# 세미나 및 콜로퀴엄

2018-12
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2019-01
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구글 Calendar나 iPhone 등에서 구독하면 세미나 시작 전에 알림을 받을 수 있습니다.

A signed graph is a pair (G, σ), where G is a graph and σ: E(G) → {1,-1} is a signature of G. A set S of integers is symmetric if I∈S implies that -i∈S. A k-colouring of (G,σ) is a mapping f:V(G) → Nk such that for each edge e=uv, f(x)≠σ(e) f(y), where Nk is a symmetric integer set of size k. We define the signed chromatic number of a graph G to be the minimum integer k such that for any signature σ of G, (G, σ) has a k-colouring.

Let f(n,k) be the maximum signed chromatic number of an n-vertex k-chromatic graph. This paper determines the value of f(n,k) for all positive integers n ≥ k. Then we study list colouring of signed graphs. A list assignment L of G is called symmetric if L(v) is a symmetric integer set for each vertex v. The weak signed choice number ch±w(G) of a graph G is defined to be the minimum integer k such that for any symmetric k-list assignment L of G, for any signature σ on G, there is a proper L-colouring of (G, σ). We prove that the difference ch±w(G)-χ±(G) can be arbitrarily large. On the other hand, ch±w(G) is bounded from above by twice the list vertex arboricity of G. Using this result, we prove that ch±w(K2⋆n)= χ±(K2⋆n) = ⌈2n/3⌉ + ⌊2n/3⌋. This is joint work with Ringi Kim and Xuding Zhu.

Host: Sang-il Oum     미정     2019-01-24 12:20:45

In this talk, I will introduce the idea to study the Noether inequality for 3-folds of general type with the geometric genus less than 21. This is my project working in progress with Bingru Li.

Host: 이용남     영어     2019-01-16 14:33:54

A Verra fourfold is a smooth projective complex variety defined as a double cover of P^2x P^2 branched along a divisor of bidegree (2,2).
These varieties are similar to cubic fourfolds in several ways (Hodge theory, relation to hyperkaehler fourfolds, derived categories).
Inspired by these multiple analogies, I consider the Chow ring of a Verra fourfold. Among other things, I will show that the multiplicative structure of this Chow ring has a curious K3-like property.

Host: 박진현     Contact: 박진현 (2734)     영어     2018-12-19 18:50:47

The generalized Franchetta conjecture as formulated by O’Grady is about algebraic cycles on the universal K3 surface. It is natural to consider a similar conjecture for algebraic cycles on universal families of hyperkaehler varieties. This has close ties to Beauville’s conjectural splitting property’’, and the Beauville-Voisin conjecture (stating that the Chow ring of a hyperkaehler variety has a certain subring injecting into cohomology). In my talk, I will attempt to give an overview of these conjectures, and present some cases where they can be proven. This is joint work with Lie Fu, Charles Vial and Mingmin Shen.

Host: 박진현     Contact: 박진현 (2734)     영어     2018-12-19 18:49:02

A flag Bott tower is a sequence of flag bundles such that each stage of which comes from the induced full-flag bundle of a sum of holomorphic line bundles. A flag Bott manifold is not toric variety but it has a torus action. In this talk, we consider the standard torus action on a flag Bott manifold and compute its equivariant cohomology ring.

Host: 송종백     미정     2018-12-27 11:32:55

Problems such as Vertex Cover and Multiway Cut have been well-studied in parameterized complexity. Cygan et al. 2011 drastically improved the running time of several problems including Multiway Cut and Almost 2SAT by employing LP-guided branching and aiming for FPT algorithms parameterized above LP lower bounds. Since then, LP-guided branching has been studied in depth and established as a powerful technique for parameterized algorithms design.

In this talk, we make a brief overview of LP-guided branching technique and introduce the latest results whose parameterization is above even stronger lower bounds, namely μ(I)=2LP(I)-IP(dual-I). Here, LP(I) is the value of an optimal fractional solution and IP(dual-I) is the value of an optimal integral dual solution. Tutte-Berge formula for Maximum Matching (or equivalently Edmonds-Gallai decomposition) and its generalization Mader’s min-max formula are exploited to this end. As a result, we obtain an algorithm running in time 4^(k-μ(I)) for multiway cut and its generalizations, where k is the budget for a solution.

This talk is based on a joint work with Yoichi Iwata and Yuichi Yoshida from NII.

Host: 엄상일     미정     2018-12-28 09:58:28

A celebrated conjecture of Sidorenko and Erdős–Simonovits states that, for all bipartite graphs H, quasirandom graphs contain asymptotically the minimum number of copies of H taken over all graphs with the same order and edge density. This conjecture has attracted considerable interest over the last decade and is now known to hold for a broad range of bipartite graphs, with the overall trend saying that a graph satisfies the conjecture if it can be built from simple building blocks such as trees in a certain recursive fashion.

Our contribution here, which goes beyond this paradigm, is to show that the conjecture holds for any bipartite graph H with bipartition A∪B where the number of vertices in B of degree k satisfies a certain divisibility condition for each k. As a corollary, we have that for every bipartite graph H with bipartition A∪B, there is a positive integer p such that the blow-up H_A^p formed by taking p vertex-disjoint copies of H and gluing all copies of A along corresponding vertices satisfies the conjecture. Joint work with David Conlon.

Host: 엄상일     미정     2018-12-28 09:57:00

The prime geodesic theorem allows one to count the number of closed geodesics having length less than X in a given hyperbolic manifold. As a naive generalization of the prime geodesic theorem, we are interested in the the number of immersed totally geodesic surfaces in a given hyperbolic manifold. I am going to talk about this question when the underlying hyperbolic manifold is an arithmetic hyperbolic $3$-manifold corresponding to a Bianchi group SL(2,O_{-d}), where O_{-d} is the ring of integers of Q[sqrt{-d}] for some positive integer d.

