Monday, August 15, 2022

2022-08-19 / 13:00 ~ 15:00

by 권봉석(울산과학기술원)

In this talk, I will mostly discuss the singularity formation of Burgers equation. It is well-known that, when the initial data has negative gradient at some point, the solutions blow up in a finite time. We shall study the properties of the blow-up profile of Burgers equation by introducing the self-similar variables and the modulations, which can be used to study the blow-up for general nonlinear hyperbolic systems. If time permits, I will also discuss the singularity formation for the 1D compressible Euler equations and the related open questions.

2022-08-18 / 13:00 ~ 15:00

학과 세미나/콜로퀴엄 - PDE 세미나:

by 권봉석(울산과학기술원)

2022-08-17 / 13:00 ~ 15:00

학과 세미나/콜로퀴엄 - PDE 세미나:

by 권봉석(울산과학기술원)

2022-08-16 / 13:00 ~ 14:00

SAARC 세미나 - SAARC 세미나:

by 권봉석()

Various plasma phenomena will be discussed using a fundamentalfluid model for plasmas, called the Euler-Poisson system. These include plasma sheaths and plasma soliton. First we will briefly introduce recent results on the stability of plasma sheath solutions, and the quasi-neutral limit of the Euler-Poisson system in the presence of plasma sheaths. Another example of ourinterest is plasma solitary waves, for which we discuss existence, stability, and the time-asymptotic behavior. To study the nonlinear stability of solitary waves, the global existence of smooth solutions must be established, which is completelyopen. As a negative answer for global existence, we look into the finite-time blow-up results for the Euler-Poisson system, and discuss the related open questions.

2022-08-16 / 14:00 ~ 15:00

SAARC 세미나 - SAARC 세미나:

by (경기대학교)

In this talk, we propose the Landau-Lifshitz type system augmented with Chern-Simons gauge terms, which can be considered as the geometric analog of so-called the Chern-Simons-Schrodinger equations. We first derive its self-dual equations through the energy minimization so that we can provide $N$-equivariant solitons. We next deliver basic ideas of constructing $N$-equivariant solitary waves for non-self-dual cases and investigating their qualitative properties.

2022-08-17 / 10:30 ~ 12:30

학과 세미나/콜로퀴엄 - 대수기하학:

by ()

In this talk, we present a Weisfielier-Leman Isomorphism test algorithm of featured graphs and how it can be used to extract representing features of nodes or entire graphs. This leads to a message passing framework of Aggregate-Combine of node-features which is one of the fundamental procedures to currently uesd graph neural networks. We proceed by showing various basic examples arised in real-world non-standard datasets like social network, knowledge graph and chemical compounds.

2022-08-16 / 15:30 ~ 17:30

학과 세미나/콜로퀴엄 - 대수기하학:

by ()

It has been told that deep learning is a black box. The universal approximation theorem was the key theorem which makes the stories going on. On the other hand, in the perspective of the function classes generated by deep neural network, it can be analyzed by in terms of the choice of the various activation functions. The piecewise linear functions, fourier series, wavelets and many other classes would be considered for the purpose of the tasks such as classification, prediction and generation models which heavily depend on the data sets. It might be a challenging problem for mathematicians to develop a new optimization theory depending on the various function classes.

2022-08-16 / 14:00 ~ 15:00

학과 세미나/콜로퀴엄 - 대수기하학:

by ()

Abstract: Let S:=S(a_{1}, ..., a_{n}) \subset P^{n} be a smooth rational normal n-fold scroll. Then the dimension of the projective automophism group {rm Aut}(S,``VecP^ {N} ) of S is \dim(Aut(S, P^{N})) = 2+ \frac{n(n+1)}{2}-(n+1)(N-n+1)+2 sum _{ n} ^{ j=1} ja_j + #{(i,j)|i

2022-08-16 / 16:30 ~ 17:30

IBS-KAIST 세미나 - 이산수학: Testing first-order definable properties on bounded degree graphs

by Noleen Köhler(CNRS, LAMSADE)

Property testers are probabilistic algorithms aiming to solve a decision problem efficiently in the context of big-data. A property tester for a property P has to decide (with high probability correctly) whether a given input graph has property P or is far from having property P while having local access to the graph. We study property testing of properties that are definable in first-order logic (FO) in the bounded-degree model. We show that any FO property that is defined by a formula with quantifier prefix ∃*∀* is testable, while there exists an FO property that is expressible by a formula with quantifier prefix ∀*∃* that is not testable. In the dense graph model, a similar picture is long known (Alon, Fischer, Krivelevich, Szegedy, Combinatorica 2000), despite the very different nature of the two models. In particular, we obtain our lower bound by a first-order formula that defines a class of bounded-degree expanders, based on zig-zag products of graphs. This is joint work with Isolde Adler and Pan Peng.

Events for the 취소된 행사 포함