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0111 · Jan 200519922001200920172026
7 results for pinwheel

The study explores pinwheels in symplectic surfaces and non-squeezing of rational homology balls.

problem Understanding when Lagrangian pinwheels embed in symplectic rational and ruled surfaces.
method Almost toric fibrations and symplectic rational blow-up.
result A rational homology ball embeds into a rational homology cylinder if and only if the parameter is greater than or equal to 1.

Study symplectic forms on manifolds to find Lagrangian pinwheels that can be separated.

problem Determine conditions for symplectic forms to carry disjoint Lagrangian pinwheels.
method Use rational blow-up to analyze Lagrangian pinwheels in symplectic manifolds.
result Conditions for disjunction of Lagrangian pinwheels in specific manifolds.

We give a necessary and sufficient condition for the addition of a collection of disjoint bypasses to a convex surface to be universally tight -- namely the nonexistence of a polygonal region which we call a virtual pinwheel.

2005-01-21abs ↗pdf ↗

We study Lagrangian embeddings of a class of two-dimensional cell complexes Lp,qL_{p,q} into the complex projective plane. These cell complexes, which we call pinwheels, arise naturally in algebraic geometry as vanishing cycles for quotient singularities of type 1p2(pq1,1)\frac{1}{p^2}(pq-1,1) (Wahl singularities). We show that …

2016-06-28abs ↗pdf ↗

We present a method for finding embedded nullhomologous tori in standard 4-manifolds which can be utilized to change their smooth structure. As an application, we show how to obtain infinite families of simply connected smooth 4-manifolds with b^+ = 1 and b^- = 2,...,7, via surgery on nullhomologous tori embedded in th…

2010-04-18abs ↗pdf ↗

We consider a novel stochastic multi-armed bandit setting, where playing an arm makes it unavailable for a fixed number of time slots thereafter. This models situations where reusing an arm too often is undesirable (e.g. making the same product recommendation repeatedly) or infeasible (e.g. compute job scheduling on ma…

2019-07-27abs ↗pdf ↗