Monday, September 9, 2024

2024-09-13 / 14:00 ~ 16:00

by 김현(IBS 의생명수학그룹)

In this talk, we discuss the paper “Deep learning linking mechanistic models to single-cell transcriptomics data reveals transcriptional bursting in response to DNA damage” by Zhiwei Huang, et. al., bioRxiv, 2024.

2024-09-12 / 11:50 ~ 12:40

대학원생 세미나 - 대학원생 세미나:

by 조대희()

In this presentation, I will present an analytic non-iterative approach for recovering a planar isotropic elastic inclusion embedded in an unbounded medium from the elastic moment tensors (EMTs), which are coefficients for the multipole expansion of field perturbation caused by the inclusion. EMTs contain information about the inclusion's material and geometric properties and, as is well known, the inclusion can be approximated by a disk from leading-order EMTs. We define the complex contracted EMTs as the linear combinations of EMTs where the expansion coefficients are given from complex-valued background polynomial solutions. By using the layer potential technique for the Lamé system and the theory of conformal mapping, we derive explicit asymptotic formulas in terms of the complex contracted EMTs for the shape of the inclusion, treating the inclusion as a perturbed disk. These formulas lead us to an analytic non-iterative algorithm for elastic inclusion reconstruction using EMTs. We perform numerical experiments to demonstrate the validity and limitations of our proposed method.

2024-09-13 / 10:30 ~ 12:30

학과 세미나/콜로퀴엄 - 대수기하학:

by ()

I will describe recent joint work with Keller VandeBogert on constructing pure free resolutions over quadric hypersurface rings. Along the way I will describe some connections between total positivity and Koszul algebras and some conjectures regarding the homotopy Lie algebra and its "fattened" versions.

2024-09-12 / 14:00 ~ 16:00

학과 세미나/콜로퀴엄 - 응용수학 세미나:

by ()

In this series of lectures, we will discuss fundamental concepts of Bayesian inference and its applications to dynamical systems in the context of data assimilation. The focus is on the assimilation step, which combines observation data with a prediction model. The lectures will discuss Gaussian and non-Gaussian approaches, including Kalman and particle filters. We will also discuss implementations of various algorithms and consider their computational benefits and efficiency. It is recommended to know basic numerical analysis for predictions, but it is optional to understand the main ideas of the lectures.

2024-09-11 / 15:00 ~ 17:00

학과 세미나/콜로퀴엄 - 응용수학 세미나:

by ()

2024-09-12 / 16:15 ~ 17:15

학과 세미나/콜로퀴엄 - 콜로퀴엄:

by 오정석(서울대학교 수리과학부)

There have been at least two surprising events to geometers in 80-90s that they had to admit physics really helps to solve classical problems in geometry. Donaldson proved the existence of exotic 4-dimensional Euclidean space using gauge theory and Givental counts rational curves in quintic threefolds using Feynman diagram in string theory. These events hugely popularised new mathematical topics such as mirror symmetry and enumerative geometry via moduli spaces. In this talk, we present what happened in this field in a past few decades and something happening right now.

2024-09-12 / 10:30 ~ 11:30

학과 세미나/콜로퀴엄 - 대수기하학:

by ()

The lecture series gives a view on computational methods and their some applications to existence and classfication problems. In the first lectures I will introduce Groebner basis and their basic applications in commutative algebra such as computing kernel and images of morphism between finitely presented modules over polynomial rings. As a theoretical application of Groebner basis I will give Petri's analysis of the equations of a canonical curve. The second topic will be Computer aided existence and unirationality proofs of algebraic varieties and their moduli spaces. In case of curves liaison theory is needed, which will be developed. For existence proofs random searches over finite fields is a technique that has not been exploited very much. I will illustrate this technique in a number of examples, in particular for the construction of certain surfaces. Classification of non-minimal surfaces uses adjunction theory. We will discuss this from a computational point of view.

2024-09-10 / 10:30 ~ 11:30

학과 세미나/콜로퀴엄 - 대수기하학:

by ()

2024-09-10 / 16:30 ~ 17:30

IBS-KAIST 세미나 - 이산수학: The Helly number of Hamming balls and related problems

by Zhihan Jin(ETH Zürich)

We prove the following variant of Helly’s classical theorem for Hamming balls with a bounded radius. For $n > t$ and any (finite or infinite) set $X$, if in a family of Hamming balls of radius $t$ in $X$, every subfamily of at most $2^{t+1}$ balls have a common point, so do all members of the family. This is tight for all $|X| > 1$ and all $n > t$. The proof of the main result is based on a novel variant of the so-called dimension argument, which allows one to prove upper bounds that do not depend on the dimension of the ambient space. We also discuss several related questions and connections to problems and results in extremal finite set theory and graph theory. This is joint work with N. Alon and B. Sudakov.

Events for the 취소된 행사 포함