Monday, February 8, 2021

2021-02-09 / 11:00 ~ 12:00

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Introduction: In this lecture series, we'll discuss algebro-geometric study on fundamental problems concerning tensors via higher secant varieties. We start by recalling definition of tensors, basic properties and small examples and proceed to discussion on tensor rank, decomposition, and X-rank for any nondegenerate variety $X$ in a projective space. Higher secant varieties of Segre (resp. Veronese) embeddings will be regarded as a natural parameter space of general (resp. symmetric) tensors in the lectures. We also review known results on dimensions of secants of Segre and Veronese, and consider various techniques to provide equations on the secants. In the end, we'll finish the lectures by introducing some open problems related to the theme such as syzygy structures and singularities of higher secant varieties.

2021-02-09 / 14:00 ~ 16:00

학과 세미나/콜로퀴엄 - PDE 세미나:

by 성기훈(카이스트)

The purpose of this reading seminar is to study the following: (1) Bourgain's invariant measure argument in stochastic PDE, (2) Uniqueness of the invariant measure (Gibbs measure) and its ergodicity, (3) Exponential converence to the Gibbs equilibrium. This seminar is mainly based on [1, 2, 3]. Tuesday, February 9, 2021 - 14:00 to 16:00 Bourgain's invariant measure argument in stochastic PDE and almost sure global existence of stochastic Gross-Pitaevskii equation

2021-02-08 / 14:00 ~ 16:00

학과 세미나/콜로퀴엄 - PDE 세미나:

by 성기훈(카이스트)

The purpose of this reading seminar is to study the following: (1) Bourgain's invariant measure argument in stochastic PDE, (2) Uniqueness of the invariant measure (Gibbs measure) and its ergodicity, (3) Exponential converence to the Gibbs equilibrium. This seminar is mainly based on [1, 2, 3]. Monday, February 8, 2021 - 14:00 to 16:00 Parabolic stochastic quantization, canonical stochastic quantization, Gaussian eld and Gibbs measures.

2021-02-08 / 16:00 ~ 17:00

학과 세미나/콜로퀴엄 - 대수기하학: Equivariant virtual classes

by Bhamidi Sreedhar(KIAS)

For a scheme with a group scheme action and an equivariant perfect obstruction theory we shall outline a proof of a virtual equivariant Riemann-Roch theorem. This is an extension of a result of Fantechi-Göttsche to the equivariant context. We shall further discuss a non-abelian virtual localization theorem, relating the virtual classes of the stack and virtual classes of the associated inertia stack for a naturally induced perfect obstruction theory. This talk is based on joint work with Charanya Ravi.

2021-02-09 / 17:00 ~ 18:00

학과 세미나/콜로퀴엄 - 대수기하학: The Green-Tao theorem for number fields II

by Wataru Kai(Tohoku University, Japan)

In the latter one hour, I will explain our generalization of their work to the general number fields based on my joint work with my Tohoku colleagues Masato Mimura, Akihiro Munemasa, Shin-ichiro Seki and Kiyoto Yoshino (arxiv:2012.15669). Time permitting, I will also touch upon its positive characteristic analog (arxiv:2101.00839). The case of the polynomial rings had also been conjectured by Green-Tao in the same paper and settled by Lê in 2011.

2021-02-09 / 16:00 ~ 17:00

학과 세미나/콜로퀴엄 - 대수기하학: The Green-Tao theorem for number fields I

by Wataru Kai(Tohoku University, Japan)

A famous theorem of Green and Tao says there are arbitrarily long arithmetic progressions consisting of prime numbers. In that 2008 paper, they predicted that similar statements should hold for prime elements of other number fields and the case of the Gaussian integers $Z[i]$ was subsequently settled by Tao. In the first of my two talks, I would like to share my (limited) knowledge about the background and history underlying their work.

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