YMSC seminar on complex algebraic geometry | Counting l-adic local systems on a curve over a fini...

Abstract： In 1981, Drinfeld enumerated the number of irreducible l-adic local systems of rank two on a projective smooth curve fixed by the Frobenius endomorphism. Interestingly, this number looks

Moduli Spaces and Related Topics | Universal holomorphic maps, conflict between fully

Abstract： In the space O(C,C) of entire functions, equipped with the open-compact topology, an element is called universal if its translation orbit is dense. It is hypercyclic w.r.t some translati...

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求真大讲堂讲座回顾｜ 第五十一讲：深度神经网络架构漫谈

引言 求真书院强调通识教育，旨在培养大师级“通才”。“求真大讲堂”是求真书院学生的通识必修环节，由求真书院院长丘成桐先生倡议设立，主题内容包罗万象，从人文诗词到天文科技，从沟通表达到艺术美学，皆聘请...

Optimization Methods for Machine Learning

Introduction Stochastic Gradient Descent (SGD), in one form or another, serves as the workhorse method for training modern machine learning models. Amidst its myriad variations, the SGD domain is

Operator algebras, bi-unitary connections and tensor networks

Introduction Tensor categories have emerged as a new type of "quantum symmetry" generalizing classical group symmetry in various fields of mathematics and physics such as quantum groups, quantum

Elliptic complex reflection groups and SeibergWitten integrable systems | BIMSA Integrable System...

Abstract For any abelian variety X with an action of a finite complex reflection group W, Etingof, Felder,Ma and Veselov constructed a family of integrable systems on T*X. When X is a product

Hypergraph decompositions and their applications | Research seminar in Discrete Mathematics

Abstract Many combinatorial objects can be thought of as a hypergraph decomposition, i.e. a partition of(the edge set of) one hypergraph into (the edge sets of) copies of some other hypergraphs.

Model of Josephson junction, dynamical systems on T2, isomonodromic deformations and Painleve 3

Abstract The tunneling effect predicted by B.Josephson (Nobel Prize, 1973) concerns the Josephsoniunction: two superconductors separated by a arrow dielectric. lt states existence

Differential Geometry Seminar | The volume of a divisor and cusp excursions of geodesics in

Abstract： The volume of a divisor on an algebraic variety measures the growth rate of the dimension of the space of sections of tensor powers of the associated line bundle. In the case of certain