Paper finds explicit optimal lower bound for J-functional in Kähler geometry.
problem Finding optimal lower bounds for Donaldson's J-functional in Kähler geometry.
method Provided an explicit formula for the optimal lower bound of Donaldson's J-functional.
result Explicit formula for the optimal lower bound of Donaldson's J-functional, leading to new existence criteria for cscK metrics.
We consider projective rational strong Calabi dream surfaces: projective smooth rational surfaces which admit a constant scalar curvature Kähler metric for every Kähler class. We show that there are only two such rational surfaces, namely the projective plane and the quadric surface. In particular, we show that all rat…
DREAM learns optimal strategies in imperfect games without needing a simulator.
problem Learning optimal strategies in imperfect-information games with multiple agents.
method DREAM is a deep reinforcement learning algorithm that converges to Nash Equilibria and coarse correlated equilibria.
result DREAM achieves state-of-the-art performance in benchmark games and is competitive with simulator-based algorithms.
Dream Distillation compresses models without data, achieving high accuracy.
problem Model compression without real data.
method Data-independent model compression framework.
result Achieves 88.5% accuracy on CIFAR-10 test set.
DREAM model improves computational efficiency for non-linear effects in relational event models.
problem Efficiently modeling non-linear effects in dynamic relational networks.
method Introduces Deep Relational Event Additive Model (DREAM) using Neural Additive Models.
result Demonstrates superior computational efficiency compared to traditional REM approaches.
Learning to control robots directly based on images is a primary challenge in robotics. However, many existing reinforcement learning approaches require iteratively obtaining millions of robot samples to learn a policy, which can take significant time. In this paper, we focus on learning a realistic world model capturi…
LiDER refreshes past experiences in RL by dreaming about them.
problem Improving data efficiency in off-policy RL algorithms.
method Refreshing past experiences in a replay buffer using the current policy.
result LiDER consistently improves performance in Atari games.
Reduces symplectic Hamiltonian systems to contact systems, realizing Poincaré's dream.
problem Scaling symmetries in Hamiltonian systems.
method Contact reduction of symplectic Hamiltonian systems.
result Generically possible reduction to contact Hamiltonian systems, reducing inputs needed.
ESCHER avoids importance sampling to estimate regret in large games.
problem Estimating Nash equilibria in large games with high variance.
method Computes a history value function to estimate regret without importance sampling.
result ESCHER reduces regret estimation variance significantly compared to existing methods.
Study shows non-polyhedral structure in moduli spaces for n≥8.
problem Identifying non-polyhedral structure in moduli spaces of pointed stable curves.
method Constructing an extremal non-polyhedral ray via maps on meromorphic strata of differentials.
result Moduli spaces are not Mori Dream Spaces for n≥8.
Compactifies Calabi-Yau to weak Fano manifolds.
problem Compactifying Calabi-Yau manifolds to weak Fano manifolds.
method Generalized Tian-Yau construction and asymptotically Calabi metrics.
result Calabi-Yau structure arises from compactification.
The abstract discusses how generalized Calabi-Gray manifolds help solve non-Kähler geometry questions.
problem Non-Kähler complex manifolds with explicit geometry.
method Demonstrates the use of generalized Calabi-Gray manifolds to address non-Kähler geometry questions.
result Generalized Calabi-Gray manifolds provide a framework to answer specific non-Kähler geometry problems.
Constructs complete Calabi-Yau metrics from smoothed Calabi-Yau intersections.
problem Creating complete Calabi-Yau metrics on non-compact manifolds.
method Extending Székelyhidi's work, constructing metrics with varying complex structures and possible singularities.
result Produces Calabi-Yau metrics with fibers having varying complex structures and possibly isolated singularities.
RL research overhypes potential but lacks deployable solutions.
problem Current RL research overhypes potential and lacks deployable solutions.
method Identifies and critiques current RL research practices.
result Current RL research direction is unlikely to lead to practical, economically viable solutions.
Study of twisted Calabi flow connecting J-flow and Calabi flow on Kähler manifolds.
problem Existence and convergence of twisted Calabi flow on compact Kähler manifolds.
method Analysis of a family of twisted Calabi flows connecting J-flow and Calabi flow, showing long-time existence and convergence to cscK metrics.
result Long-time existence and convergence of twisted Calabi flow to cscK metrics, implying openness of continuity method.
Holomorphic connections on Calabi-Yau manifolds are flat.
problem Existence of holomorphic connections on Calabi-Yau manifolds.
method Proving the existence of flat holomorphic connections for holomorphic vector bundles.
result Holomorphic vector bundles over compact Kähler Calabi-Yau manifolds admit flat holomorphic connections.
