세미나 및 콜로퀴엄

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구글 Calendar나 iPhone 등에서 구독하면 세미나 시작 전에 알림을 받을 수 있습니다.

The Erdos-Ko-Rado Theorem is a classic result about intersecting families of sets. More recently, analogous “EKR-type” type theorems have been developed for other types of objects. For example, non-trivially intersecting vector spaces, and overlapping strings. In this seminar we will give a proof of the EKR Theorem for permutations in Sn due to Godsil and Meagher. Along the way we will see some useful tools from algebraic graph theory. Namely, a bound on the maximum size of an independent set in a graph, equitable partitions, and eigenpolytopes.

 

Host: 엄상일     미정     2017-04-17 09:41:35

Let X be a smooth projective rational surface over an algebraically closed field. One version of a long standing conjecture asks whether the set of self-intersections of reduced curves is bounded below. This question can be reduced to studying singular plane curves. One approach is to measure how singular the curve is using a recently introduced quantity called an H-constant. This has raised some new open problems I will discuss.

Host: 이용남     영어     2017-04-11 09:45:36
Waldschmidt constants and Seshadri constants are asymptotic measure of effectivity and nefness related to plane curves. Evaluating them is related to the occurrence of curves of negative self-intersection on blow ups of the plane. I will discuss recent work on computing and bounding these quantities.
영어     2017-04-11 18:11:09

Chudnovsky posed a still open conjectural lower bound for Waldschmidt constants. I will relate this conjecture to certain open conjectures about ideal containments, which themselves are related to Waldschmidt constants.

Host: 이용남     영어     2017-04-11 09:53:16

2017 제2회 정오의 수학산책

 

 

 

강연자: 이윤원 (인하대)

일시: 2017년 4월 28일(금) 12:00 ~ 13:15

장소: 카이스트 자연과학동 E6-1 3435호

 

제목: Atiyah-Singer index theorem

내용: TBA

 

등록: 2017년 4월 26일(수) 오후 3시까지

        https://goo.gl/forms/0lqSboiW5A9vv9rd2

 

문의: hskim@kias.re.kr / 내선:8545

 

 

Host: 이지운     한국어     2017-02-28 16:12:46

Probabilistic methods in geometric group theory have recently gained in importance. In the course I will focus on the setting where a countable group G acts on a (possibly nonproper) Gromov hyperbolic space X. Examples include a mapping class group acting on the associated curve complex, or Out(F_n) acting on the complex of free factors, or a group acting on the contact graph of a CAT(0) cube complex it acts on. Under minor assumptions, Maher-Tiozzo show that a random walk on G, projected to X, almost surely converges to a point in the Gromov boundary of X. I will discuss the proof of this theorem. As an application, we will see that "generic" elements of mapping class groups are pseudo-Anosov, and (following Horbez) we will give a random walk proof of the classical theorem of Ivanov classifying subgroups of mapping class groups.

Host: 백형렬     영어     2017-04-18 14:17:32

Probabilistic methods in geometric group theory have recently gained in importance. In the course I will focus on the setting where a countable group G acts on a (possibly nonproper) Gromov hyperbolic space X. Examples include a mapping class group acting on the associated curve complex, or Out(F_n) acting on the complex of free factors, or a group acting on the contact graph of a CAT(0) cube complex it acts on. Under minor assumptions, Maher-Tiozzo show that a random walk on G, projected to X, almost surely converges to a point in the Gromov boundary of X. I will discuss the proof of this theorem. As an application, we will see that "generic" elements of mapping class groups are pseudo-Anosov, and (following Horbez) we will give a random walk proof of the classical theorem of Ivanov classifying subgroups of mapping class groups.

Host: 백형렬     영어     2017-04-18 14:24:53

Probabilistic methods in geometric group theory have recently gained in importance. In the course I will focus on the setting where a countable group G acts on a (possibly nonproper) Gromov hyperbolic space X. Examples include a mapping class group acting on the associated curve complex, or Out(F_n) acting on the complex of free factors, or a group acting on the contact graph of a CAT(0) cube complex it acts on. Under minor assumptions, Maher-Tiozzo show that a random walk on G, projected to X, almost surely converges to a point in the Gromov boundary of X. I will discuss the proof of this theorem. As an application, we will see that "generic" elements of mapping class groups are pseudo-Anosov, and (following Horbez) we will give a random walk proof of the classical theorem of Ivanov classifying subgroups of mapping class groups.

Host: 백형렬     영어     2017-04-18 14:28:40

This talk will review previous work on quadrupedal gaits and recent work on a generalized model for binocular rivalry proposed by Hugh Wilson. Both applications show how rigid phase-shift synchrony in periodic solutions of coupled systems of differential equations can help understand high level collective behavior in the nervous system.

