We consider a complex Ginibre ensemble of random matrices with a deformation $H=H_0+A$, where $H_0$ is a Gaussian complex Ginibre matrix and $A$ is a rather general deformation matrix. The...
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The notion of an abstract group encapsulates and illuminates concrete manifestations of symmetry. Recently in quantum field theory there have been discussions of "higher symmetry" and "noninvertiblesymmetry" and their applications. ...
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Erdos-Kleitman-Rothschild proved that the number of triangle-free graphs on n vertices is asymptotic to the number of bipartite graphs; or in other words, a typical triangle-free graph is a random...
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Transcendental numbers form a mysterious and large class of complex numbers: they are defined as complex numbers that are not the solution of a polynomial equation, and include the numbers...
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It is important to understand if the `solutions' of non-linear evolutionary PDEs persist for all time or become extinct in finite time through the blow-up of invariant entities. Now the...
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I will speak about my recent work (joint with Sam Panitch) constructing the 3d quantum trace map, a homomorphism from the Kauffman bracket skein module of an ideally triangulated 3-manifold...
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When is a real smooth manifold secretly a complex manifold? For this, it is necessary, but not sufficient, for the manifold’s tangent bundle to be a complex vector bundle, a...
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My thesis discusses a bridge between equivariant topology and combinatorics. The kind of problem I look at is an inherently discrete problem which can be solved by translating the problem into...
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Last time we saw how to identify THH(ell^hZ)\otimes V with THH(ell^BZ)\otimes V at the level of spectra with Frobenius, for V a type 2 complex. I will explain how this...
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In 2016, Doran, Harder, and I conjectured a mirror symmetric relationship between Tyurin degenerations and splittings of codimension 1 fibrations on Calabi-Yau manifolds. In this talk I will discuss recent...
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