Friday, October 21, 2022

2022-10-28 / 11:00 ~ 13:00

by 최성수()

In mathematics, every mathematical object is generated along with a set of processes setting up boundaries and relationships as recently emphasized in Prof. June Huh's public lecture (July 13, 2022), commemorating his Fields Medal award. These days we live in the era of the 4th industrial revolution in which the advent of “the era of expanding technological super-gap on a global scale” is expected. More than ever including the era of Gauss (German: Gauß; 30 April 1777 – 23 February 1855) when he emphasized, "Mathematics is the queen of sciences, often condescending to render service to other sciences, but in all relations, she is entitled to the first rank," the role of mathematics is apparently getting much more important as time goes by in the era of the digital revolution. The importance of raising awareness of this cannot be overemphasized. In this talk according the above, three concrete examples are introduced to show how mathematics can practically contribute to the improvement of the human digital civilization in view of the processes setting up boundaries and relationships: 1) mathematics and "the smallest object" in physics, 2) first-principles(ab initio) in physics and mathematics, and 3) building up and utilizing our own first-principles allowing to flexibly cross boundaries between academic fields, which often makes it much easier for us to deal with various important problems. As for the practical examples, some of our recent works are briefly introduced as well, including mathematical conceptualizaiton of metaverse, construction of "physical system for linguistic data" with its ab initio-based utilization, etc; we might as well say that a sort of "Academic Continuation (analogous to analytic continuation)" is applied in each case. From this talk, we learn to boldly seek out useful mathematical connections crossing boundaries as above, more enriching the digital revolution; various academic/theoretical fields considered different from each other actually share an amount of common/similar mathematical structures.

2022-10-28 / 16:00 ~ 17:00

학과 세미나/콜로퀴엄 - PDE 세미나:

by 김세익(연세대)

Unlike Green's functions for elliptic equations in divergence form, Green's function for elliptic operators in nondivergence form do not possess nice pointwise bounds even in the case when the coefficients are uniformly continuous. In this talk, I will describe how to construct and get pointwise estimates for elliptic PDEs in non-divergence form with coefficients satisfying the so called Dini mean oscillation condition. I will also mention the parallel result for parabolic equations in non-divergence form.

2022-10-25 / 17:00 ~ 18:00

학과 세미나/콜로퀴엄 - Mathematics & Beyond Seminar:

by 박종욱 변호사()

2022-10-26 / 16:00 ~ 17:00

IBS-KAIST 세미나 - 수리생물학:

by ()

We’re all familiar with sleep, but how can we mathematically model it? And what determines how long and when we sleep? In this talk I’ll introduce the nonsmooth coupled oscillator systems that form the basis of current models of sleep-wake regulation and discuss their dynamical behaviour. I will describe how we are using models to unravel environmental, societal and physiological factors that determine sleep timing and outline how we are using models to inform the quantitative design of light interventions for mental health disorders and address contentious societal questions such as whether to move school start time for adolescents.

2022-10-21 / 11:00 ~ 12:00

IBS-KAIST 세미나 - 수리생물학:

by ()

Cellular, chemical, and population processes are all often represented via networks that describe the interactions between the different population types (typically called the “species”). If the counts of the species are low, then these systems are often modeled as continuous-time Markov chains on the d-dimensional integer lattice (with d being the number of species), with transition rates determined by stochastic mass-action kinetics. A natural (broad) mathematical question is: how do the qualitative properties of the dynamical system relate to the graph properties of the network? For example, it is of particular interest to know which graph properties imply that the stochastically modeled reaction network is positive recurrent, and therefore admits a stationary distribution. After a general introduction to the models of interest, I will discuss this problem, giving some of the known results. I will also discuss recent progress on the Chemical Recurrence Conjecture, which has been open for decades, which is the following: if each connected component of the network is strongly connected, then the associated stochastic model is positive recurrent.

2022-10-21 / 10:30 ~ 11:00

IBS-KAIST 세미나 - 수리생물학:

by ()

TBA

2022-10-28 / 10:00 ~ 11:00

SAARC 세미나 - SAARC 세미나:

by ()

In this talk, we will first review some recent results on the eigenvectors of random matrices under fixed-rank deformation, and then we will focus on the limit distribution of the leading eigenvectors of the Gaussian Unitary Ensemble (GUE) with fixed-rank (aka spiked) external source, in the critical regime of the Baik-Ben Arous-Peche (BBP) phase transition. The distribution is given in terms of a determinantal point process with extended Airy kernel. Our result can be regarded as an eigenvector counterpart of the BBP eigenvalue phase transition. The derivation of the distribution makes use of the recently rediscovered eigenvector-eigenvalue identity, together with the determinantal point process representation of the GUE minor process with external source. This is a joint work with Dong Wang (UCAS).

2022-10-27 / 16:15 ~ 17:15

학과 세미나/콜로퀴엄 - 콜로퀴엄:

by ()

We study the problem of maximizing a continuous DR-submodular function that is not necessarily smooth. We prove that the continuous greedy algorithm achieves a [(1-1/e)OPT-ε] guarantee when the function is monotone and Hölder-smooth, meaning that it admits a Hölder-continuous gradient. For functions that are non-differentiable or non-smooth, we propose a variant of the mirror-prox algorithm that attains a [(1/2)OPT-ε] guarantee. We apply our algorithmic frameworks to robust submodular maximization and distributionally robust submodular maximization under Wasserstein ambiguity. In particular, the mirror-prox method applies to robust submodular maximization to obtain a single feasible solution whose value is at least [(1/2)OPT-ε]. For distributionally robust maximization under Wasserstein ambiguity, we deduce and work over a submodular-convex maximin reformulation whose objective function is Hölder-smooth, for which we may apply both the continuous greedy method and the mirror-prox method. This is joint work with Duksang Lee, a fifth-year Ph.D. student at KAIST Math, and Nam Ho-Nguyen from the University of Sydney.

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