Given a variation of Hodge structures $V$ on a smooth complex quasi-projective variety $S$, its Hodge locus is the set of points $s$ in $S$ where the Hodge structure $V_s$...
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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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I shall discuss a recent work on how p-adic strings can produce perturbative quantum gravity, and an adelic physics interpretation of Tate's thesis. Zoom: https://harvard.zoom.us/j/91780604388?pwd=d3BqazFwbDZLQng0cEREclFqWkN4UT09
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High‐temperature superconductivity in cupper oxides, with critical temperature well above what was anticipated by the BCS theory, remains a major unsolved physics problem. The problem is fascinating because it is...
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Lacunary trigonometric sums are known to exhibit several properties that are typical of sums of iid random variables such as the central limit theorem, established by Salem and Zygmund, and...
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The analysis of complex systems often hinges on our ability to extract the relevant degrees of freedom from among the many others. Recently the information bottleneck (IB), a signal processing tool,...
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I'll talk about basic ruler and compass constructions, about math as exploration, about making space in mathematics, and about Harvard. Oh, and of course, the election. Please go to the...
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For any positive integer $n$, we explain why the total number of order $n$ elements in class groups of quadratic fields of discriminant having absolute value at most $X$ is...
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The increasing dimensionality of data in the modern machine learning age presents new challenges and opportunities. The high-dimensional settings allow one to use powerful asymptotic methods from probability theory and...
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The SSK model was introduced by Kosterlitz, Thouless and Jones as a simplification of the usual SK model with Ising spins. Fluctuations of its observables may be related to quantities...
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