Discrete and Continuous Duality Algebras
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.
Tropical Vector Bundles and Matroids
Delve into advanced geometric concepts exploring toric vector bundles, matroids, and their tropical counterparts through classification, equivariant K-theory, and characteristic classes.
Log Symplectic Pairs and Mixed Hodge Structures
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.
Enumerative Geometry and the Quantum Torus
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.
Mirror Symmetry for Fano Orbifolds - Lecture 01
Explore mirror symmetry for Fano orbifolds, covering key concepts like differential operators and torque variety in this advanced mathematics lecture.
Adelic Toric Varieties and Loop Groups
Explore proalgebraic spaces, adelic abelian algebraic groups, and vector bundle categories. Discover adelic loop groups, Grassmannians, and the Birkhoff-Grothendieck theorem for holomorphic bundles.
Compactification of Moduli Spaces of Quantum Toric Stacks
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".
Evgeny Feigin - PBW Degenerations, Quiver Grassmannians, and Toric Varieties
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.
Cluster Algebras and Mirror Symmetry - Lecture 1
Explore the intricate connection between cluster algebras and mirror symmetry in mathematics, delving into advanced concepts and their applications in algebraic geometry.
On Some Fans and Toric Varieties Related to Branching Laws for Reductive Groups
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.
The KSBA Moduli Space of Log Calabi-Yau Surfaces - Part 1
Explore the KSBA moduli space of log Calabi-Yau surfaces, delving into its properties, conjectures, and recent developments in algebraic geometry and mirror symmetry.
Rouquier Dimension Equals Krull Dimension for Toric Varieties
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.
Homology of the Real Toric Varieties Associated with the Weyl Group of Types E7 and E8
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.
Classification of Locally Standard Torus Actions
Explore the classification of locally standard torus actions in this advanced mathematical talk, delving into complex topological concepts and their applications.
Toric Varieties Arising from Polygon Dissections
Explore toric varieties derived from polygon dissections, examining their geometric properties and applications in algebraic geometry and combinatorics.
Holomorphic Torus Fibre Bundles over Toric Varieties - Generalised Calabi-Eckmann Fibrations
Explore holomorphic torus fibre bundles, Calabi-Eckmann fibrations, and complex structures on moment-angle manifolds in this advanced mathematics lecture by Taras Panov.
Toric Varieties, Exponential Actions, Gale Duality, and Moment-Angle Manifolds
Explore toric varieties, exponential actions, Gale duality, and moment-angle manifolds in this advanced mathematics lecture by Taras Panov from Moscow State University.
Equivariant Quantum Volumes and Symplectic Cuts - Lecture 2
Explore advanced concepts in equivariant quantum volumes and symplectic cuts, delving into mathematical theories and applications in theoretical physics.
Equivariant Quantum Volumes and Symplectic Cuts - Lecture 1
Explore equivariant quantum volumes and symplectic cuts in this advanced mathematics lecture, delving into complex geometric concepts and their applications.
Toric Fiber Products in Geometric Modeling
Explore toric fiber products and their applications in geometric modeling, enhancing your understanding of advanced mathematical concepts in computer graphics.
The KSBA Moduli Space of Stable Log Calabi-Yau Surfaces
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.