The well-known classical Eichler-Shimura relation for modular curves asserts that the Hecke operator $T_p$ is equal, as an algebraic correspondence over the special fiber, to the sum of Frobenius and...
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We review how historically the problem of string phenomenology lead theoretical physics first to algebraic/diffenretial geometry, and then to computational geometry, and now to data science and AI. With the...
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Hierarchical spin glasses such as the generalised random energy model are known to faithfully model typical energy landscapes in the classical theory of mean-field spin glasses. Their built-in hierarchical structure...
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Simplified as it is, the Hubbard model embodies much of the complexity of the `strong correlation problem’ and has established itself as a paradigmatic model in the field. In this...
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I will discuss the problem of understanding the collapsing behavior of Ricci-flat Kahler metrics on a Calabi-Yau manifold that admits a holomorphic fibration structure, when the Kahler class degenerates to...
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I will discuss recent work on computing the top weight cohomology of A_g for g up to 7. We use combinatorial methods coming from the relationship between the top weight...
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Economics and social science research often require analyzing datasets of sensitive personal information at fine granularity, with models fit to small subsets of the data. Unfortunately, such fine-grained analysis can...
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Consider a free group and its group von Neumann algebra A. Finding criteria on the boundedness or complete boundedness of multipliers on the Lp(A) is a major subject of analysis on...
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TITLE: Classical and quantum integrable systems in enumerative geometry ABSTRACT: For more than a quarter of a century, thanks to the ideas and questions originating in modern high energy physics, there has been a...
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We report on a new development in asymptotic Hodge theory, arising from work of Golyshev--Zagier and Bloch--Vlasenko, and connected to the Gamma Conjectures in Fano/LG-model mirror symmetry. The talk will...
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