In this talk, I will describe how symmetry can enrich strong-randomness quantum critical points and phases, and lead to robust topological edge modes coexisting with critical bulk fluctuations. Our approach provides a...
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In this talk, I will introduce the Gopakumar-Vafa(GV) invariant and show one calculation on the nonreduced cycle. The GV invariant is an integral invariant predicted by physicists that counts the...
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Deep learning has revolutionized our ability to generate novel images and 3D shapes. Typically neural networks are trained to map a high-dimensional latent code to full realistic samples. In this...
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Inspired by fractional quantum Hall physics and Tannaka-Krein duality, it is conjectured that every modular tensor category (MTC) or (2+1)-topological quantum field theory (TQFT) can be realized as the representation...
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TITLE: Kunihiko Kodaira and complex manifolds. ABSTRACT: Kodaira’s motivation was to generalize the theory of Riemann surfaces in Weyl’s book to higher dimensions. After quickly recalling the chronology of Kodaira, I will...
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In the 90s', Witten gave a physical derivation of an isomorphism between the Verlinde algebra of $GL(n)$ of level $l$ and the quantum cohomology ring of the Grassmannian $\text{Gr}(n,n+l)$. In...
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TITLE: Birational geometry ABSTRACT: About main achievements in birational geometry during the last fifty years. Written articles will accompany each lecture in this series and be available as part of the...
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The infamous sign problem leads to an exponential complexity in Monte Carlo simulations of generic many-body quantum systems. Nevertheless, many phases of matter are known to admit a sign-problem-free representative,...
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TITLE: Hodge structures and the topology of algebraic varieties ABSTRACT: We review the major progress made since the 50’s in our understanding of the topology of complex algebraic varieties. Most of...
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The geometry of rhombic tilings and tessellations like the Penrose tiling have captivated mathematicians and artists alike. Hidden in the geometry of certain rhombic tilings of certain polygons, though, is...
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