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Explore homotopy theories of simplicial coalgebras, extending algebraic models for p-adic homotopy theory to include fundamental groups. Discover key ideas and potential G-equivariant analogs.
Explore equivariant A-theory and h-cobordisms, focusing on Waldhausen's algebraic K-theory of manifolds and its role in classifying manifolds and diffeomorphisms.
Explore manifold invariants, cut-and-paste equivalence, and cobordism relations. Discover recent advancements in categorifying these concepts and their connections to algebraic K-theory.
Explore the stringy spectrum as an additive invariant of orbifolds, its properties, and its connection to isolated hypersurface singularities through examples and explanations.
Explore advanced mathematical concepts in gauge theory, including Cohomological Hall algebras, Nekrasov instantons, and their connections to geometric representation theory and 3D Calabi-Yau manifolds.
Explore quantum spectrum in algebraic geometry, focusing on quantum blow-up formula and its applications in birational geometry, motivic measures, and singularity resolution.
Explore orbifolds as stacks, twisted sectors, stringy cohomology, and localization methods in advanced mathematics with expert Ernesto Lupercio from CINVESTAV.
Explore functional inequalities, their applications, and recent developments in stability theory. Learn strategies for optimizing constants and functions in various mathematical fields.
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.
Explore the Curved Cartan Complex's role in computing gauged algebras and categories, its connection to the Toda system, and applications in 2D mirror symmetry.
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.
Explore open Gromov-Witten invariants for the conifold, examining operator equations, mirror curves, and connections to colored HOMFLYPT polynomials in this advanced mathematics lecture.
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.
Explores moduli spaces of quantum toric stacks and their compactification, extending toric varieties to stacky generalizations with finitely generated subgroups of R^d as "lattices".
Explore techniques for constructing generators in derived categories in nonzero characteristic, including joint research findings on this advanced mathematical topic.
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