An elliptic curve.
Does N divide its order?
Let’s work out the odds.
Everett W. Howe
Center for Communications Research, La Jolla
Dissertation: Elliptic curves and ordinary abelian varieties over finite fields (U.C. Berkeley, 1993)
The first part of my dissertation involved calculating estimates for the probability that a randomly-chosen elliptic curve over a finite field would have a given integer N dividing its number of points.
somewhere spherical, elsewhere
Saint Mary’s College, Notre Dame, IN
My work on differential geometry and dynamical systems, specifically geometric singularities, studies the ways that spheres can be deformed and certain points called umbilics (and higher-order generalizations thereof) that arise in isolated (sometimes unpredictable) locations on the deformed surface.
Umbilics are called locally spherical because they are locations where the original spherical shape is more or less preserved.
Less is more. More’s less.
Some is more than emptiness.
Count them, more or less.
Title: Range Searching: Emptiness, Reporting and Approximate Counting
Given a set of points in high dimensional space, we show how to preprocess them into a data structure such that given a range in space we can determine quickly whether this range is empty. We extending and improve the results of Matousek (1992), whose result was only for hyper planes, and Matousek & Agarwal (1994) who counted the points (with worse time bounds).
Our result has many applications such as, ray shooting on fat triangles being faster than on thin triangles (Less is more. More is less), various emptiness problems (Some is more than emptiness) and approximate counting data structures (Count them, more or less)
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