DT Invariants and Holomorphic Curves in Complex Integrable Systems
Explore the correspondence between Donaldson-Thomas invariants and holomorphic curves, focusing on mirror symmetry and applications in enumerative geometry.
Heegaard Branes and Exact Results for Non-perturbative Complex Chern-Simons Theory
Explore Heegaard branes in moduli spaces of Higgs bundles and their applications in mathematics, from geometric Langlands to low-dimensional topology and complex Chern-Simons theory.
On Resurgent Poisson Structures and Deformations
Explore Z-resurgent series algebra, alien derivations, and their applications in constructing Poisson structures and non-commutative deformations of algebraic products.
Introduction to Resurgence via Wall-crossing Structures - Lecture 4
Explore alternative approach to Borel-Écalle resummation using analytic wall-crossing structures. Delve into holomorphic bundles, gauge transformations, and geometric interpretations with practical examples.
Introduction to Resurgence via Wall-crossing Structures - Lecture 3
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.
A Conjectural Reciprocity Law for Realizations of Motives
Explore a conjectural reciprocity law connecting realizations of motives, drawing parallels to classical number theory and expanding on Hodge theory's comparison isomorphisms.
Spectral Gap of the Laplacian for Random Hyperbolic Surfaces - Part 2
Explore spectral gap of Laplacian for random hyperbolic surfaces using trace method and asymptotic expansions in large genus limit. Analyze Weil-Petersson measure and Friedman-Ramanujan property.
Hodge Theory and Lagrangian Fibrations in Holomorphic Symplectic Manifolds
Explore Hodge theory and Lagrangian fibrations in holomorphic symplectic manifolds. Delve into conjectures, isomorphisms, and decomposition theorems in this advanced mathematical discourse.
Enumerative Geometry Through Sheaves
Explore enumerative geometry, sheaf counting, and their applications in algebraic geometry. Discover new approaches to generalized Donaldson-Thomas invariants on Calabi-Yau threefolds.
Universality for Random Polynomials: Framework and Applications
Explore universality in random polynomials, its applications to root distribution, and solutions to classical problems. Learn about a general framework for establishing universality properties.
Hilbert Spaces of Square Integrable Holomorphic Functions
Explore square integrable holomorphic functions, their historical development, and recent advancements in complex analysis and geometry through Bergman spaces.
Stable Degenerations of Singularities
Explore stable degenerations of singularities in algebraic geometry, focusing on Li-Xu's Stable Degeneration Conjecture and its implications for metric tangent cones in Kähler-Einstein manifolds.
Real Loci of Non-Real Varieties - Mathematics Department Colloquium
Explore cooriented submanifolds in real algebraic geometry, focusing on their properties, intersections, and linking numbers. Gain insights into the geometry of pencils and real projective spaces.
Towards a Mathematical Theory of 3D Mirror Symmetry
Explore the mathematical implications of 3D mirror symmetry, connecting quantum field theory dualities to algebraic geometry and symplectic topology. Uncover links to geometric Langlands and symplectic duality.
Chain Level String Bracket and Punctured Holomorphic Discs
Explore Audin's conjecture and its generalization to Liouville manifolds. Discover connections between holomorphic discs and string topology operations, focusing on chain level string brackets.
Local-Global Principles for Homogeneous Spaces Over Arithmetic Function Fields
Explore local-global principles for homogeneous spaces over arithmetic function fields, focusing on function fields of curves over complete discretely valued fields and related patching methods.
Mirror Structure Constants via Non-Archimedean Analytic Disks
Explore mirror structure constants for smooth affine log Calabi-Yau varieties using non-archimedean analytic disks, generalizing previous constructions and discussing positivity, integrality, and potential extensions.
Nonabelian Mixed Hodge Structures
Explore nonabelian mixed Hodge structures, their relation to rational homotopy, and applications to character varieties and schematic homotopy types. Examine weights from noncompact bases and parabolic structures.
Quantitative Ell-Adic Sheaf Theory
Explore quantitative bounds for étale cohomology groups and their applications in algebraic geometry. Learn about complexity measures for sheaves and how they interact with various functors.
Counting Curves in Calabi-Yau Threefolds
Explore enumerative invariants and a universal approach to counting curves in Calabi-Yau threefolds. Discover how cluster formalism aids computations and potentially simplifies conjectural identities between invariants.
Computing the Weil Representation of Superelliptic Curves
Explore the Weil representation of superelliptic curves, focusing on local Galois representations and stable reductions in algebraic geometry.