Mohammed Abouzaid: Bordism and Floer Theory
Explore the intersection of Morse theory and infinite-dimensional spaces in topology. Learn about recent advances in Floer theory and its applications to generalized homology and derived orbifold bordism.
A Local Torelli Theorem for Log Symplectic Manifolds
Explore log symplectic manifolds, their moduli space, and local Torelli theorem. Discover new components in Pn's moduli space of log symplectic structures.
Brauer Groups, Twisted Derived Categories, and Hodge Theory
Explore recent developments in Brauer group theory, examining the period-index problem through derived categories, Hodge theory, and enumerative geometry methods.
Deformation of Representation and Fusion Rings for a Lie Algebra by Swarnava Mukhopadhyay
Explores deformation theory in representation and fusion rings of Lie algebras, discussing mathematical concepts and their applications in algebraic and combinatorial methods.
Hochschild Cohomology and Deformation Theory of Hilbert Schemes of Points on Surfaces
Explore Hochschild cohomology of Hilbert schemes, its impact on deformation theory, and connections to symmetric quotient stacks. Gain insights into twisted Hodge numbers and recent research developments.
Osamu Fujino- Minimal Model Program for Projective Morphisms Between Complex Analytic Spaces
Explore advanced algebraic geometry concepts, focusing on minimal model program for projective morphisms between complex analytic spaces, extending results to new contexts.
Rational Points on Modular Curves - Lecture 3
Explore advanced techniques for studying rational points on modular curves, focusing on geometry, Q-rational points, Chabauty methods, and computational aspects in arithmetic geometry.
Rational Points on Modular Curves - Lecture 2
Explore advanced techniques for studying rational points on modular curves, focusing on geometry, Q-rational points, Chabauty methods, and computational aspects in arithmetic geometry.
Classical and Quadratic Chabauty - Lecture 2
Explore advanced techniques in arithmetic geometry: Classical and Quadratic Chabauty methods for studying rational points on modular curves, with applications to elliptic curves.
Vertex Algebras and Associated Varieties - Lecture 2
Explore vertex algebras and associated varieties in this advanced lecture, delving into modern representation theory and its connections to mathematics and physics.
Categorical Aspects of the KSB Correspondence I
Exploring M-resolutions, N-resolutions, and the KSB correspondence for cyclic quotient singularities, with insights on MMP-induced braid group actions and applications to Dolgachev surfaces.
Generic Prym-Torelli Theorem for Cyclic Coverings of Genus 2 Curves
Explore cyclic unramified coverings of genus 2 curves and their associated Prym varieties, focusing on the injectivity of the Prym map for Sophie Germain prime degree coverings.
Moduli of Bundles in Low Genus, Coble Hypersurfaces and Degeneracy Loci
Explore the geometry of moduli spaces for semistable bundles, focusing on Coble hypersurfaces and their connections to Abelian varieties, K3 surfaces, and cubic fourfolds.
On the Classification of Compactified Jacobians of Nodal Curves
Explore modular degenerations of Jacobians when smooth curves become nodal, with insights from recent Pagani-Tommasi findings in algebraic geometry.
On Categorification of GKZ Hypergeometric Systems - Work in Progress
Explore the categorification of GKZ hypergeometric systems and its connection to local toric mirror symmetry through isotrivial families of triangulated categories.
On the Smoothing Problem for Cycles in the Whitney Range
Explores cycle smoothability in algebraic geometry, focusing on the Whitney range. Presents new results and conjectures on constructing cycles from products of divisors.
Cinzia Casagrande- Fano 4-Folds With B2 Greater Than 12 Are Products of Surfaces
Explore complex Fano 4-folds and their properties, focusing on the relationship between second Betti numbers and surface products in algebraic geometry.
Birational Invariants for Sing Fano Over Algebraically Non-Closed Fields
Explore birational invariants of singular Fano varieties over non-algebraically closed fields, delving into advanced algebraic geometry concepts and their applications.
Recent Developments on the Shafarevich Conjecture
Explore recent advancements in the Shafarevich conjecture, focusing on holomorphic convexity of universal covers in quasi-projective varieties, with emphasis on nilpotent and reductive cases.
A Brief History of Geometry II: The European Epoch - From Cartesian to Differential Geometry
Explore the European evolution of geometry, from Cartesian to differential, highlighting key developments and their impact on mathematics. Gain insights into this fundamental discipline's historical significance.
Calculus on the Unit Circle - Arithmetic and Geometry Math Foundations 78
Explore algebraic calculus on unit circles, covering subderivatives, Taylor expansions, tangents, and 3D visualizations. Gain insights into foundational mathematics with a unique approach to this fundamental topic.