The paper studies the twisted Calabi flow on Kähler manifolds.
problem Analyzing the behavior of the twisted Calabi flow on compact Kähler manifolds.
method Establishing convexity, proving short-time existence, and demonstrating stability of the flow.
result The stability of the twisted Calabi flow near twisted constant scalar curvature Kähler metrics.
In this paper, we construct simply connected symplectic Calabi-Yau 6-manifolds by applying Gompf's symplectic fiber sum operation along T4. Using our construction, we also produce symplectic non-Kähler Calabi-Yau 6-manifolds with fundamental group Z. In this paper, we also produce the first examples of simply con…
Gluing theorem for collapsing warped-QAC Calabi-Yau manifolds verified.
problem Behavior of warped-QAC Calabi-Yau metrics on affine quadrics.
method Gluing construction for collapsing warped-QAC Calabi-Yau manifolds.
result Verification of Yang Li's conjecture on warped QAC Calabi-Yau metrics.
Reductive quotients preserve klt singularities in algebraic geometry.
problem Preserving klt singularities in quotients of klt singularities.
method Proving that the quotient of a klt type singularity by a reductive group is of klt type.
result The quotient of a klt variety by a reductive group results in a klt variety with a suitable boundary.
Study on collapsing Calabi-Yau manifolds and their metrics.
problem Understanding degenerations of Calabi-Yau manifolds with Ricci-flat Kahler metrics.
method Survey of recent developments, focusing on volume collapsing metrics.
result New insights into the behavior of Calabi-Yau manifolds under volume collapse.
Dimofte, Gaiotto and Gukov introduced a powerful invariant, the 3D-index, associated to a suitable ideal triangulation of a 3-manifold with torus boundary components. The 3D-index is a collection of formal power series in q1/2 with integer coefficients. Our goal is to explain how the 3D-index is a generating serie…
Solves Calabi-Yau equation on complex manifolds with non-positive astheno-Ricci curvature.
problem Solving the form type Calabi-Yau equation on complex manifolds.
method Defined astheno-Ricci curvature and proved existence of solution under non-positive curvature condition.
result Existence of solution for Calabi-Yau equation with non-positive astheno-Ricci curvature.
Study on Calabi-Yau metrics and their degenerations.
problem Understanding degenerations of Ricci-flat Kahler metrics on Calabi-Yau manifolds.
method Survey of recent results on questions about degenerations.
result Survey of recent results on degenerations of metrics.
Study on Calabi-Yau locally conformally Kähler manifolds proving they are Vaisman.
problem Characterizing Calabi-Yau locally conformally Kähler manifolds.
method Analyzing properties of Calabi-Yau locally conformally Kähler manifolds, proving they are Vaisman.
result Calabi-Yau locally conformally Kähler manifolds are Vaisman.
Study shows Calabi-Yau manifolds are non-hyperbolic via mirror symmetry.
problem Proving non-hyperbolicity of Calabi-Yau manifolds.
method Using mirror symmetry, entire curves are found on Calabi-Yau manifolds.
result Calabi-Yau manifolds are Kobayashi non-hyperbolic.
Extends Kodaira Spencer to higher-dimensional Calabi-Yau manifolds.
problem No specific problem stated; extension of functional.
method Extension to Calabi-Yau manifolds of arbitrary dimension.
result Extension of the Kodaira Spencer functional.
Constructs non-Kähler Calabi-Yau manifolds with large Betti numbers.
problem Finding non-Kähler Calabi-Yau manifolds with high Betti numbers.
method Smoothing normal crossing varieties to create K3 fibrations over smooth projective varieties.
result Examples of non-Kähler Calabi-Yau manifolds with arbitrarily large 2nd Betti numbers.
In this paper, we study the convergence of Calabi-Yau manifolds under Kähler degeneration to orbifold singularities and complex degeneration to canonical singularities (including the conifold singularities), and the collapsing of a family of Calabi-Yau manifolds.
We address the issue why Calabi-Yau manifolds exist with a mirror pair. We observe that the irreducible spinor representation of the Lorentz group Spin(6) requires us to consider the vector spaces of two-forms and four-forms on an equal footing. The doubling of the two-form vector space due to the Hodge duality doubles…
In the present paper we provide a description of complete Calabi-Yau metrics on the canonical bundle of generalized complex flag manifolds. By means of Lie theory we give an explicit description of complete Ricci-flat Kähler metrics obtained through the Calabi ansatz technique. We use this approach to provide several e…
Calabi flow works well with bounded curvature on compact manifolds.
problem Stability of extremal Kähler metrics under the Calabi flow.
method Extending the Calabi flow with Lp scalar curvature bounds. result Calabi flow converges exponentially to extremal Kähler metrics.
