Geometric Recursion - Lecture I
Explore geometric recursion, its relation to topological recursion, and applications in Teichmüller spaces, moduli spaces, and mapping class group invariant functions.
A Proposal for Open DT Invariants
Explore open DT invariants, refined invariance, and boundary conditions in moduli spaces with Sergei Gukov. Delve into generating series, topological vertex, and infinite projects in this advanced mathematics lecture.
Floer Homotopy Without Spectra
Explore advanced mathematical concepts in Floer homotopy, including manifold categories, moduli spaces, and K-homology, without relying on spectral theory.
Periods, Shafarevich Maps and Applications in Algebraic Geometry
Explore periods, Shafarevich maps, and their applications in mathematics, covering key concepts, historical context, and advanced theoretical proofs.
Rigid Compact Complex Manifolds - Properties and Examples
Explore rigid compact complex manifolds, their properties, and recent findings in product-quotient varieties, addressing long-standing questions in algebraic geometry.
The Miyaoka-Yau Equality for Pairs
Explore Miyaoka-Yau Equality for klt pairs, characterizing ball quotients through Chern classes. Gain insights into this advanced mathematical concept and its applications.
A Homological Interpretation of Higher Du Bois and Higher Rational Singularities
Explore homological interpretations of higher Du Bois and rational singularities, focusing on hypersurfaces and characteristic classes. Gain insights into advanced algebraic geometry concepts.
Homological Mirror Symmetry - Lagrangian SYZ Fibrations
Explore Lagrangian SYZ fibrations in symplectic geometry, focusing on integral affine manifolds with singularities and the construction of local models and gluing techniques.
Homological Mirror Symmetry - Toward the Logarithmic Hilbert Scheme
Explore logarithmic geometry and its applications in mirror symmetry, focusing on the development of a logarithmic Hilbert scheme and its implications for degenerations and tropical mathematics.
Homological Mirror Symmetry - Atsushi Takahashi, Osaka University
Exploring generalized root systems of type D, constructing Frobenius manifolds, and examining their potential applications in algebraic geometry and mathematical physics.
Homological Mirror Symmetry - Nikita Nekrasov
Explore homological mirror symmetry and integrable systems through Lax operators, intersection theory, and gauge theory. Delve into Garnier models, Hitchin systems, and quiver gauge theories.
Homological Mirror Symmetry - Moduli Space of Non-Archimedean Holomorphic Disks Pt. II
Explore non-Archimedean holomorphic disks in affine log Calabi-Yau varieties, covering boundary conditions, smoothness, dimension, and properness. Gain insights into non-Archimedean mirror symmetry and related theories.
Homological Mirror Symmetry - Categorical Donaldson-Thomas Theory of C^3 and Beyond
Explore advanced concepts in Donaldson-Thomas theory, including categorifications, refinements, and applications to C^3 and beyond, with a focus on categorical invariants and correspondences.
An Application of Symplectic Topology to Algebraic Geometry
Explore symplectic topology's application to algebraic geometry, connecting Rouquier's triangulated category dimension to Krull dimension via homological mirror symmetry.
Canonical Wall Structures via Punctured Gromov-Witten Theory
Exploration of canonical wall structures in logarithmic Calabi-Yau pairs using punctured Gromov-Witten theory, connecting intrinsic mirror construction with earlier approaches.
Moduli Spaces on K3 Categories Are Irreducible Symplectic Varieties
Explore irreducible symplectic varieties as building blocks in singular projective varieties, focusing on moduli spaces of Bridgeland stable objects in Kuznetsov components of specific fourfolds.
Homology Planes and Fundamental Groups
Explore homology planes and fundamental groups in complex surfaces, focusing on an algorithm for line arrangements and its applications to log-general type surfaces with infinite fundamental groups.
Windows and the BGMN Conjecture
Explore the BGMN Conjecture in algebraic geometry using moduli spaces, derived categories, and GIT wall crossing. Uncover insights into vector bundles and symmetric powers of curves.
Birational Geometry of Moduli Spaces via the Essential Skeleton
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.
K-Stability of Fano Varieties
Explores K-stability of Fano varieties, connecting complex geometry and algebraic geometry. Discusses recent developments, including solved conjectures and the construction of a moduli space for Fano varieties.
Higgs Bundles on Elliptic Surfaces and Logarithmic Transformations
Explore Higgs bundles on elliptic surfaces and their transformations, examining vector bundles' importance in mathematics and the impact of logarithmic transformations on these structures.