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Title:ÌýDiscrete quantum walks, embeddings and designs

Abstract:

We construct a quantum walk from an embedding of a graph.

Title:ÌýPerfect state transfer on Hadamard diagonalizable graphs

Abstract:

A (weighted) graph whose Laplacian matrix is diagonalizable by a Hadamard matrix is said to be Hadamard diagonalizable.

Title:ÌýBoundary measurement and sign variation in real projective space

Abstract:

Title:ÌýSublinear separators in intersection graphs of convex shapes

Abstract:Ìý

A balanced separator of an n-vertex graph is set of vertices whose deletion leaves only components of size at most 2n/3.

Title:ÌýCutting a square into triangles of equal area

Abstract:

Suppose you are given a square and asked to cut it into n triangles of equal area. If n is even the problem is almost trivial, but when n is odd the problem becomes much harder.

Title:ÌýPerfect state transfer on Cayley graphs

Abstract:

Perfect state transfer on Cayley graphs

Title:ÌýInterpolated versions of the Central Limit Theorem, and crossings of pair-partitions

Abstract:

Title:ÌýEdge-maximal graphs on surfaces

Abstract:

It is straightforward to show that, with the exception ofÌýsmall complete graphs, every edge-maximal planar graphÌýtriangulates the plane.

Title:ÌýMaximizing non-monotone submodular functions

Abstract:

Optimization of non-monotone submodular functions has applications in the maximum cut and maximum directed cut problems for graphs.

Title:ÌýA Quantum Query Complexity Trichotomy for Regular Languages

Abstract:

We consider theÌýquantumÌýquery complexity of regular languages and discover a surprising trichotomy: each regular language has query complexity either Theta(1), ~Theta(sqrt(n)) or Theta(n).Ìý