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#Birational Geometry

Showing: 37 courses
Instituto de Matemática Pura e Aplicada

A Short Introduction to Sarkisov Theory

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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.
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1 Lesons
27 minutes
On-Demand
Free-Video
IMSA

The Calabi Problem from a Birational Geometer's Viewpoint - Part 2

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Explore the Calabi problem in Fano manifolds, focusing on recent developments in birational geometry and K-polystability. Gain insights from a renowned algebraic geometer.
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1 Lesons
53 minutes
On-Demand
Free-Video
IMSA

The Calabi Problem from a Birational Geometer's Viewpoint - Part 1

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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.
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1 Lesons
54 minutes
On-Demand
Free-Video
Kyoto-U OCW - Unofficial

The Minimal Model Program for Varieties of Log General Type - Lecture 3

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Delve into advanced birational geometry and minimal model program concepts with Distinguished Professor Christopher Hacon, exploring complex projective varieties and canonical ring theory.
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1 Lesons
1 hour 52 minutes
On-Demand
Free-Video
IMSA

Minimal Exponents of Singularities

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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.
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9 Lesons
1 hour 6 minutes
On-Demand
Free-Video
IMSA

Birational Geometry of Moduli Spaces via the Essential Skeleton

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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.
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10 Lesons
53 minutes
On-Demand
Free-Video
IMSA

Birational Geometry of Sextic Double Solids with a Compound A_n Singularity

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Explore birational geometry of sextic double solids with compound A_n singularities, examining rigidity properties and divisorial contractions in this advanced algebraic geometry topic.
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11 Lesons
53 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

New Results on Rationality in Algebraic Geometry - Lecture 1

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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.
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37 Lesons
1 hour 17 minutes
On-Demand
Free-Video
International Mathematical Union

Floer Cohomology and Birational Geometry

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Explore Floer cohomology applications in birational geometry, including McKay correspondence and quantum cohomology of Calabi-Yau manifolds.
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8 Lesons
46 minutes
On-Demand
Free-Video
IMSA

Finite Generation and K-Stability

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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.
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1 Lesons
1 hour 3 minutes
On-Demand
Free-Video
IMSA

Multispectra

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Explore new birational invariants in algebraic geometry with Professor Ludmil Katzarkov, delving into advanced mathematical concepts and their applications.
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1 Lesons
55 minutes
On-Demand
Free-Video
IMSA

Equivariant Birational Types

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Explore recent developments and constructions in equivariant birational geometry, delving into advanced mathematical concepts and their applications.
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1 Lesons
1 hour 8 minutes
On-Demand
Free-Video
IMSA

Complex Surfaces with P_g=Q=0 via Birational Geometry, Derived Category and Gauge Theory

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Exploration of complex surfaces with p_g=q=0, examining their significance and recent developments through birational geometry, derived category, and gauge theory perspectives.
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1 Lesons
1 hour 4 minutes
On-Demand
Free-Video
IMSA

Decomposition of the Diagonal and Abel Jacobi Map - Lecture II

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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.
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1 Lesons
1 hour 11 minutes
On-Demand
Free-Video
IMSA

Intermediate Jacobians of Gushel-Mukai Varieties

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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.
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1 Lesons
1 hour 5 minutes
On-Demand
Free-Video
IMSA

A Look at Fourier-Mukai Transforms and GIT in the Smooth and Singular Settings

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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.
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1 Lesons
1 hour 6 minutes
On-Demand
Free-Video
IMSA

Integral PL Actions from Birational Geometry

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Explore birational automorphisms, tropicalization, and their applications to Calabi-Yau varieties. Discover connections between algebraic geometry and piece-wise linear homeomorphisms.
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1 Lesons
1 hour 2 minutes
On-Demand
Free-Video
ICTP Mathematics

Superficies Racionales sobre un Cuerpo - AGRA IV Minicourse 2, Lecture 2

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Explora superficies racionales sobre cuerpos, profundizando en conceptos avanzados de geometría algebraica y teoría de números con expertos internacionales.
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1 Lesons
55 minutes
On-Demand
Free-Video
ICTP Mathematics

On the Geometry of Hyperkähler Manifolds

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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.
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1 Lesons
1 hour 43 minutes
On-Demand
Free-Video
IMSA

Equivariant Birational Geometry of Linear Actions

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Explore equivariant birational geometry of linear actions, focusing on Burnside group formalism and its applications in 2D and 3D projective spaces and smooth quadrics.
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1 Lesons
31 minutes
On-Demand
Free-Video
Fields Institute

Studying the Birational Geometry of Complex Fano Hypersurfaces via Characteristic

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Explore complex Fano hypersurfaces' birational geometry through characteristic analysis, delving into advanced mathematical concepts and their applications in algebraic geometry.
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1 Lesons
52 minutes
On-Demand
Free-Video
IMSA

Birational Invariants for Sing Fano Over Algebraically Non-Closed Fields

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Explore birational invariants of singular Fano varieties over non-algebraically closed fields, delving into advanced algebraic geometry concepts and their applications.
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1 Lesons
40 minutes
On-Demand
Free-Video
IMSA

