Wednesday, April 14, 2021

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

콜로퀴엄 - Discrete Math:

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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.

2021-04-15 / 17:00 ~ 17:30

학과 세미나/콜로퀴엄 - 기타: Practical considerations for measuring the effective reproductive number

by 최선화()

2021-04-15 / 16:30 ~ 17:00

학과 세미나/콜로퀴엄 - 기타: Mathematical modeling for infectious disease using epidemiological data

by 이효정(NIMS-Busan Center for Medical Mathematics)

TBA

2021-04-14 / 17:00 ~ 18:00

학과 세미나/콜로퀴엄 - Discrete Math: Ramsey properties of semilinear graphs

by István Tomon(Department of Mathematics, ETH Zurich)

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

학과 세미나/콜로퀴엄 - 수리생물학:

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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.

2021-04-15 / 11:00 ~ 12:00

학과 세미나/콜로퀴엄 - 수리생물학:

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This talk will be presented online. Zoom link: 709 120 4849 (pw: 1234) Abstract: Life science has been a prosperous subject for a long time, and is still developing with high speed now. One of its major aims is to study the mechanisms of various biological processes on the basis of biological big-data. Many statistics-based methods have been proposed to catch the essence by mining those data, including the popular category classification, variables regression, group clustering, statistical comparison, dimensionality reduction, and component analysis, which, however, mainly elucidate static features or steady behavior of living organisms due to lack of temporal data. But, a biological system is inherently dynamic, and with increasingly accumulated time-series data, dynamics-based approaches based on physical and biological laws are demanded to reveal dynamic features or complex behavior of biological systems. In this talk, I will present a new concept “dynamics-based data science” and the approaches for studying dynamical bio-processes, including dynamical network biomarkers (DNB), autoreservoir neural networks (ARNN) and partical cross-mapping. These methods are all data-driven or model-free approaches but based on the theoretical frameworks of nonlinear dynamics. We show the principles and advantages of dynamics-based data-driven approaches as explicable, quantifiable, and generalizable. In particular, dynamics-based data science approaches exploit the essential features of dynamical systems in terms of data, e.g. strong fluctuations near a bifurcation point, low-dimensionality of a center manifold or an attractor, and phase-space reconstruction from a single variable by delay embedding theorem, and thus are able to provide different or additional information to the traditional approaches, i.e. statistics-based data science approaches. The dynamical-based data science approaches will further play an important role in the systematical research of biology and medicine in future.

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:

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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.

2021-04-14 / 15:30 ~ 16:30

학과 세미나/콜로퀴엄 - 정수론:

by 황원태(고등과학원)

Let $X$ be an abelian variety of dimension $g$ over a field $k$. In general, the group $\textrm{Aut}_k(X)$ of automorphisms of $X$ over $k$ is not finite. But if we fix a polarization $\mathcal{L}$ on $X$, then the group $\textrm{Aut}_k(X,\mathcal{L})$ of automorphisms of the polarized abelian variety $(X,\mathcal{L})$ over $k$ is known to be finite. Then it is natural to ask which finite groups can be realized as the full automorphism group of a polarized abelian variety over some field $k.$ In one of earlier works, a complete classification of such finite groups was given for the case when $k$ is a finite field, $g$ is an odd prime, and $X$ is simple. One interesting thing is that the maximal such a finite group was a cyclic group of order $4g+2$ only when $g$ is a Sophie Germain prime. Another notable thing is the fact that the abelian variety that was constructed to achieve the maximal cyclic group splits over $\overline{k}$, an algebraic closure of $k.$ \\ In this talk, we provide a construction of an absolutely simple abelian variety of dimension $g$ ($g$ being a Sophie Germain prime) over a finite field $k$, which attains the maximal automorphism group. This can be regarded as the counterpart for the previous construction. Also, we briefly describe the asymptotic behavior of the characteristic of the base field $k$ for which we can give such a construction. Finally, if time permits, we take a closer look at the case of $g=5$ by introducing the Newton polygon of an abelian variety of dimension $5.$ (If you want to join the seminar, please contact Bo-Hae Im to get the zoom link.)

2021-04-15 / 16:15 ~ 17:15

콜로퀴엄 - 콜로퀴엄: Geometry of Elie Cartan´s ˝Pfaffian systems in 5 variables˝

by 황준묵(IBS 복소기하학 연구단장)

Elie Cartan's celebrated paper ˝Pfaffian systems in 5 variables˝ in 1910 studied the equivalence problem for general Pfaffian systems of rank 3 in 5 variables as the curved version of the Pfaffian system with G_2 symmetry. The G_2 case admits a beautiful geometric correspondence with Engel's PDE system. We give a historical overview of Cartan's paper and discuss recent works extending the correspondence to curved cases, which is based on ideas from geometric control theory and algebraic geometry.

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