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#Toric Varieties

Showing: 35 courses
Institute for Advanced Study

Discrete and Continuous Duality Algebras

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Delve into Poincare duality algebras and their extensions, exploring connections to toric varieties, spherical varieties, and K-rings through homogeneous and weighted homogeneous polynomials on vector spaces and lattices.
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1 Lesons
1 hour 5 minutes
On-Demand
Free-Video
Institute for Advanced Study

Tropical Vector Bundles and Matroids

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Delve into advanced geometric concepts exploring toric vector bundles, matroids, and their tropical counterparts through classification, equivariant K-theory, and characteristic classes.
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1 Lesons
1 hour 3 minutes
On-Demand
Free-Video
IMSA

Log Symplectic Pairs and Mixed Hodge Structures

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Explores log symplectic pairs, their connection to hyperkaehler variety degenerations, and classification of pure weight pairs. Discusses analogies with log Calabi-Yau surfaces and implications for mixed Hodge structures.
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15 Lesons
54 minutes
On-Demand
Free-Video
IMSA

Enumerative Geometry and the Quantum Torus

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Explore enumerative geometry through tropical curves, pseudotropical curves, and their connection to Lie algebras and quantum torus. Discover innovative approaches to classical counting problems in algebraic geometry.
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10 Lesons
1 hour
On-Demand
Free-Video
ICTP Mathematics

Mirror Symmetry for Fano Orbifolds - Lecture 01

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Explore mirror symmetry for Fano orbifolds, covering key concepts like differential operators and torque variety in this advanced mathematics lecture.
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9 Lesons
47 minutes
On-Demand
Free-Video
IMSA

Adelic Toric Varieties and Loop Groups

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Explore proalgebraic spaces, adelic abelian algebraic groups, and vector bundle categories. Discover adelic loop groups, Grassmannians, and the Birkhoff-Grothendieck theorem for holomorphic bundles.
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1 Lesons
47 minutes
On-Demand
Free-Video
IMSA

Compactification of Moduli Spaces of Quantum Toric Stacks

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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".
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1 Lesons
49 minutes
On-Demand
Free-Video
International Mathematical Union

Evgeny Feigin - PBW Degenerations, Quiver Grassmannians, and Toric Varieties

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Explore connections between Lie theory, quiver Grassmannians, and flag variety degenerations, focusing on PBW filtration in highest weight representations and its impact on degenerate flag varieties.
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1 Lesons
45 minutes
On-Demand
Free-Video
ICTP Mathematics

Cluster Algebras and Mirror Symmetry - Lecture 1

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Explore the intricate connection between cluster algebras and mirror symmetry in mathematics, delving into advanced concepts and their applications in algebraic geometry.
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1 Lesons
1 hour 2 minutes
On-Demand
Free-Video
IMSA

On Some Fans and Toric Varieties Related to Branching Laws for Reductive Groups

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Explore algebraic group embeddings and their representation theory through Geometric Invariant Theory, focusing on H-invariant vectors and the GIT-fan's role in encoding information.
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1 Lesons
1 hour 5 minutes
On-Demand
Free-Video
IMSA

The KSBA Moduli Space of Log Calabi-Yau Surfaces - Part 1

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Explore the KSBA moduli space of log Calabi-Yau surfaces, delving into its properties, conjectures, and recent developments in algebraic geometry and mirror symmetry.
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1 Lesons
58 minutes
On-Demand
Free-Video
IMSA

Rouquier Dimension Equals Krull Dimension for Toric Varieties

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Explore the equality of Rouquier and Krull dimensions for toric varieties, delving into homological mirror symmetry and a multi-graded version of Hilbert's syzygy theorem.
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1 Lesons
57 minutes
On-Demand
Free-Video
Fields Institute

Homology of the Real Toric Varieties Associated with the Weyl Group of Types E7 and E8

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Explore the homology of real toric varieties linked to E_7 and E_8 Weyl groups in this advanced mathematical talk by Seonghyeon Yu from Ajou University.
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1 Lesons
17 minutes
On-Demand
Free-Video
Fields Institute

Classification of Locally Standard Torus Actions

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Explore the classification of locally standard torus actions in this advanced mathematical talk, delving into complex topological concepts and their applications.
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1 Lesons
45 minutes
On-Demand
Free-Video
Fields Institute

Toric Varieties Arising from Polygon Dissections

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Explore toric varieties derived from polygon dissections, examining their geometric properties and applications in algebraic geometry and combinatorics.
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1 Lesons
46 minutes
On-Demand
Free-Video
Fields Institute

Holomorphic Torus Fibre Bundles over Toric Varieties - Generalised Calabi-Eckmann Fibrations

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Explore holomorphic torus fibre bundles, Calabi-Eckmann fibrations, and complex structures on moment-angle manifolds in this advanced mathematics lecture by Taras Panov.
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1 Lesons
1 hour 3 minutes
On-Demand
Free-Video
Fields Institute

Toric Varieties, Exponential Actions, Gale Duality, and Moment-Angle Manifolds

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Explore toric varieties, exponential actions, Gale duality, and moment-angle manifolds in this advanced mathematics lecture by Taras Panov from Moscow State University.
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1 Lesons
1 hour 3 minutes
On-Demand
Free-Video
Galileo Galilei Institute

