Holomorphic Floer Theory, Quantum Wave Functions and Resurgence
Explore holomorphic Floer theory, exponential integrals, and resurgence in algebraic geometry. Discover connections to quantum wave functions and infinite-dimensional applications.
Derived Categories and Motives of Moduli Spaces of Vector Bundles on Curves
Explore derived categories and motives of moduli spaces of vector bundles on curves, their relationships, and recent developments in algebraic geometry.
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.
Extensions in MHM and Hain's Biextension Line Bundle - Part 2
Explores biextension line bundles, their extensions, and algebraic structures. Presents a formula for Q-line bundles, building on Hain and Pearlstein's work on normal functions and complex manifolds.
The Nilpotent Orbit Theorem, New and Old
Explore Schmid's proof and a new approach to the nilpotent orbit theorem for polarized complex variations of Hodge structure, with insights on local monodromy.
Extensions in MHM and Hain's Biextension Line Bundle - Part 1
Explore complex manifolds, biextension line bundles, and normal functions in algebraic geometry. Discover formulas for Q-line bundle extensions and their topological invariants.
Equivariant Birational Geometry of Three-Dimensional Projective Space
Explore finite group actions on 3D projective space, focusing on G-solid cases and their G-Mori fiber spaces. Gain insights into advanced algebraic geometry concepts.
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.
Constructible Sheaves and Filtered D-Modules
Explore the Riemann-Hilbert correspondence and its p-adic analogue, connecting constructible sheaves to filtered D-modules with applications in algebraic geometry.
Hyper-Kähler Manifolds - Part 1
Explore the foundations of hyper-Kähler manifolds, their connection to K3 surfaces, and key properties in this advanced mathematics lecture by renowned expert Claire Voisin.
Quantum Representations and Bogomolov-Katzarkov Surfaces
Exploring quantum representations and their application to Bogomolov-Katzarkov surfaces, addressing the Shafarevich conjecture on holomorphic convexity in algebraic geometry.
Hilbert Schemes of Plane Curve Singularities and Matrix Factorizations
Explore connections between algebraic geometry and topology through plane curve singularities, Hilbert schemes, and matrix factorizations in this advanced mathematics lecture.
Moduli Spaces for Rational Elliptic Surfaces - of Index 1 and 2
Explore rational elliptic surfaces, their construction from pencils of curves, and recent developments in moduli space construction for surfaces with multiple fibers.
Virtual Reductions and Intersection Theory on Moduli Space of Sheaves on Calabi-Yau 4 Folds
Explore virtual reductions of fundamental classes on moduli spaces of sheaves in Calabi-Yau 4-folds, examining applications to Donaldson-Thomas invariants and connections to threefold theories.
Degeneration of Cubic Threefolds with Nodes
Explore the degeneration of cubic threefolds with nodes, focusing on intermediate Jacobians, Fano varieties, and Prym varieties. Gain insights into irrationality proofs and limiting behaviors.
Quantum Toric Geometry II - Non-Commutative Geometric Invariant Theory
Explore quantum geometric invariant theory, extending classical GIT to non-commutative cases. Gain insights into cutting-edge research in quantum toric geometry.
A Construction of Apéry Constants from Landau Ginzberg Models
Explores construction of Apéry constants from Landau-Ginzberg models, linking quantum differential equations of Fano threefolds to mirror symmetry and geometric higher normal functions.
Topological Recursion for Hurwitz Theory and Intersection Theory of Moduli Spaces of Curves
Explore topological recursion in Hurwitz theory and its connections to moduli spaces of curves. Discover ELSV-type formulae and their impact on understanding ramifications and cohomological field theories.
Prequels and Possible Sequels to Topological Recursion
Exploration of topological recursion's origins, connections to Hopf algebras, and potential future developments, bridging discrete data and moduli spaces through cubical complexes.
Open-Relative Correspondence and Topological Recursion
Explore the connection between open Gromov-Witten invariants and relative Gromov-Witten invariants in symplectic geometry, and their relation to topological recursion.
Exceptional Collections and Rationality
Explore the relationship between exceptional collections and rationality in algebraic geometry, focusing on non-closed fields and toric varieties. Gain insights into recent developments and open questions in this area.