Department Seminars & Colloquia




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Cohomology jump loci are topological invariants generalizing the usual singular cohomology groups. I will give a survey on the theory of cohomology jump locus, especially the structure theorems developed by Simpson, Schnell, Budur and myself. As an application, I will give an example of non-Kahler Calabi-Yau symplectic-complex manifold. This example is joint work with Lizhen Qin. 

English     2016-06-20 11:35:28

In this talk, we will survey the book "Arithmeticity in the theory of automorphic forms - G.Shimura (2000)".

 

Host: 윤동성     Korean     2016-07-25 09:03:36

In this talk, I will introduce normally ordered product and other equivalent definitions of vertex algebras via Borcherds identity.

 

Host: 윤동성     Korean     2016-07-25 09:13:47

Graphical models capture the conditional independence structure among random variables via the existence of edges among vertices. One way of inferring a graph is to use a partial correlation coefficient using the fact that a zero partial correlation coefficient is equivalent to conditional independence under the Gaussian assumption. In order to relax the distributional assumption, we propose kernel partial correlation which is a new conditional independence measure. It is a direct nonparametric extension of the partial correlation coefficient and estimated using a combination of two statistical methods. First, a support vector regression is employed to separate non-random components of conditional distributions, and then the dependence between remaining random components is assessed through a kernel-based association measure.  The proposed method is not only a flexible conditional independence measure but also can be estimated robustly under high levels of noise owing to the robustness of the employed nonparametric approaches. Upon comparisons to existing approaches, our method outperforms others when it is applied to simulated data as well as real data from single-cell RNA-sequencing experiments.

Host: 김성호     Korean     2016-07-21 10:50:34

   A Gaussian graphical model (GGM) is one of the most widely-used tools for statistical network analysis, partly because it turns estimation of a graph into sparse estimation of a high-dimensional precision matrix. To relax the multivariate Gaussian assumption, there have been many developments in non-Gaussian graphical models, through the use of either nonparametric copula transformation or generalized additive models. However, each of these methods has limitations, where the copula transformation cannot capture general non-linear associations and the generalized additive model is not able to detect dependences through conditional variances. In this talk, I will discuss two recent graphical model approaches that extend the GGM approach. The first one is an additive semigraphoid model approach that infers a graph based on additive conditional independence (ACI) relation. The ACI is different from conditional independence, but it satisfies the axioms for a semigraphoid that capture the essence of a graph. The second one is a sparse quantile-based graphical model (SQGM) that infers a graph based on the components of quantile regression. As an inverse mapping function of a conditional probability function, conditional quantile is able to characterize a complete picture of conditional dependence. Utilizing this feature, SQGM is able to broaden the scope of graphical models. Finally, the applications of these approaches to real biological datasets from genomics will be presented.

Host: 김성호     Korean     2016-07-13 10:24:45

We consider a class of stochastic processes, which can be regarded as
the perturbation of deterministic dynamics in a potential field. These
processes exhibit a phenomenon known as metastable behavior if the
potential field has several local minima. Metastable behavior is the
phenomenon in which a process starting from one of local minima
arrives at the neighborhood of the global minimum after a sufficiently
long time scale. The precise asymptotic analysis of this transition
time has been known only for the reversible dynamics, based on the
potential theory of reversible Markov processes. In this presentation,
we review this metastability theory for reversible dynamics, and
introduce our recent generalization to the non-reversible dymamics.
(joint work with C. Landim)

Host: 강완모     English     2016-06-21 11:15:07

In this talk, we will survey the book "Arithmeticity in the theory of automorphic forms - G.Shimura (2000)".

Host: 윤동성     Korean     2016-07-05 16:58:43

This talk is a part of lecture series introducing vertex algebras. Last time, I explained motivations and definitions of vertex algebras. In this lecture, I will explain more about the locality axiom using formal distributions and the decomposition theorem. Also, I will introduce normally ordered products of a vertex algebra. 

