TITLE: Knot Invariants From Gauge Theory in Three, Four, and Five Dimensions ABSTRACT: I will explain connections between a sequence of theories in two, three, four, and five dimensions and...
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A multidimensional polynomial system is said to be sparse when the monomials present in the polynomials are fixed a priori. I will present classic and recent upper and lower bounds...
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This talk is organized as follows: 1. Physical Principles leading to Loop-current order and quantum criticality as the central feature in the physics of Cuprates. 2. Summary of the essentially...
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We consider eigenvector statistics of large symmetric random matrices. When the matrix entries are sampled from independent Gaussian random variables, eigenvectors are uniformly distributed on the sphere and numerous properties...
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The complexity of biological systems (among others) makes demands on the complexity of the mathematical modeling enterprise that could be satisfied with mathematical artificial intelligence of both symbolic and numerical...
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For a smooth proper (formal) scheme X defined over a valuation ring of mixed characteristic, the crystalline cohomology H of its special fiber has the structure of an F-crystal, to...
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Symmetry protected topological (SPT) phases are inevitable phases of quantum matter that are distinct from trivial phases only in the presence of unbroken global symmetries. These are characterized by anomalous boundaries...
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The 2D Toda system consists of a complicated set of infinitely many coupled PDEs in infinitely many variables that is known to assemble into an infinite-dimensional integrable system. Krichever and...
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Recent advances in deep learning exploit the structure in data and architectures. Graph Neural Network (GNN) is a powerful framework for learning with graph-structured objects, and for learning the interaction...
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How does a child learn to speak, without prior direct communication, nor with having dictionary to translate words from another language? How do we learn to play chess, with no...
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