Friday, April 16, 2021

2021-04-23 / 16::0 ~ 17::0

by 김영락()

Sheaf cohomology and direct images are fundamental objects in algebraic geometry. However, they are defined in an abstract way (as right derived functors), and thus they are often hard to compute in explicit examples. In this talk, we briefly review Bernstein-Gel'fand-Gel'fand (BGG) correspondence and resolutions over an exterior algebra. Then, we review Tate resolutions and how it can be used to understand a given coherent sheaf and its cohomology groups in terms of Beilinson monad. Finally, we discuss an algorithm to compute direct images using Eisenbud-Erman-Schreyer's generalization on products of projective spaces. A part of the talk is a joint work in progress with J. Barrott and F.-O. Schreyer.

2021-04-21 / 17:00 ~ 18:00

콜로퀴엄 - Discrete Math:

by ()

Traditional clustering identifies groups of objects that share certain qualities. Tangles do the converse: they identify groups of qualities that typically occur together. They can thereby discover, relate, and structure types: of behaviour, political views, texts, or proteins. Tangles offer a new, quantitative, paradigm for grouping phenomena rather than things. They can identify key phenomena that allow predictions of others. Tangles also offer a new paradigm for clustering in large data sets. The mathematical theory of tangles has its origins in the theory of graph minors developed by Robertson and Seymour. It has recently been axiomatized in a way that makes it applicable to a wide range of contexts outside mathematics: from clustering in data science to predicting customer behaviour in economics, from DNA sequencing and drug development to text analysis and machine learning. This very informal talk will not show you the latest intricacies of abstract tangle theory (for which you can find links on the tangle pages of my website), but to win you over to join our drive to develop real tangle applications in areas as indicated above. We have some software to share, but are looking for people to try it out with us on real-world examples! Here are some introductory pages from a book I am writing on this, which may serve as an extended abstract: https://arxiv.org/abs/2006.01830

2021-04-20 / 16:30 ~ 17:30

학과 세미나/콜로퀴엄 - Discrete Math:

by 엄상일()

Bouchet introduced isotropic systems in 1983 unifying some combinatorial features of binary matroids and 4-regular graphs. The concept of isotropic system is a useful tool to study vertex-minors of graphs and yet it is not well known. I will give an introduction to isotropic systems.

2021-04-21 / 17:00 ~ 18:30

학과 세미나/콜로퀴엄 - 수리생물학:

by ()

This talk will be presented online. Zoom link: 709 120 4849 (pw: 1234) Age brings the benefit of experience and looking back at my job as a professor, there are a couple of things that fall into the category “I wish someone had told me that earlier”. In this seminar, I would like to share some of the things I learned and which, I hope, will be useful for younger scientists. The questions I will touch upon include What is productivity, for a scientist? What are qualities of successful people? How can one create motivation and success? How to organize myself? (project management; getting things done) How to communicate effectively? Seeking fulfillment The seminar is targeted at PhD students, postdocs, and junior group leaders.

2021-04-23 / 16:00 ~ 17:00

학과 세미나/콜로퀴엄 - 대수기하학: Introduction to infinity-categories V

by 조창연(QSMS Seoul National University)

This is part V of the lectures on the foundations of infinity-categories. After continued discussion about the role of model categories in the theory of infinity-categories, the simplicial and differential graded nerve constructions will be presented to provide a plethora of examples of infinity-categories. Finally, I'll talk about an analogy between the theories of ordinary categories and infinity-categories, which wraps up this series of talks.

2021-04-16 / 16:00 ~ 17:00

학과 세미나/콜로퀴엄 - 대수기하학: Introduction to infinity-categories IV

by 조창연(QSMS Seoul National University)

This is part IV of the series of lectures on the foundations of infinity-categories. n the first half, we'll cover the precise definition of infinity-categories based on quasi-categories. Some relationship between infinity-categories and model categories will be presented to help better understand the theory of infinity-categories in the remaining half.

2021-04-16 / 16:00 ~ 17:00

학과 세미나/콜로퀴엄 - PDE 세미나:

by ()

In this talk, I will present a result on the existence of 2-dimensional subsonic steady compressible flows around a finite thin profile with a vortex line at the trailing edge, which is a special case in the celebrated lifting line theory by Prandtl. Such a flow pattern is governed the two-dimensional steady compressible Euler equations. The vortex line attached to the trailing edge is a free interface corresponding to a contact discontinuity. Such a flow pattern is obtained as a consequence of structural stability of a uniform contact discontinuity. The problem is formulated and solved by an application of the implicit function theorem in a suitable weighted space. The main difficulties are the possible singularities at the fitting of the profile and the vortex line and the subtle instability of the vortex line. Some ideas of the analysis will be presented. This talk is based on joint works with Jun Chen and Aibin Zang at Yichun University. The research is supported in part by Hong Kong Earmarked Research Grants CUHK 14305315, CUHK 14302819, CUHK 14300917, and CUHK 14302917.

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