Imagine the universe is a periodic crystal. If gravity makes space negatively curved, the thin walls of the crystalline structure might trace out a pattern of circles in the sky, visible...
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A ray in a graph G = (V, E) is a sequence X (possibly infinite) of distinct vertices x0, x1, . . . such that, for every i, E(xi ,...
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I'll discuss a recent connection between two seemingly unrelated problems: how to measure a collection of quantum states without damaging them too much ("gentle measurement"), and how to provide statistical...
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There is a large literature about points of bounded height on varieties, and about number fields of bounded discriminant. We explain how to unify these two questions by means of...
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We provide a new parton theory for hole doped cuprates. We will describe both a pseudogap metal with small Fermi surfaces and the conventional Fermi liquid with large Fermi surfaces...
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**CANCELED** Most 4-manifolds do not admit symplectic forms, but most admit 2-forms that are "nearly" symplectic. Just like the Seiberg-Witten (SW) invariants, there are Gromov invariants that are compatible with...
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Graph theory is important in information theory. We introduce a quantization process on graphs and apply the quantized graphs in quantum information. The quon language provides a mathematical theory to...
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I will construct LG mirrors for the Johnson-Kollár series of anticanonical del Pezzo surfaces in weighted projective 3-spaces. The main feature of these surfaces is that their anticanonical linear system...
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For a moduli space $M$ of stable sheaves over a K3 surface $X$, we propose a series of conjectural identities in the Chow rings $CH_\star (M \times X^\ell),\, \ell \geq...
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Symplectic embedding problems are at the core of symplectic topology. Many results have been found involving balls, ellipsoids and polydisks. More recently, there has been progress on problems involving lagrangian...
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