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- KEVIN COSTELLO
- 2004

This is the first of two papers which construct a purely algebraic counterpart to the theory of Gromov-Witten invariants (at all genera). These GromovWitten type invariants depend on a Calabi-Yau A∞ category, which plays the role of the target in ordinary Gromov-Witten theory. When we use an appropriate A∞ version of the derived category of coherent sheaves… (More)

Let Qn denote a random symmetric n by n matrix, whose upper diagonal entries are i.i.d. Bernoulli random variables (which take values 0 and 1 with probability 1/2). We prove that Qn is non-singular with probability 1 − O(n−1/8+δ) for any fixed δ > 0. The proof uses a quadratic version of Littlewood-Offord type results concerning the concentration functions… (More)

- Kevin Costello
- 2010

- Kevin Costello
- 2004

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)

In this note, I discuss a dual version of the ribbon graph decomposition of the moduli spaces of Riemann surfaces with boundary and marked points, which I introduced in the unpublished preprint [1], and used in [2] to construct open-closed topological conformal field theories. This dual version of the ribbon graph decomposition is a compact orbi-cell… (More)

- Steve Butler, Kevin P. Costello, Ronald L. Graham
- Experimental Mathematics
- 2010

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)

- Kevin Costello, Owen Gwilliam
- 2012

- KEVIN COSTELLO
- 2007

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)

- Kevin P. Costello, Asaf Shapira, Prasad Tetali
- SODA
- 2011

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)

- Kevin P. Costello, Prasad Tetali, Pushkar Tripathi
- ArXiv
- 2012

We consider the following stochastic optimization problem first introduced by Chen et al. in [7]. We are given a vertex set of a random graph where each possible edge is present with probability pe. We do not know which edges are actually present unless we scan/probe an edge. However whenever we probe an edge and find it to be present, we are constrained to… (More)