For links with vanishing pairwise linking numbers, the link components bound pairwise disjoint surfaces in . In this paper, we describe the set of genera of such surfaces in terms of the -function, which is a link invariant from Heegaard Floer homology. In particular, we use the -function to give lower bou…
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17 results for “H-functional”
We study Heegaard Floer homology and various related invariants (such as the -function) for two-component L-space links with linking number zero. For such links, we explicitly describe the relationship between the -function, the Sato-Levine invariant and the Casson invariant. We give a formula for the Heegaard Fl…
The paper explores fibered and quasi-positive links, introducing new families and invariants.
problem Understanding the structure of -space links and their properties.
method Using the H-function as a concordance link invariant.
result Introduced a subfamily of fibered strongly quasi-positive -space links and an infinite family of non-quasi-positive -space links.
Researchers introduce new functionals to measure distance from Kähler-Einstein metrics.
problem Estimating how close a metric is to Kähler-Einstein.
method Introducing Ricci-Calabi and H-functionals, and proving moment weight inequalities and Hessian formulas.
result Established inequalities and formulas to measure distance and conditions for existence of Kähler-Einstein metrics.
It it known that the set of L-space surgeries on a nontrivial L-space knot is always bounded from below. However, already for two-component torus links the set of L-space surgeries might be unbounded from below. For algebraic two-component links we provide three complete characterizations for the boundedness from below…
An immersed concordance between two links is a concordance with possible self-intersections. Given an immersed concordance we construct a smooth four-dimensional cobordism between surgeries on links. By applying -invariant inequalities for this cobordism we obtain inequalities between the -functions of links, whi…
New method aligns diffusion models for inference-time properties without retraining.
problem Aligning pre-trained diffusion models for desired inference-time properties.
method Variationally stable Doob's matching for provable guidance estimation.
result Consistent estimator of guidance with non-asymptotic convergence guarantees.
We compute different versions of link Floer homology and for any -space link with two components. The main approach is to compute the -function of the filtered chain complex which is determined by the Alexander polynomials of every sublink of the -space link. As an application, Thurst…
Study area and coarea formulas for graphs and submanifolds in Carnot groups.
problem Understanding geometric properties of submanifolds in Carnot groups.
method Developed area and coarea formulas for intrinsic graphs and submanifolds.
result Deduced density properties for Hausdorff measures and coarea formula for Carnot groups.
In recent work, Boltzmann and Fokker-Planck equations were derived for the "Yard-Sale Model" of asset exchange. For the version of the model without redistribution, it was conjectured, based on numerical evidence, that the time-asymptotic state of the model was oligarchy -- complete concentration of wealth by a single …
Paper proves Łojasiewicz inequalities near simple bubble trees on surfaces.
problem Proving Łojasiewicz inequalities for critical points on surfaces.
method Deriving sufficient conditions for Łojasiewicz inequalities near almost-critical points in a Hilbert space.
result Sequences of almost critical points satisfy Łojasiewicz inequalities as they approach the first non-trivial bubble tree.
We present a complete classification of Einstein metrics on the space M = I \times S^3, where I is the interval (0,l) or (0,\infty) or their closures, and we consider separate metric functions f and h (functions of I) for the base and fiber of the Hopf fibration S^1 -> S^3 -> S^2. All such metrics yielding smooth and c…
The Kähler-Ricci flow yields bounds on optimal degenerations and Fano manifolds.
problem Bounding optimal degenerations and Fano manifolds using the Kähler-Ricci flow.
method Using the Kähler-Ricci flow to establish bounds on the Donaldson-Futaki invariant.
result Lower bound for Donaldson-Futaki invariant of optimal degenerations.
Unique K-polystable degenerations for Fano varieties confirmed.
problem Algebraic uniqueness of Kähler-Ricci flow limits on Fano manifolds.
method Study of optimal degeneration problems via new functionals of real valuations.
result Confirm algebraic uniqueness of Kähler-Ricci flow limits on Fano manifolds.
We prove that on Fano manifolds, the Kähler-Ricci flow produces a "most destabilising" degeneration, with respect to a new stability notion related to the H-functional. This answers questions of Chen-Sun-Wang and He. We give two applications of this result. Firstly, we give a purely algebro-geometric formula for the su…
Efficiently reduces computational burden of rollout acquisition functions in Bayesian optimization.
problem Expensive computation of rollout acquisition functions in Bayesian optimization.
method Combines quasi-Monte Carlo, common random numbers, and control variates to reduce computational burden. Formulates a policy-search approach to eliminate the need to optimize the rollout acquisition function.
result Significant reduction in computational burden of rollout acquisition functions.
We derive generalized estimators for a number of spatial statistics that have been used in the analysis of spatially resolved omics data, such as Ripley's K, H and L functions, clustering index, and degree of clustering, which allow these statistics to be calculated on data modelled by arbitrary random measures (RMs). …