Equivariant Geometry of Cubics - Applications to Cubic Threefolds and Fourfolds

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Explore applications of new invariants in equivariant birational geometry to cubic threefolds and fourfolds, advancing understanding in algebraic geometry and related fields.
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1 Lesons
1 hour
On-Demand
Free-Video
Institut des Hautes Etudes Scientifiques (IHES)

Birational and Singularity Invariants from Non-Commutative Hodge Theory

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Explore new additive invariants of smooth projective varieties called Hodge atoms, their applications to birational equivalence, and novel singularity invariants in algebraic geometry.
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1 Lesons
1 hour 3 minutes
On-Demand
Free-Video
BIMSA

On the Direct Summand Conjecture and Beyond

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Explore the direct summand conjecture's history, proof, and impact on commutative algebra and mixed characteristic birational geometry.
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1 Lesons
47 minutes
On-Demand
Free-Video
BIMSA

Geometry and Integers - Connections Between Number Theory and Geometric Structures

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Explore connections between non-negative integer sets and diverse geometries, examining functions associated with primitive integer vectors and their relation to convex, toric, and birational geometries.
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1 Lesons
1 hour 8 minutes
On-Demand
Free-Video
BIMSA

Rationality Problems in Algebraic Geometry - ICBS 2024

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Explore geometric ideas and constructions in the study of rationality of higher-dimensional algebraic varieties, focusing on recent developments and challenges.
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1 Lesons
1 hour 3 minutes
On-Demand
Free-Video
BIMSA

Derived Approach to Highest Weight Categories

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Explore highest weight categories in Representation Theory, examining their interpretation through exact categories, abelian envelops, and exceptional collections in derived categories.
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1 Lesons
1 hour 10 minutes
On-Demand
Free-Video
Instituto de Matemática Pura e Aplicada

Surfaces with Wahl Singularities and Their Applications - Lecture 1

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Explore surfaces with Wahl singularities and their applications in algebraic geometry. Gain insights from expert Giancarlo Urzúa in this comprehensive lecture from the V Latin American School of Algebraic Geometry.
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1 Lesons
1 hour 13 minutes
On-Demand
Free-Video
Instituto de Matemática Pura e Aplicada

Higher Dimensional Fano Varieties - Lecture 4

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Explore higher dimensional Fano varieties in algebraic geometry. Delve into advanced concepts and recent developments in this field with expert insights from UCLA researcher Joaquín Moraga.
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1 Lesons
1 hour 34 minutes
On-Demand
Free-Video
Instituto de Matemática Pura e Aplicada

Higher Dimensional Fano Varieties - Lecture 1

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Explore higher dimensional Fano varieties in this advanced algebraic geometry lecture. Delve into complex mathematical concepts and theories presented by expert Joaquín Moraga from UCLA.
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1 Lesons
1 hour 24 minutes
On-Demand
Free-Video
Instituto de Matemática Pura e Aplicada

Surfaces with Wahl Singularities and Their Applications - Lecture 4

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Explore surfaces with Wahl singularities and their applications in algebraic geometry. Gain insights from expert Giancarlo Urzúa in this advanced mathematics lecture from the V Latin American School of Algebraic Geometry.
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1 Lesons
1 hour 14 minutes
On-Demand
Free-Video
Instituto de Matemática Pura e Aplicada

Surfaces with Wahl Singularities and Their Applications - Lecture 3

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Explore surfaces with Wahl singularities and their applications in algebraic geometry. Gain insights from expert Giancarlo Urzúa in this advanced mathematics lecture from the V Latin American School of Algebraic Geometry.
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1 Lesons
1 hour 10 minutes
On-Demand
Free-Video
Instituto de Matemática Pura e Aplicada

Foliation Theory and Algebraic Geometry - Moduli Problems and Birational Geometry

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Explore cutting-edge research on holomorphic foliations and algebraic geometry. Gain insights from experts on moduli problems, birational geometry, and their interactions in complex mathematics.
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1 Lesons
56 minutes
On-Demand
Free-Video
Instituto de Matemática Pura e Aplicada

Cox Rings of Algebraic Surfaces

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Explore Cox rings of algebraic surfaces in this panoramic talk by Michela Artebani, part of the V Latin American School of Algebraic Geometry. Gain insights into advanced algebraic geometry concepts.
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1 Lesons
47 minutes
On-Demand
Free-Video
Instituto de Matemática Pura e Aplicada

Fano Manifolds and the Lefschetz Defect - Class 4

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Explore Fano manifolds and Lefschetz defect in this advanced algebraic geometry lecture. Gain insights into complex mathematical concepts and their applications in modern research.
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1 Lesons
1 hour 26 minutes
On-Demand
Free-Video
IMSA

Homological Mirror Symmetry - Progress in Quantum Toric Geometry

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Explore recent developments in quantum toric geometry, moduli spaces of toric varieties, and their conjectural links to birational geometry, drawing from cutting-edge research in the field.
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1 Lesons
56 minutes
On-Demand
Free-Video