 

Host: 윤동성     Korean     2016-07-05 17:04:33

양자컴퓨터의 개발이 가시화 되면서 포스트 퀀텀 암호에 대한 관심이 급증하고 있다. 특히 2015년 8월 NSA suite B 암호를 교체한다는 발표와 2016년 2월 NIST에서 새로운 암호를 공모한다는 발표에 따라 많은 암호학자들이 포스트 퀀텀 암호를 눈여겨보고 있다. 이번 강의에서는 포스트 퀀텀 암호들 중에서 격자 기반 암호에 대하여 전반적으로 알아보고, 관련 문제들을 토론하는 시간을 가지도록 한다.

Host: 한상근     Korean     2016-07-05 16:45:16

양자컴퓨터의 개발이 가시화 되면서 포스트 퀀텀 암호에 대한 관심이 급증하고 있다. 특히 2015년 8월 NSA suite B 암호를 교체한다는 발표와 2016년 2월 NIST에서 새로운 암호를 공모한다는 발표에 따라 많은 암호학자들이 포스트 퀀텀 암호를 눈여겨보고 있다. 이번 강의에서는 포스트 퀀텀 암호들 중에서 격자 기반 암호에 대하여 전반적으로 알아보고, 관련 문제들을 토론하는 시간을 가지도록 한다.

Host: 한상근     Korean     2016-07-05 16:47:24

양자컴퓨터의 개발이 가시화 되면서 포스트 퀀텀 암호에 대한 관심이 급증하고 있다. 특히 2015년 8월 NSA suite B 암호를 교체한다는 발표와 2016년 2월 NIST에서 새로운 암호를 공모한다는 발표에 따라 많은 암호학자들이 포스트 퀀텀 암호를 눈여겨보고 있다. 이번 강의에서는 포스트 퀀텀 암호들 중에서 격자 기반 암호에 대하여 전반적으로 알아보고, 관련 문제들을 토론하는 시간을 가지도록 한다.

Host: 한상근     Korean     2016-07-05 16:50:26

양자컴퓨터의 개발이 가시화 되면서 포스트 퀀텀 암호에 대한 관심이 급증하고 있다. 특히 2015년 8월 NSA suite B 암호를 교체한다는 발표와 2016년 2월 NIST에서 새로운 암호를 공모한다는 발표에 따라 많은 암호학자들이 포스트 퀀텀 암호를 눈여겨보고 있다. 이번 강의에서는 포스트 퀀텀 암호들 중에서 격자 기반 암호에 대하여 전반적으로 알아보고, 관련 문제들을 토론하는 시간을 가지도록 한다.

Host: 한상근     Korean     2016-07-05 16:34:34

양자컴퓨터의 개발이 가시화 되면서 포스트 퀀텀 암호에 대한 관심이 급증하고 있다. 특히 2015년 8월 NSA suite B 암호를 교체한다는 발표와 2016년 2월 NIST에서 새로운 암호를 공모한다는 발표에 따라 많은 암호학자들이 포스트 퀀텀 암호를 눈여겨보고 있다. 이번 강의에서는 포스트 퀀텀 암호들 중에서 격자 기반 암호에 대하여 전반적으로 알아보고, 관련 문제들을 토론하는 시간을 가지도록 한다.

Host: 한상근     Korean     2016-07-05 16:38:41

BDDC(Balancing Domain Decomposition by Constraints) methods based on an adaptive selection of primal constraints for problems posed in H(div) are introduced. Our methods are fully algebraic and deal with highly oscillating coefficients. Bounds on the condition number of the preconditioned linear system are also provided which are independent of the values and jumps. This is joint work with Olof Widlund(Courant Institute), Stefano Zampini(KAUST), and Clark Dohrmann(Sandia National Lab).

