Tropical Analog of the Hodge Conjecture for Smooth Algebraic Varieties Over Trivially Valued Fields
Explore tropical geometry's approach to cycle class maps, focusing on a proof of the Hodge conjecture's tropical analog for smooth algebraic varieties over trivially valued fields.
Complex Surfaces with P_g=Q=0 via Birational Geometry, Derived Category and Gauge Theory
Exploration of complex surfaces with p_g=q=0, examining their significance and recent developments through birational geometry, derived category, and gauge theory perspectives.
Decomposition of the Diagonal and Specialization - Lecture I
Explore the decomposition of the diagonal and specialization method for studying stable irrationality in algebraic geometry, focusing on smooth projective varieties.
Completions of Period Mappings
Explore properties and results of period mapping completions in algebraic geometry, featuring insights from renowned mathematician Philip Griffiths.
Decomposition of the Diagonal and Abel Jacobi Map - Lecture II
Explores decomposition of the diagonal and Abel-Jacobi map, focusing on invariants related to coniveau in algebraic geometry. Builds on specialization method from previous lecture.
Intermediate Jacobians of Gushel-Mukai Varieties
Explore intermediate Jacobians of Gushel--Mukai varieties, focusing on threefolds and fivefolds. Discover their connection to Albanese varieties of double EPW surfaces and related birational and categorical aspects.
NCHS and Rationality
Explore new approaches to nonrationality through Mirror Symmetry, delving into advanced mathematical concepts and their applications in algebraic geometry.
A Look at Fourier-Mukai Transforms and GIT in the Smooth and Singular Settings
Explore recent advancements in derived equivalences and birational geometry, focusing on Fourier-Mukai functors and geometric invariant theory quotients in both smooth and singular settings.
A Biased Survey of Some Results Inspired by Stable Rationality Problem for Cubic Hypersurfaces
Explore recent developments in algebraic geometry, focusing on the (stable) rationality problem for cubic hypersurfaces and advancements in degeneration methods involving p-torsion and prelog Chow groups.
Rigid, Not Infinitesimally Rigid Surfaces of General Type with Ample Canonical Bundle
Explore construction of surfaces with unique properties using line configurations and abelian cover theory. Delve into advanced algebraic geometry concepts and their applications.
Loci of Rational Varieties
Explore structure theorems and examples like cubic fourfolds to understand rationality in smooth complex projective varieties with Brendan Hassett from Brown University.
Finite-Dimensional DG Algebras and Their Properties
Explore finite-dimensional DG algebras, perfect complexes, and their role in noncommutative schemes. Discover connections to DG categories with (semi)exceptional collections.
Rationality, Unirationality and Infinite Transitivity
Explore classical approaches to proving rationality and the relationship between unirationality and infinite transitivity in algebraic geometry with expert Fedor Bogomolov.
Old and New Birational Invariants
Explore new birational invariants combining Hodge theory and Symplectic Geometry in this advanced mathematics lecture by Ludmil Katzarkov.
Integral PL Actions from Birational Geometry
Explore birational automorphisms, tropicalization, and their applications to Calabi-Yau varieties. Discover connections between algebraic geometry and piece-wise linear homeomorphisms.
Donaldson-Thomas and Gromov-Witten Theories - Part 10
Explore moduli spaces of algebraic curves and coherent sheaves, their invariants, and connections to geometry, topology, and string theory. Includes computations of Gromov-Witten and Donaldson-Thomas invariants.
Donaldson-Thomas and Gromov-Witten Theories - Part 9
Explore moduli spaces of algebraic curves and coherent sheaves, their invariants, and connections to geometry, topology, and string theory. Includes computations of Gromov-Witten and Donaldson-Thomas invariants.
Donaldson-Thomas and Gromov-Witten Theories - Part 8
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.
Donaldson-Thomas and Gromov-Witten Theories - Part 7
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 VI
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.
Donaldson-Thomas and Gromov-Witten Theories - Part 5
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.