Nonrational Toric Geometry III - Quasifolds, Foliations, Combinatorics and One-parameter Families
Explores nonrational toric geometry through quasifolds, foliations, and combinatorics, extending classical toric geometry to new contexts and examining one-parameter families of toric quasifolds.
Nonrational Toric Geometry II - Quasifolds, Foliations, Combinatorics and One-parameter Families
Explore complex toric quasifolds, their structure, and relation to rational toric varieties. Learn about extending constructions to nonsimple convex polytopes in symplectic and complex settings.
Wall Finiteness Obstruction for DG Categories II
Exploration of Wall finiteness obstruction theorem for DG categories, including applications to phantom DG categories and derived categories of algebraic varieties. Discusses extensions to algebras over DG operads.
Holomorphic Bisectional Curvature and Applications to Deformations and Rigidity of Mixed Hodge Structure
Explore holomorphic bisectional curvature in Hodge theory, focusing on mixed Hodge metrics, rigidity results, and applications to geometric examples.
A Tropical Approach to Homological Mirror Symmetry of Quadrics
Tropical geometry approach to homological mirror symmetry of quadrics, exploring new anti-canonical divisor and potential construction. Compares with previous work and discusses exceptional collections.
Period Mapping at Infinity
Explore Hodge theory's global study of period mapping at infinity, including new invariants, moduli space implications, and geometric insights for singular varieties.
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 - 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 - 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.
Special Lecture Series on Numerical Geometry - Tristan Collins
Explore complete Calabi-Yau metrics on Fano manifolds with singular divisors, focusing on two-component cases and discussing potential generalizations to more complex scenarios.
Research Seminar - Arc-Connectedness of the Space of 1-Dimensional Commuting Diffeomorphisms
Explore arc-connectedness in 1D commuting diffeomorphisms with Andrés Navas. Gain insights into group actions, community spaces, and rotational concepts in this advanced mathematics seminar.
Functional Inequalities and Improvements: Stability - Part 2
Explore functional inequalities, their optimal constants, and stability properties. Learn strategies for addressing these issues and recent developments in improved inequalities for non-optimizers.
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.
On the Nielsen Realization Problem and Cohomology of Mapping Class Groups of Non-orientable Surfaces
Exploración del problema de realización de Nielsen y cohomología de grupos de clases de mapeo en superficies no orientables, con aplicaciones en topología y teoría de grupos.
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.
Lattice Cohomology - Part 1
Explore topological lattice cohomology in plumbed 3-manifolds, its connection to Heegaard Floer theory, and its applications in analyzing surface singularities and geometric structures.
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.
Windows and Geometric Invariant Theory
Explore windows theory in algebraic geometry, its applications to GIT constructions, and its impact on derived categories and stability conditions in various mathematical contexts.