Host: 이창옥     To be announced     2016-06-22 19:12:24

 A set F of graphs has the Erdős-Posa property if there exists a function f such that every graph either contains k disjoint subgraphs each isomorphic to a member in F or contains a set of at most f(k) vertices intersecting all such subgraphs. In this talk I will address the Erdős-Posa property with respect to three closely related graph containment relations: minor, topological minor, and immersion. We denote the set of graphs containing H as a minor, topological minor and immersion by M(H),T(H) and I(H), respectively. Robertson and Seymour in 1980’s proved that M(H) has the Erdős-Posa property if and only if H is planar. And they left the question for characterizing H in which T(H) has the Erdős-Posa property in the same paper. This characterization is expected to be complicated as T(H) has no Erdős-Posa property even for some tree H. In this talk, I will present joint work with Postle and Wollan for providing such a characterization. For immersions, it is more reasonable to consider an edge-variant of the Erdős-Posa property: packing edge-disjoint subgraphs and covering them by edges. I(H) has no this edge-variant of the Erdős-Posa property even for some tree H. However, I will prove that I(H) has the edge-variant of the Erdős-Posa property for every graph H if the host graphs are restricted to be 4-edge-connected. The 4-edge-connectivity cannot be replaced by the 3-edge-connectivity.

Host: 엄상일     English     2016-06-22 09:32:39

In this talk, we will survey the book "Arithmeticity in the theory of
automorphic forms - G.Shimura (2000)".

To be announced     2016-06-27 09:44:43

A vertex algebra is an algebraic structure which is constructed to explain
conformal field theory (CFT) rigorously. So a vertex algebra is endowed
with a non-associative product called normally ordered product which shows
operator product expansions in CFT. On the other hand, purely
mathematically, it is closely related to the theory of affine Lie algebras.
In this talk, I will introduce the most well-known definition of vertex
algebras and show simple examples.

To be announced     2016-06-27 09:47:47

Type 2 diabetes (T2D) is generally thought to result from the combination of two metabolic defects, insulin resistance, which increases the level of insulin required to maintain glucose within the normal range, and failure of insulin-secreting pancreatic beta cells to compensate for the increased demand. We have built up a comprehensive mathematical model of progression to T2D. The dynamics of failure and compensation can be described on two-dimensional slow manifold to investigate the mechanisms of progression to diabetes. In addition, we have extended our mathematical model by adding daily meals and hepatic glucose production, which is helpful for studying the clinical implications. These enhancements allow us to look at the mechanistic defects that underlie observed pathologies such as impaired fasting glucose (IFG) and impaired glucose tolerance (IGT). The model supports associations found in experiments between IFG and excess HGP and between IGT and peripheral insulin resistance. The model suggests how to personalize therapeutic approaches for subjects based on their underlying metabolic abnormalities.

Host: 김재경     English     2016-05-11 13:59:35

This talk deals with some questions concerning the convergence of the solu-tions to a dynamic equation on time scale. It is also concerned with the stability domains, the spectrum of matrix pairs, the exponential stability and its robustness measure for linear implicit dynamic equations of arbitrary index.

Host: 국가수리과학연구소     To be announced     2016-06-13 11:47:20

In this talk I will discuss research with the goal of building models of brain anatomy. The neuronanatomical structures of interest can be broadly subdivided into two categories - cortical and non-cortical. Cortical structures (particularly the cerbral cortex) are typically highly folded, thin sheets of gray matter. Functionally, the cerebral cortex has been shown to have a "columnar" architecture. For this reason, we construct surface-based models for analysis of cortical properties. The construction of such models is a difficult task due to the high degree of folding of the cortical manifold in conjunction with the limited (~ 1 mm) resolution of current neuroimaging technologies. Once constructed, the cortical models can be deformed for morphometry, visualization and registration purposes. I will show some results of this type of analysis, including the morphometric changes that the cortex undergoes in disorders such as schizophrenia, Alzheimer's disease, and Huntington's disease, as well as healthy aging.
A different set of techniques have been developed for the construction of models of subcortical structures. Here, we model the segmentation as an anisotropic nonstationary Markov Random Field. The anisotropy lets us model the local spatial relationships that exist between neuroanatomical structures (e.g. hippocampus is anterior and inferior to amygdala), while the nonstationarity facilitates the encoding of inhomogeneous properties of the tissue within a structure. This approach is based on extracting the relevant model parameters from a manually labeled training set, and has been shown to be comparable in accuracy to the manual labeling.

