A Short Introduction to Sarkisov Theory
Explore Sarkisov theory with Sokratis Zikas in this concise introduction, part of IMPA's algebra community showcase featuring new postdoc fellows and their research interests.
The Calabi Problem from a Birational Geometer's Viewpoint - Part 2
Explore the Calabi problem in Fano manifolds, focusing on recent developments in birational geometry and K-polystability. Gain insights from a renowned algebraic geometer.
The Calabi Problem from a Birational Geometer's Viewpoint - Part 1
Explore the Calabi problem in complex geometry, focusing on Kähler-Einstein metrics and recent developments in birational geometry. Learn from renowned algebraic geometer Carolina Araujo.
The Minimal Model Program for Varieties of Log General Type - Lecture 3
Delve into advanced birational geometry and minimal model program concepts with Distinguished Professor Christopher Hacon, exploring complex projective varieties and canonical ring theory.
Minimal Exponents of Singularities
Explore advanced mathematical concepts like minimal exponents, Bernstein-Sato polynomials, and their connections to D-modules, Hodge theory, and birational geometry in this in-depth lecture.
Birational Geometry of Moduli Spaces via the Essential Skeleton
Explore the essential skeleton in birational geometry, linking it to tropical geometry and moduli spaces, with a focus on $\mathcal{M}_{0,n}$ and potential applications to hyperplane arrangements.
Birational Geometry of Sextic Double Solids with a Compound A_n Singularity
Explore birational geometry of sextic double solids with compound A_n singularities, examining rigidity properties and divisorial contractions in this advanced algebraic geometry topic.
New Results on Rationality in Algebraic Geometry - Lecture 1
Explore new results on algebraic variety rationality, focusing on obstructions to rationality in higher dimensions and the powerful degeneration method for distinguishing rational and unirational varieties.
Floer Cohomology and Birational Geometry
Explore Floer cohomology applications in birational geometry, including McKay correspondence and quantum cohomology of Calabi-Yau manifolds.
Finite Generation and K-Stability
Explore recent advances in birational geometry and their impact on K-stability, including finite generation of valuations and connections to major conjectures in algebraic geometry.
Multispectra
Explore new birational invariants in algebraic geometry with Professor Ludmil Katzarkov, delving into advanced mathematical concepts and their applications.
Equivariant Birational Types
Explore recent developments and constructions in equivariant birational geometry, delving into advanced mathematical concepts and their applications.
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 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.
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.
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.
Superficies Racionales sobre un Cuerpo - AGRA IV Minicourse 2, Lecture 2
Explora superficies racionales sobre cuerpos, profundizando en conceptos avanzados de geometría algebraica y teoría de números con expertos internacionales.
On the Geometry of Hyperkähler Manifolds
Explore hyperkähler manifolds, their properties, and examples. Delve into deformation types, moduli spaces of stable sheaves, and the birational geometry of K3-type manifolds with symplectic actions.
Equivariant Birational Geometry of Linear Actions
Explore equivariant birational geometry of linear actions, focusing on Burnside group formalism and its applications in 2D and 3D projective spaces and smooth quadrics.
Studying the Birational Geometry of Complex Fano Hypersurfaces via Characteristic
Explore complex Fano hypersurfaces' birational geometry through characteristic analysis, delving into advanced mathematical concepts and their applications in algebraic geometry.