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Explore quantum spectrum in algebraic geometry, focusing on quantum blow-up formula and its applications in birational geometry, motivic measures, and singularity resolution.
Explores Rouquier dimension of wrapped Fukaya categories, linking symplectic topology to algebraic geometry through homological mirror symmetry. Discusses applications to Lagrangian intersections and Lefschetz fibrations.
Explores graded matrix factorizations of invertible polynomials and stability conditions in homological mirror symmetry for singularities, continuing from a previous lecture.
Explore homological mirror symmetry for hypersurface singularities, covering basic definitions, Berglund-Hubsch duality, known results, and detailed examples in this advanced mathematics lecture.
Explore Steenbrink spectra in singularity categories, focusing on non-commutative mixed Hodge structures and dimensional properties. Gain insights into natural and mysterious appearances of this concept.
Explore Steenbrink spectra's role in singularity categories, examining how spectral numbers manifest in triangulated singularity categories associated with singularities.
Explore Alexander polynomials of algebraic links, their definitions, examples, and connections to algebraic geometry. Discover the relationship between plane curve singularity spectra and link polynomials.
Explore the connection between surface singularities and their link's topology, focusing on quantum invariants and their relation to the spectrum of Brieskorn spheres.
Explores Hodge theory, Higgs bundles, and their applications to moduli spaces and hyperbolicity, focusing on complex geometry and variation of Hodge structures.
Explores recent advancements in Hodge theory, focusing on asymptotic properties of period maps and their applications to moduli spaces beyond classical cases of ppav and K3s.
Explores compactifications of moduli spaces for abelian varieties and K3 surfaces, comparing geometric and Hodge-theoretic approaches. Discusses recent work on stable K3 surfaces and recognizable divisors.
Explore the fascinating parallel between Coxeter groups and matroids in combinatorial cohomology, featuring recent research on singular Hodge theory for combinatorial geometries.
Explore o-minimal methods in algebraic geometry, focusing on volume estimates for definable sets and their application to affine GAGA theorems, with implications for Hodge theory.
Explore connections between Deligne-Simpson problem and Hitchin systems, delving into SCF Theories of Class S and 3D mirror symmetry in this advanced mathematics lecture.
Explore the derivative of period maps for Kaehler elliptic surfaces, examining the relationship with j-invariants and proving a generic Torelli theorem for simple elliptic surfaces.
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