New meta-RL method avoids exploration-exploitation trade-off.
problem Learning to explore and exploit simultaneously in meta-RL.
method Developed new objectives for exploration and exploitation.
result DREAM outperforms existing methods on complex tasks.
We show that Calabi-Yau manifolds are emergent from the commutative limit of six-dimensional noncommutative Hermitian U(1) instantons. Therefore we argue that the noncommutative Hermitian U(1) instantons correspond to quantized Calabi-Yau manifolds.
Study on Hermitian Calabi functional in complexified orbits of symplectic manifolds.
problem Analyzing the Hermitian Calabi functional on complexified orbits of symplectic manifolds.
method Explicit formula for Hessian of Hermitian Calabi functional, semi-positive definiteness proof, and weak parabolicity of Hermitian Calabi flow.
result Hessian of Hermitian Calabi functional is semi-positive definite on complexified orbits.
Calabi flow extended with bounded curvature integrals.
problem Extending Calabi flow on compact Kähler manifolds.
method Using bounded Lp scalar curvature integrals. result Calabi flow can be extended under certain curvature conditions.
Study of large mass limits of G2 and Calabi-Yau monopoles on specific manifolds.
problem Understanding the behavior of monopoles in the large mass limit on G2 and Calabi-Yau manifolds.
method Developed a structure theory for the limit of SU(2) G2-monopoles and Calabi-Yau monopoles, extracting singular abelian G2-monopoles with Dirac singularities. result Proved an energy identity for monopole bubbles in the large mass limit.
In this paper, the relationship between the existence of special lagrangian submanifolds and the collapsing of Calabi-Yau manifolds is studied. First, special lagrangian fibrations are constructed on some regions of bounded curvature and sufficiently collapsed in Ricci-flat Calabi-Yau manifolds. Then, in the opposite d…
Simplified argument for second order estimate in quaternionic Calabi-Yau problem.
problem Second order estimates for quaternionic Calabi-Yau problem on hyperkähler manifolds.
method Simplified argument to derive the estimate.
result Simplified derivation of second order estimate.
A generalized Calabi-Yau structure is a geometrical structure on a manifold which generalizes both the concept of the Calabi-Yau structure and that of the symplectic one. In view of a result of Lin and Tolman in generalized complex cases, we introduce in this paper the notion of a generalized moment map for a compact L…
In this paper, we study the behavior of Ricci-flat Kähler metrics on Calabi-Yau manifolds under algebraic geometric surgeries: extremal transitions or flops. We prove a version of Candelas and de la Ossa's conjecture: Ricci-flat Calabi-Yau manifolds related by extremal transitions and flops can be connected by a path c…
This paper classifies Calabi-Yau manifolds near cones.
problem Classifying Calabi-Yau manifolds near cones.
method Complete classification of smooth complete Calabi-Yau manifolds asymptotic to a given cone.
result Classification of all smooth complete Calabi-Yau manifolds near a given cone.
Superminimal surfaces in certain Einstein manifolds have a Calabi-Yau property.
problem Characterizing superminimal surfaces in specific Einstein manifolds.
method Utilizing twistor spaces and properties of holomorphic Legendrian curves.
result Superminimal surfaces in self-dual or anti-self-dual Einstein four-manifolds can be uniformly approximated by complete superminimal surfaces.
Solves Calabi-Yau equation on symplectic manifolds using measurable Kahler metrics.
problem Solving the Calabi-Yau equation on symplectic manifolds.
method Global deformation of almost complex structures compatible with symplectic form, constructing measurable Lipschitz Kahler metric.
result Existence theorem for solutions to the one-form type Calabi-Yau equation on closed symplectic manifolds.
Study explores Laplacian coflow versions on Calabi-Yau 7-manifolds.
problem Analyzing G2-structures on Calabi-Yau 7-manifolds. method Reduced Ansätze for the Laplacian coflow on various Calabi-Yau 7-manifolds.
result Obtained a modified Kähler-Ricci flow.
Uniform estimates for Calabi-Yau degenerations proved.
problem Calabi-Yau degenerations of polarised algebraic manifolds.
method Uniform Skoda and L∞-estimates for Kähler potentials. result Uniform Skoda type estimate and L∞-estimate for Calabi-Yau Kähler potentials proved. Estimates symplectic Calabi-Yau equation using Cheng-Yau method.
problem Estimating solutions to the Calabi-Yau equation on symplectic 4-manifolds.
method Applies a Cheng-Yau type estimate in the symplectic setting.
result Proves an a priori estimate for the symplectic Calabi-Yau equation.
New complete Calabi-Yau metrics found in complex space.
problem Finding metrics on complex spaces with specific conditions.
method Generalized Calabi ansatz, non-archimedean Monge-Ampère equation.
result Complete Calabi-Yau metrics constructed in Fano manifolds.