Wednesday, July 10, 2024

2024-07-12 / 14:00 ~ 16:00

by 채석주()

Stochastic models of gene expression are routinely used to explain large variability in measured mRNA levels between cells. These models typically predict the distribution of the total mRNA level per cell but ignore compartment-specific measurements which are becoming increasingly common. Here we construct a two-compartment model that describes promoter switching between active and inactive states, transcription of nuclear mRNA and its export to the cytoplasm where it decays. We obtain an analytical solution for the joint distribution of nuclear and cytoplasmic mRNA levels in steady-state conditions. Based on this solution, we build an efficient and accurate parameter inference method which is orders of magnitude faster than conventional methods. If you want to participate in the seminar, you need to enter IBS builiding (https://www.ibs.re.kr/bimag/visiting/). Please contact jaekkim@kaist.ac.kr if you first come IBS to get permission to enter IBS building.

2024-07-12 / 16:00 ~ 17:00

SAARC 세미나 - SAARC 세미나:

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In this talk, we prove the Aleksandrov--Bakelman--Pucci estimate for non-uniformly elliptic equations in non-divergence form. Moreover, we investigate local behaviors of solutions of such equations by developing local boundedness and weak Harnack inequality. Here we impose an integrability assumption on ellipticity representing degeneracy or singularity, instead of specifying the particular structure of ellipticity.

2024-07-12 / 15:00 ~ 16:00

SAARC 세미나 - SAARC 세미나:

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This talk presents the C^{1,\alpha}-regularity for viscosity solutions of degenerate/singular fully nonlinear parabolic equations. For this purpose, we develop a new type of Bernstein technique in view of the difference quotient to obtain a priori estimates of the regularized equations. Also, we establish the well-posedness and the uniform C^{1,\alpha}-estimates for the regularized Cauchy-Dirichlet problem.

2024-07-12 / 14:00 ~ 15:00

SAARC 세미나 - SAARC 세미나:

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The classical nonlinear potential theory has recently been extended to nonlocal nonlinear potential theory, which studies harmonic functions associated with nonlocal nonlinear operators. In this talk, we focus on the harmonic functions solving the nonlocal Dirichlet problem. As in the study of classical Dirichlet problem, the nonlocal Dirichlet problem can be solved by using Sobolev and Perron solutions. We provide several properties of such solutions. This talk is based on joint works with Anders Björn, Jana Björn, Ki-Ahm Lee and Se-Chan Lee.

2024-07-17 / 14:00 ~ 16:00

학과 세미나/콜로퀴엄 - 기타: Introduction to complex algebraic geometry and Hodge theory #9

by 김재홍(KAIST)

This is part of an informal seminar series to be given by Mr. Jaehong Kim, who has been studying the book "Hodge theory and Complex Algebraic Geometry Vol 1 by Claire Voisin" for a few months. It will summarize about 70-80% of the book.

2024-07-10 / 16:00 ~ 18:00

학과 세미나/콜로퀴엄 - 위상수학 세미나:

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In the 1980's Casson and Gordon produced the first non slice knots which are trivial in Levine's algebraic concordance group, and in 2003 Cochran-Orr-Teichner produced the first no slice knots undetectable by Casson and Gordon's invariants. They do so by producing a filtration of the concordance group by subgroups a knot in the 1.5th term of this filtration has vanishing Casson-Gordon invariants. Since then this work has been central to the study of knot concordance. We will introduce this filtration and review just enough of the theory of L^2 homology to prove that the successive quotients of this filtration are nontrivial.

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