Secondary Fan, Theta Functions, and Moduli of Calabi-Yau Pairs
Explore the conjecture on moduli space of triples, unirational components, and toric variety covers. Discover generalizations of secondary fans and universal family constructions in algebraic geometry.
On the P=W Conjecture II
Exploration of the mirror P=W conjecture, its evidence in low dimensions, and potential verification methods using Lagrangian torus fibrations. Discusses work with Katzarkov-Przyjalkowski and Katzarkov-Pantev.
Differential Equations and Mixed Hodge Structures
Explores asymptotic Hodge theory, focusing on period-theoretic aspects through examples. Discusses motivic Gamma functions and their role in encoding invariants of variations of Hodge structures on P^1.
D-Modules and Toric Schobers
Exploring mirror symmetry using perverse sheaves of categories and schobers, with focus on B-side category in toric homological mirror symmetry and associated D-module characteristic cycles.
Hodge-Theoretic Aspects of Mirror Symmetry
Explores mirror symmetry for Fano varieties through Hodge theory, discussing Hodge diamond rotation, Katzarkov--Kontsevich--Pantev conjectures, and the mirror P=W conjecture in relation to mixed Hodge structures.
NCHS and Rationality
Explore new approaches to nonrationality through Mirror Symmetry, delving into advanced mathematical concepts and their applications in algebraic geometry.
Mixed Hodge Structures Attached to Hybrid Landau–Ginzburg Models
Explores mixed Hodge structures in Landau-Ginzburg models, focusing on functorial behavior and a new spectral sequence relating decomposed functions, with applications in mirror symmetry.
Discriminants and Toric Birational Geometry
Explore Gorenstein toric singularities, B-side categories in toric homological mirror symmetry, and GKZ hypergeometric D-modules. Discover the conjectural construction of associated spherical functors.
Non-Archimedean Quantum K-Theory and Gromov-Witten Invariants
Explore non-archimedean geometry's role in Gromov-Witten invariants, focusing on derived approaches, K-theory, and motivic cohomology. Learn about geometric relations and their implications for numerical invariants.
Homological Knot Invariants from Mirror Symmetry
Explore homological knot invariants through the lens of mirror symmetry, delving into advanced mathematical concepts and their interconnections in topology and geometry.
Cluster Algebras and Mirror Symmetry - Lecture 2
Explore connections between cluster algebras and mirror symmetry in algebraic geometry, delving into advanced mathematical concepts and their applications.
Cluster Algebras and Mirror Symmetry - Lecture 1
Explore the intricate connection between cluster algebras and mirror symmetry in mathematics, delving into advanced concepts and their applications in algebraic geometry.
The Rogers-Ramanujan Identities and the Icosahedron - Lecture 4
Exploración profunda de las identidades Rogers-Ramanujan, su conexión con el icosaedro y sus implicaciones en teoría de números, formas modulares, combinatoria y teoría de campos conformes.
Raf Bocklandt: Deforming Dimers
Explore deformation theory of dimer models, their relation to mirror symmetry for Riemann surfaces, and various aspects illustrated with examples.