We study local and global Hamiltonian dynamical behaviors of some Lagrangian submanifolds near a Lagrangian sphere S in a symplectic manifold X. When dim S = 2, we show that...
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Quantum entanglement has played a key role in studying emergent phenomena in strongly-correlated many-body systems. Remarkably, The entanglement properties of the ground state encodes information on the nature of excitations. ...
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We consider the problem of finding 3 positive integers (a,b,c) such that a/(b+c)+b/(c+a)+c/(a+b)=4. We will examine how the problem became a viral post on Facebook, solve the problem using elliptic...
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Graph-structured data is ubiquitous throughout the natural and social sciences, from telecommunication networks to quantum chemistry. Building relational inductive biases into deep learning architectures is crucial if we want systems...
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The Langlands program is a far-reaching collection of conjectures that relate different areas of mathematics including number theory and representation theory. A fundamental problem on the representation theory side of...
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I'll review the basic construction of Randall-Sundrum braneworlds and some of their applications to formal problems in quantum field theory. I will highlight some recent results regarding scenarios with mismatched...
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We consider a monopolist who wishes to sell n goods to a single additive buyer, where the buyer's valuations for the goods are drawn according to independent distributions. It is...
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This talk aims to summarize a project I was involved in during the past 5 years, which links together many areas in math, CS and physics. I hope to explain our...
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I will describe an analogue of Saito's theory of primitive forms for Calabi-Yau A-infinity categories. Under some conditions on the Hochschild cohomology of the category, this construction recovers the (genus...
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Certain patterns of symmetry fractionalization in (2+1)D topologically ordered phases of matter can be anomalous, which means that they possess an obstruction to being realized in purely (2+1)D. In this...
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