Topology and Artificial Intelligence - Applications and Recent Progress
Explore recent advancements in algebraic topology and AI, including language models for homotopy groups and statistical modeling for complex networks and diseases.
Curvature-Homogeneous Riemannian 3-Manifolds and Integrable Systems
Explore curvature-homogeneous Riemannian 3-manifolds, surveying known examples and recent discoveries. Delve into connections with integrable systems, particularly Toda lattices, to construct new explicit examples.
Knot Invariants from Finite Dimensional Integration
Explore finite dimensional integration for computing powerful knot invariants, surpassing traditional methods in efficiency and rigor while challenging established notions in knot theory.
Higher Gromov-Witten Invariants of Calabi-Yau Threefolds
Explore mixed-spin-p-fields method for Calabi-Yau quintics, its application to BCOV Feynman summation rule, and generalization to hypersurfaces in toric varieties.
Symplectic Topology, Stability Conditions and Quadratic Differentials
Explore connections between symplectic topology, stability conditions, and quadratic differentials in Fukaya categories and mapping class groups.
Symplectic Topology, Stability Conditions and Quadratic Differentials
Explore connections between symplectic topology, stability conditions, and quadratic differentials in Fukaya categories and mapping class groups.
Exotic Calabi-Yau Metric and Holomorphic Fibration
Explore complete Calabi-Yau metrics, from historical developments to recent constructions on C^3, with insights into collapsing metrics on Calabi-Yau 3-folds.
Metric SYZ Conjecture for Calabi-Yau Manifolds - ICBS 2024
Explore special Lagrangian torus fibrations on Calabi-Yau manifolds, focusing on recent progress and the Fermat family of hypersurfaces.
Generic and Random Behavior of Minimal Surfaces
Explore minimal surfaces in Differential Geometry, focusing on recent quantitative findings under genericity and randomness conditions. Discover spatial equidistribution and hyperbolic properties.
Geometric Analysis of Phase Retrieval
Explore geometric analysis of phase retrieval, examining nonconvex heuristics and proving benign geometric structure for efficient signal recovery using iterative optimization methods.
Semiclassical Measures on Compact Hyperbolic Surfaces
Explore semiclassical measures on compact hyperbolic surfaces, focusing on eigenfunctions of the Laplacian operator and the quantum ergodicity theorem. Delve into fractal uncertainty principles and their implications.
Tightness and Legendrian Surgery in Contact Structures
Explore contact structures, open book decompositions, and tightness characterization in 3-manifolds. Investigate preservation of tightness under Legendrian surgery.
Complex Brunn-Minkowski Theory and Uniqueness Theorems in Kähler Geometry
Explore complex Brunn-Minkowski theory and its applications in Kähler geometry, focusing on uniqueness theorems and generalizations of Bando-Mabuchi's work on Kähler-Einstein metrics.
Categorification of Lagrangian Floer Theory and Its Relation to Various Mathematics
Explore categorification of Lagrangian Floer theory and its connections to diverse mathematical fields with renowned mathematician Kenji Fukaya.
Ricci Limit Spaces are Semi-Locally Simply Connected
Explore Ricci limit spaces and their semi-local simple connectivity, delving into fundamental groups and Gromov-Hausdorff convergence of Riemannian manifolds.
Locally Symmetric Varieties with Moduli Interpretation
Explore complex algebraic geometry, focusing on realizing moduli spaces as locally symmetric varieties through Hodge theory. Survey existing results and examine Calabi-Yau manifolds with complex hyperbolic ball periods.
Hyperbolic and Mixed-Type Problems in Gas Dynamics and Geometry
Explore hyperbolic and mixed-type PDEs in gas dynamics and geometry, focusing on transonic flows and isometric embedding.
Recent Progress in Ramsey Theory
Explore recent advancements in Ramsey Theory, focusing on new techniques and proofs related to Ramsey numbers and graph coloring. Gain insights into geometric, algebraic, probabilistic, and combinatorial methods.
Finiteness Questions for Étale Coverings with Bounded Wild Ramification at the Boundary
Explore finiteness questions for étale coverings with bounded wild ramification at the boundary in characteristic p>0 algebraic geometry, including recent work and open problems.
Applications of Additive Combinatorics to Problems in Fractal Geometry
Explore applications of additive combinatorics in fractal geometry, focusing on self-similar sets with overlaps and recent advancements in the field.
Computing Differentials in the Adams Spectral Sequence and the Last Kervaire Invariant Problem
Explore advanced methods for computing differentials in the Adams spectral sequence and uncover recent progress on the Last Kervaire Invariant Problem in dimension 126.