Thursday, November 26, 2020

2020-11-26 / 15:00 ~ 18:00

학과 세미나/콜로퀴엄 - PDE 세미나: DYNAMICAL STABILITY OF UNIFORMLY ROTATING BINARY STARS AND GALAXIES

by 석진명(경기대학교)

In this talk, we are concerned with dynamically stability of uniformly rotating binary stars and galaxies, which are represented as stationary solutions to Euler-Poisson equations and VlasovPoisson equations respectively. These solutions were constructed as minimizers of suitable variational problems by McCann in which some kind of structural stability on them is discussed. This talk focuses on the nonlinear dynamical stability of them, based on Cazenave-Lions type arguments exploiting variational characterization of stationary solutions. We will see that the uniqueness of a minimizer, which is one of the main results of our work, plays an indispensable role in analysis. This talk is based on a joint work with Prof. Juhi Jang at USC.

2020-11-26 / 15:00 ~ 18:00

학과 세미나/콜로퀴엄 - PDE 세미나: Some results on bound state and semi-classical solutions of Kirchhoff type problem

by 시에 치린(Guangdong University of Technology)

In this talk, I will give some existence results on nontrivial solutions of Kirchhoff type problem by the variational methods. In this first parts, the bound state solutions of this problem with a critical exponent have been obtained by deformation results after a local compactness result has been recovered. We found a different and interesting results when this problem is considered in a high dimension N larger than 4. In the second parts, I will give some results on semi-classical solutions

2020-11-27 / 14:00 ~ 15:30

학과 세미나/콜로퀴엄 - PDE 세미나:

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In this introductory talk, we will discuss how to describe and study various hydrodynamic models in Lagrangian variables, following the framework introduced by Constantin. In a unified framework and with less regularity, local well-posedness theory can be established for a range of models, including the incompressible Euler equation, the surface quasi-geostrophic equation, the Boussinesq system, the Oldroyd-B system, and more.

2020-11-26 / 13:00 ~ 14:00

학과 세미나/콜로퀴엄 - 대수기하학:

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For a very ample line bundle L on a projective scheme X, we say that (X,L) satisfies property QR(k) if the homogeneous ideal of the linearly normal embedding can be generated by quadrics of rank <= k. Many classical varieties such as Segre-Veronese embeddings, rational normal scrolls and curves of high degree satisfy the property QR(4). In this talk, we will briefly show that the second and higher Veronese embeddings satisfies the property QR(3). And we will discuss about the asymptotic behavior of property QR(3) for any projective scheme.

2020-12-02 / 17:00 ~ 18:00

학과 세미나/콜로퀴엄 - Discrete Math:

by 이준경()

A graph $H$ is \emph{common} if the number of monochromatic copies of $H$ in a 2-edge-colouring of the complete graph $K_n$ is minimised by the random colouring. Burr and Rosta, extending a famous conjecture by Erd\H{o}s, conjectured that every graph is common. The conjectures by Erd\H{o}s and by Burr and Rosta were disproved by Thomason and by Sidorenko, respectively, in the late 1980s. Despite its importance, the full classification of common graphs is still a wide open problem and has not seen much progress since the early 1990s. In this lecture, I will present some old and new techniques to prove whether a graph is common or not.

2020-11-30 / 17:00 ~ 18:00

학과 세미나/콜로퀴엄 - Discrete Math:

by 이준경()

Abstract: Ramsey's theorem states that, for a fixed graph $H$, every 2-edge-colouring of $K_n$ contains a monochromatic copy of $H$ whenever $n$ is large enough. Perhaps one of the most natural questions after Ramsey's theorem is then how many copies of monochromatic $H$ can be guaranteed to exist. To formalise this question, let the \emph{Ramsey multiplicity} $M(H;n)$ be the minimum number of labelled copies of monochromatic $H$ over all 2-edge-colouring of $K_n$. We define the \emph{Ramsey multiplicity constant} $C(H)$ is defined by $C(H):=\lim_{n\rightarrow\infty}\frac{M(H,n)}{n(n-1)\cdots(n-v+1)}$. I will discuss various bounds for C(H) that are known so far.

2020-11-26 / 16:30 ~ 17:30

학과 세미나/콜로퀴엄 - 콜로퀴엄: Algebraic fibre space via convex bodies

by 최성락(연세대학교)

Algebraic fibre spaces are relative versions of algebraic varieties. For an algebraic fibre space f:X->Y, the varieties X,Y and the general fibre F are deeply related by various formulas and conjectures on the invariants of varieties. For example, the Iitaka conjecture is still an open problem which predicts that the Kodaira dimension of X is at least the sum of kodaira dimensions of F and Y. We explain how the geometry of algebraic fibre spaces can be studied by convex bodies called Okounkov bodies.

Events for the 취소된 행사 포함