Host: 백형렬     미정     2018-12-21 08:42:28

Multi 차원 Black Scholes PDE 의 FDM 해법인 ADI(Alternative Direction Implicit FDM) 적용방식을 살펴보고, Hull White PDE에도 적용의 성과를 분석해본다

Host: 최건호     한국어     2018-12-27 10:27:00

I will discuss the Ramsey problem for {x,y,z:x+y=p(z)} for polynomials p over ℤ. This is joint work with Peter Pach and Csaba Sandor.

Host: 엄상일     미정     2018-12-06 09:22:47

This series of lecture will introduce the study of groups acting on the circle and the line, the moduli spaces of such actions, and the role of these spaces in questions of geometric topology, dynamics, and foliation theory.  I will focus on new rigidity results in low regularity, surveying important techniques, geometrically motivated examples, and open problems.

Host: 백형렬     영어     2018-12-07 08:36:39

We propose a novel class of Hawkes-based model that assesses two types of systemic risk in high-frequency price processes: the endogenous systemic risk within a single process and the interactive systemic risk between a couple of processes. We examine the existence of systemic risk at a microscopic level via an empirical analysis of the futures markets of the West Texas Intermediate (WTI) crude oil and gasoline and perform a comparative analysis with the conditional value-at-risk as a benchmark measure of the proposed model. Throughout the analysis, we uncover remarkable empirical findings in terms of the high-frequency structure of the two markets: for the past decade, the level of endogenous systemic risk in the WTI market was significantly higher than that in the gasoline market. Moreover, the level at which the gasoline price affects the WTI price was constantly higher than in the opposite case.  Although the two prices interact with each other at the transaction-unit level, the degree of relative influences on the two markets, that is, from the WTI to the gasoline and vice versa, was very asymmetric, but that difference has reduced gradually over time.

Host: 최건호     한국어     2018-12-10 08:58:40

Hierarchical Risk Parity approach 관련 논문과 논문 내용의 실제 데이터 적용 결과 및 문제점에 대해 살펴본다.

Host: 최건호     한국어     2018-12-10 08:59:37

This series of lecture will introduce the study of groups acting on the circle and the line, the moduli spaces of such actions, and the role of these spaces in questions of geometric topology, dynamics, and foliation theory.  I will focus on new rigidity results in low regularity, surveying important techniques, geometrically motivated examples, and open problems.

Host: 백형렬     영어     2018-12-07 08:35:21

Let H be a planar graph. By a classical result of Robertson and Seymour, there is a function f(k) such that for all k and all graphs G, either G contains k vertex-disjoint subgraphs each containing H as a minor, or there is a subset X of at most f(k) vertices such that G−X has no H-minor. We prove that this remains true with f(k)=ck log k for some constant c depending on H. This bound is best possible, up to the value of c, and improves upon a recent bound of Chekuri and Chuzhoy. The proof is constructive and yields the first polynomial-time O(log ???)-approximation algorithm for packing subgraphs containing an H-minor.

This is joint work with Wouter Cames van Batenburg, Gwenaël Joret, and Jean-Florent Raymond.

Host: 엄상일     미정     2018-12-05 09:52:03

This series of lecture will introduce the study of groups acting on the circle and the line, the moduli spaces of such actions, and the role of these spaces in questions of geometric topology, dynamics, and foliation theory.  I will focus on new rigidity results in low regularity, surveying important techniques, geometrically motivated examples, and open problems.

Host: 백형렬     영어     2018-12-07 08:34:18

I will recall some basic facts in the syzygy theory, with emphasis on connections with Koszul cohomology, and I will present a vanishing result for Koszul modules.

Host: 곽시종     미정     2018-12-05 15:43:52

I will introduce the syzygy schemes of a canonical curve and compute a few examples.

Host: 곽시종     미정     2018-12-05 15:45:46

Let X be a compact Kahler manifold of dimension n > 0. Let G be a group of zero entropy automorphisms of X.

Let G_0 be the set of elements in G which are isotopic to the identity. We prove that after replacing G by a suitable finite-index subgroup,

G/G_0 is a unipotent group of derived length at most n-1. This is a corollary of an optimal upper bound of length involving the Kodaira dimension.

We also study the algebro-geometric structure of X when it admits a group action with maximal derived length n-1.

This is a joint work with Dinh and Oguiso.

Host: 이용남     영어     2018-11-26 08:47:25

Given a group G and a manifold M, can one describe all the actions of G on M? This is a basic, natural question in geometric topology, but also a very difficult one -- even in the case where M is 1-dimensional, and G is a familiar, finitely generated group.
This talk will introduce the theory of groups acting on 1-manifolds, through the study of orderable groups.  I will describe some connections between this theory and themes in topology and dynamics (like rigidity and foliation theory ), some current open problems, and indicate new approaches coming from recent joint work with C. Rivas.

Host: 백형렬     영어     2018-08-22 11:32:45

본 발표에서는 Deep learning 방법을 위시한 인공지능 기술이 X-ray CT 영상
연구에 어떤 기여를 해왔고 또 할 수 있는지 살펴보고자 한다. Domain knowledge
영역에서 영상 재구성 및 아티팩트 제거를 위한 패러다임이 인공지능의 새로운
패러다임에서 어떤 역할을 할 수 있을지도 함께 고찰해 보고 향후 CT 영상 기술
발전의 outlook을 AI 프레임에서 논의해 보고자 한다.

Host: 이창옥     미정     2018-11-30 16:32:47