Kevin P. Costello

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The modular envelope of a cyclic operad is the smallest modular operad containing it. A modular operad is constructed from moduli spaces of Riemann surfaces with boundary; this modular operad is shown to be the modular envelope of the A∞ cyclic operad. This gives a new proof of the result of Harer-Mumford-Thurston-Penner-Kontsevich that a cell complex built(More)
Given fixed 0 = q0 < q1 < q2 < · · · < qk = 1 a constellation in [n] is a scaled translated realization of the qi with all elements in [n], i.e., p, p + q1d, p + q2d, . . . , p + qk−1d, p + d. We consider the problem of minimizing the number of monochromatic constellations in a two coloring of [n]. We show how given a coloring based on a block pattern how(More)
This paper gives a way to renormalise certain quantum field theories on compact manifolds. Examples include Yang-Mills theory (in dimension 4 only), Chern-Simons theory and holomorphic Chern-Simons theory. The method is within the framework of the Batalin-Vilkovisky formalism. Chern-Simons theory is renormalised in a way respecting all symmetries (up to(More)
We consider the performance of two classic approximation algorithms which work by scanning the input and greedily constructing a solution. We investigate whether running these algorithms on a random permutation of the input can increase their performance ratio. We obtain the following results: 1. Johnson's approximation algorithm for MAX-SAT is one of the(More)