Equivariant Quantum Volumes and Symplectic Cuts - Lecture 2

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Explore advanced concepts in equivariant quantum volumes and symplectic cuts, delving into mathematical theories and applications in theoretical physics.
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1 Lesons
1 hour 14 minutes
On-Demand
Free-Video
Galileo Galilei Institute

Equivariant Quantum Volumes and Symplectic Cuts - Lecture 1

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Explore equivariant quantum volumes and symplectic cuts in this advanced mathematics lecture, delving into complex geometric concepts and their applications.
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1 Lesons
1 hour 26 minutes
On-Demand
Free-Video
Conference GSI

Toric Fiber Products in Geometric Modeling

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Explore toric fiber products and their applications in geometric modeling, enhancing your understanding of advanced mathematical concepts in computer graphics.
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1 Lesons
18 minutes
On-Demand
Free-Video
M-Seminar, Kansas State University

The KSBA Moduli Space of Stable Log Calabi-Yau Surfaces

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Explore the KSBA moduli space of stable log Calabi-Yau surfaces, delving into its properties, connections to toric varieties, and recent developments in algebraic geometry and mirror symmetry.
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1 Lesons
56 minutes
On-Demand
Free-Video
Institut des Hautes Etudes Scientifiques (IHES)

Introduction to Resurgence via Wall-crossing Structures - Lecture 2

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Explore an alternative approach to Borel-Écalle resummation using analytic wall-crossing structures. Delve into holomorphic bundles, gauge transformations, and geometric interpretations with practical examples.
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1 Lesons
1 hour 16 minutes
On-Demand
Free-Video
Institut des Hautes Etudes Scientifiques (IHES)

Introduction to Resurgence via Wall-crossing Structures - Lecture 1

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Explore an alternative approach to Borel-Écalle resummation using analytic wall-crossing structures. Delve into holomorphic bundles, gauge transformations, and geometric interpretations with practical examples.
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1 Lesons
1 hour 15 minutes
On-Demand
Free-Video
Institut des Hautes Etudes Scientifiques (IHES)

Introduction to Resurgence via Wall-crossing Structures - Lecture 4

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Explore alternative approach to Borel-Écalle resummation using analytic wall-crossing structures. Delve into holomorphic bundles, gauge transformations, and geometric interpretations with practical examples.
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1 Lesons
1 hour 5 minutes
On-Demand
Free-Video
Institut des Hautes Etudes Scientifiques (IHES)

Introduction to Resurgence via Wall-crossing Structures - Lecture 3

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Explore an alternative approach to Borel-Écalle resummation using analytic wall-crossing structures. Delve into holomorphic bundles, gauge transformations, and geometric interpretations with practical examples.
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1 Lesons
1 hour 10 minutes
On-Demand
Free-Video
BIMSA

Higher Gromov-Witten Invariants of Calabi-Yau Threefolds

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Explore mixed-spin-p-fields method for Calabi-Yau quintics, its application to BCOV Feynman summation rule, and generalization to hypersurfaces in toric varieties.
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1 Lesons
1 hour
On-Demand
Free-Video
BIMSA

Points, Lines, and Subdivisions in Polyhedra - ICBS 2024

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Explore polyhedra's role in mathematics, from PL topology to arithmetic, and discover new insights in combinatorics and related fields.
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1 Lesons
58 minutes
On-Demand
Free-Video
Fields Institute

Equivariant K-theory of Cellular Toric Varieties and Related Spaces

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Explore equivariant K-theory of cellular toric varieties and related spaces in this advanced mathematics talk by Uma Vikraman from IIT Chennai at the Fields Institute.
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1 Lesons
43 minutes
On-Demand
Free-Video
IMSA

Quantum Toric Geometry I

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Explore quantum toric geometry, a generalization of classical toric geometry using quantum tori, allowing for irrational fans. Learn foundations and motivations behind this advanced mathematical concept.
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15 Lesons
59 minutes
On-Demand
Free-Video
IMSA

An Introductory Mini Course into Quantum Toric Geometry Lecture I - Day 1

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Explore quantum toric geometry, a non-commutative generalization of toric geometry. Learn about stacks, quantum tori, and quantum toric varieties, building on foundations of traditional toric geometry.
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17 Lesons
1 hour 2 minutes
On-Demand
Free-Video
IMSA

An Introductory Mini Course into Quantum Toric Geometry Lecture II

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Explore quantum toric geometry, including LVM theory, quantum GIT, and moduli spaces of toric varieties. Delve into non-commutative spaces and their relation to traditional toric geometry.
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1 Lesons
1 hour 4 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
Institute for Advanced Study

Derived Categories of the Permutahedral Varieties

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Delve into the geometric and combinatorial analysis of derived categories in toric varieties, exploring permutahedron's role in matroid theory through convex-geometric approaches.
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1 Lesons
55 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Machine Learning Detects Terminal Singularities in Q-Fano Varieties

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Explore machine learning applications in algebraic geometry, focusing on Q-Fano varieties and terminal singularities detection. Gain insights into new combinatorial criteria and high-dimensional Q-Fano landscapes.
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1 Lesons
48 minutes
On-Demand
Free-Video
M-Seminar, Kansas State University

Quivers, Flow Trees, and Log Curves

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Explore the connection between Donaldson-Thomas invariants, attractor flow trees, and log Gromov-Witten invariants in quiver theory and toric geometry.
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1 Lesons
1 hour 27 minutes
On-Demand
Free-Video