Determining the computational complexity of matrix multiplication has been one of the central open problems in theoretical computer science ever since in 1969 Strassen presented an algorithm for multiplication of...
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Least-mean squares (LMS) solvers such as Linear / Ridge / Lasso-Regression, SVD and Elastic-Net not only solve fundamental machine learning problems, but are also the building blocks in a variety of...
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In this talk, I present recent joint work with Tian Lan, Xiao-Gang Wen, Zhi-Hao Zhang and Hao Zheng (arXiv:2003.08898). We propose a mathematical theory of symmetry protected trivial (SPT) order,...
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In this talk, I present recent joint work with Tian Lan, Xiao-Gang Wen, Zhi-Hao Zhang and Hao Zheng (arXiv:2003.08898). We propose a mathematical theory of symmetry protected trivial (SPT) order,...
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We study the supersymmetric partition function of a 2d linear sigma-model whose target space is a torus with a complex structure that varies along one worldsheet direction and a Kähler...
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The twisted bilayer graphene (TBG) near the magic angle around 1 degree hosts topological flat moiré electron bands, and exhibits a rich tunable strongly interacting physics. Correlated insulators and Chern...
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The purest forms of functional programming use monads to define computations that happen within contexts. For instance, the IO monad, which is a standard object in Haskell as well as...
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The generalization gap of a learning algorithm is the expected difference between its performance on the training data and its performance on fresh unseen test samples. Modern deep learning algorithms...
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The local Langlands conjectures predict that (packets of) irreducible complex representations of p-adic reductive groups (such as GL_n(Q_p), GSp_2n(Q_p), etc.) should be parametrized by certain representations of the Weil-Deligne group. ...
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From the viewpoint of spin glass theory, restricted Boltzmann machines represent a veritable challenge, as to the lack of convexity prevents us to use Guerra's bounds. Therefore even the replica symmetric approximation for the free energy presents some challenges. I will...
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