Wednesday, April 21, 2021

2021-04-27 / 16:30 ~ 17:30

by 안정호()

We introduce a new subclass of chordal graphs that generalizes split graphs, which we call well-partitioned chordal graphs. Split graphs are graphs that admit a partition of the vertex set into cliques that can be arranged in a star structure, the leaves of which are of size one. Well-partitioned chordal graphs are a generalization of this concept in the following two ways. First, the cliques in the partition can be arranged in a tree structure, and second, each clique is of arbitrary size. We mainly provide a characterization of well-partitioned chordal graphs by forbidden induced subgraphs and give a polynomial-time algorithm that given any graph, either finds an obstruction or outputs a partition of its vertex set that asserts that the graph is well-partitioned chordal. We demonstrate the algorithmic use of this graph class by showing that two variants of the problem of finding pairwise disjoint paths between k given pairs of vertices are in FPT, parameterized by k, on well-partitioned chordal graphs, while on chordal graphs, these problems are only known to be in XP. From the other end, we introduce some problems that are polynomial-time solvable on split graphs but become NP-complete on well-partitioned chordal graphs. This is joint work with Lars Jaffke, O-joung Kwon, and Paloma T. Lima.

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

학과 세미나/콜로퀴엄 - 대수기하학:

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

2021-04-26 / 16:30 ~ 17:30

학과 세미나/콜로퀴엄 - 계산수학 세미나: An Image inpainting via a constrained smoothing and dynamic mode decomposition

by 이영주(Texas State Univ.)

In this talk, we present an algebraic and graph theoretic (data-based) image inpainting algorithm. The algorithm is designed to reconstruct area or volume data from one and two dimensional slice data. More precisely, given one or two dimensional slice data, our algorithm begins with a simple algebraic pre-smoothing of the data, constructs low dimensional representation of pre-smoothed data via Dynamic Mode Decomposition, performs initial area or volume reconstruction via interpolation, and finishes with smoothing the outcome using a constraint bilateral smoothing. Numerical experiments including MRI of a three year old and a CT scan of a Covid-19 patient, are presented to demonstrate the superiority of the proposed techniques in comparisons with other commercial and published methods. Some further applications we are currently doing will also be presented. This work is jointly done with Gwanghyun Jo and Ivan Ojeda-Ruiz.

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.

Events for the 취소된 행사 포함