Host: 이창옥     Korean English if it is requested     2016-06-01 12:58:35

기나긴 수학의 역사에서 관찰되는 큰 흐름은 우아함과 완전함에 대한 열망이다. 물리적 세계의 불완전함 이면에 있는 질서를 찾아내고, 수학적 단순화 과정을 거쳐 대칭과 조화를 표현하는 일에 매료된 수학자들은 역사의 도처에서 관찰된다.하지만 세상은 여전히 완전하지 않다. 우주로 간 화성탐험선은 끊임없이 지구로 영상신호를 보내지만, 태양의 자기장과 지구의 오존층에 이리 치이고 저리 치여서 엉뚱하게 변질된 신호가 지구에 도착하지 않는가? 원자의 세계는 뉴턴역학의 결정론이 아니라 양자역학의 확률적 개념으로 접근해야 한다는 사실에 아인슈타인은 “신은 주사위 놀음을 하지 않는다”고 절망하지 않았던가? 프랙탈의 개념을 처음 발견한 망델브로는 불규칙과 무질서가 자연의 본질에 더 가깝다고 결론내리지 않았는가? 수학은 이 혼란에 어떻게 대응하고 있는지 들여다 보고자 한다.

Host: 이창옥     Korean     2016-05-27 17:04:30

This presentation is about recently introduced immersed finite element (IFE) methods that can solve interface problems with structured or even Cartesian meshes advantageously in some applications. After a brief survey on FE/IFE methods based on unstructured meshes for interface problems, this presentation will explain the need to construct IFE functions as macro piecewise polynomials defined with subelements formed by partitioning each interface element with the actual material interface instead of its linear approximation. We present a unified framework for developing and analyzing immersed finite element (IFE) spaces with either linear, or bilinear, or the rotated-$Q_1$ polynomials. Functions in these IFE spaces are locally piecewise polynomials defined according to the sub-elements formed by the interface itself instead of its line approximation. We show that the unisolvence for these IFE spaces follows from the invertibility of the Sherman-Morrison matrix. A group of estimates and identities are established for the interface geometry and shape functions that are applicable to all of these IFE spaces. Most importantly, these fundamental preparations enable us to develop a unified multipoint Taylor expansion procedure for proving that these IFE spaces have the expected optimal approximation capability according to the involved polynomials.

Host: 곽도영     To be announced     2016-05-30 10:01:13

Recently, Marcus, Spielman, and Srivastava proved the  existence of infinite families of bipartite Ramanujan graphs of every  degree at least 3 by using the method of interlacing families of polynomials. In this talk, we apply their method to prove that for any  connected graph G, there exists an orientation of G such that the  spectral radius of the corresponding Hermitian adjacency matrix is at  most that of the universal cover of G.

 

 


Supported by BK21Plus.

Host: 엄상일     To be announced     2016-05-26 11:40:14

In this talk, Bayesian semiparametric methods for function estimation and model selection problems are presented. This talk is designed to provide graduate students and researchers with an introduction to Bayesian semiparametric inference. The orientation is methodological rather than theoretical, but such asymptotic theory as is necessary for a proper understanding and validating specific Bayesian methods will be also covered in detail. The materials will include three aspects of Bayesian inference, (i) Fundamentals (ii) Asymptotics and (iii) Advanced models, focusing on nonparametric and semiparametric methods. For function estimation, the Bayesian semiparametric models using Gaussian process priors are discussed. For model selection, Bayes factors are explained for dealing with lack of fit in regression and goodness of fit in density estimation problems.

Host: 정연승     Korean     2016-05-25 17:26:52