The underdoped Cuprate exhibits a rich variety of unusual properties that have been exposed after years of experimental investigations. They include a pseudo-gap near the anti-nodal points and “Fermi arcs”...
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The derived category of a Fano threefold Y of Picard rank 1 and index 2 admits a semiorthogonal decomposition. This defines a non-trivial subcategory Ku(Y) called the Kuznetsov component, which...
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The generic vanishing theorem of Green-Lazarsfeld says that for general elements in the Picard variety of a projective manifold, their cohomology groups vanish in all degrees. Moreover, the cohomological jumping...
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How can we use the theory of dynamical systems in analyzing the capabilities of neural networks? Understanding the representational power of Deep Neural Networks (DNNs) and how their structural properties (e.g.,...
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An important open problem is whether there exists a finite quantum group which cannot be cooked up from (classical) finite groups. A finite purely quantum group would be a finite dimensional Hopf C*-algebra (Kac algebra) K...
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There are many natural sequences of moduli spaces in algebraic geometry whose homology approaches a "limit", despite the fact that the spaces themselves have growing dimension. If these moduli spaces...
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I will give an overview of my work with Aasen and Mong on using fusion categories to find and analyse topological defects in two-dimensional classical lattice models and quantum chains....
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The lecture follows the title as a guiding thread. Zoom: https://harvard.zoom.us/j/96759150216
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In this talk, we will discuss a geometric construction of p-adic analogues of Maass--Shimura differential operators on automorphic forms on Shimura varieties of PEL type A or C (that is,...
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In this talk, we will discuss a geometric construction of p-adic analogues of Maass--Shimura differential operators on automorphic forms on Shimura varieties of PEL type A or C (that is,...
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