 

 

Host: 김재경     영어     2017-02-21 12:38:07

2017 제3회 정오의 수학산책

 

 

 

강연자: 이수준(경희대)

일시: 2017년 5월 12일(금) 12:00 ~ 13:15

장소: 카이스트 자연과학동 E6-1 3435호

 

제목: 양자정보이론 소개 : 디지털정보 vs 양자정보

내용: TBA

 

등록: 2017년 5월 10일(수) 오후 3시까지

          https://goo.gl/forms/TnDIENKzVJAnxy9v2

 

문의: hskim@kias.re.kr / 내선:8545

 

Host: 이지운     한국어     2017-02-28 16:16:01

   In the talk, I discuss previous works on the arithmetic of various twisted special $L$-values and dynamical phenomena behind them. Main emphasis will be put on the problem of estimating several exponential sums such as Kloosterman sums and its relation to the problem of non-vanishing of special $L$-values with cyclotomic twists. A distribution of homological cycles on the modular curves will also be discussed and as a consequence, some results on a conjecture of Mazur-Rubin-Stein about the distribution of period integrals of elliptic modular forms will be presented.  

 
미정     2017-01-16 13:37:22

In this talk, I will introduce the distribution of eigenvalues of random normal matrix ensembles. Specifically, I will discuss the existence and universality of scaling limits for the eigenvalues at a bulk singularity, an isolated point in the interior at which the equilibrium density vanishes. I will describe how to find a suitable scale and how the rescaled ward’s identity can be used to prove the universality. This is joint work with Yacin Ameur.

Host: 이지운     영어     2017-04-11 09:35:19

The continuity problem is the question when effective (or Markov computable) maps between effectively given topological spaces are effectively continuous. It will be shown that this is always the case if the the range of the map is effectively bi-regular. As will be shown, such spaces appear quite naturally in the context of the problem.

 

 

Host: 엄상일     영어     2017-04-10 10:28:56

Evolutionary games of cyclic competitions have been extensively studied
to gain insights into one of the most fundamental phenomena in nature:
biodiversity that seems to be excluded by the principle of natural selection.
The Rock-Paper-Scissors (RPS) game of three species and
its extensions [e.g., the Rock-Paper-Scissors-Lizard-Spock (RPSLS) game] are
paradigmatic models in this field.
In all previous studies, the intrinsic symmetry associated with the cyclic competitions imposes
a limitation on the resulting coexistence states, leading to only selective types of such states.
We investigate the effect of nonuniform intraspecific competitions on coexistence and
find that a wider spectrum of coexistence states can emerge and persist.
This surprising finding is substantiated using three classes of cyclic game models through stability analysis,
Monte Carlo simulations and patterns of continuous spatiotemporal dynamical evolution.
Our finding indicates that intraspecific competitions or alternative symmetry-breaking mechanisms
can promote biodiversity to a broader extent than previously thought.

한국어     2017-02-21 12:32:16

 

Recent development of high throughput sequencing and CRISPR genome editing technology have brought great advances in the understanding of molecular mechanisms underlying diseases. We studied infertility in Drosophila model: deep sequencing analyses of small RNA, mRNA, and RNA immunoprecipitation sequencing (RIP-seq) showed that a conserved mRNA export factor, Thoc5, represses the expression of transposable elements, which are deleterious mobile genetic elements that cause genome instability and germ cell death. We also found that Thoc5 binds nascent RNAs and facilitates biogenesis of small RNAs, which in turn regulated transposable elements. Furthermore, we used CRISPR-Cpf1, a recently found class 2/type V CRISPR RNA-guided endonuclease that is distinct from the common CRISPR-Cas9, to generate mutant mice. Whole genome analyses of the mutant mice showed precise alteration of DNA sequence at the target genomic locus with no detectable off-target mutation. We generated a cell line with a single base change in Isocitrate Dehydrogenase I (IDH1), a gain-of-function mutation widely found in glioma patients. We further applied CRISPR genome editing to pathogenic bacteria to generate bacterial strains with mutations in genes required for quorum sensing, which is an intercellular communication system for detection cell density. The quorum sensing mutant strains showed reduced biofilm formation, and changes in expression profile of genes in the metabolic pathway.

 

Host: 강완모,김재경     미정     2017-04-03 13:24:54

Among the most well-known examples of L-functions are the Riemann zeta
function and the L-functions associated to classical modular forms.
Less well known, but equally important, are the L-functions associated
to Maass forms, which are eigenfunctions of the Laplace-Beltrami
operator on a hyperbolic surface. Named after H. Maass, who discovered
some examples in the 1940s, Maass forms remain largely mysterious.

Fortunately, there are concrete tools to study Maass forms: trace
formulas, which relate the spectrum of the Laplace operator on a
hyperbolic surface to its geometry. After Selberg introduced his
famous trace formula in 1956, his ideas were generalised, and various
trace formulas have been constructed and studied. However, there are
few numerical results from trace formulas, the main obstacle being
their complexity. Various types of trace formulas are investigated,
constructed and used to understand automorphic representations and
their L-functions from a theoretical point of view, but most are not
explicit enough to implement in computer code.

Having explicit computations of trace formulas makes many potential
applications accessible. In this talk, I will explain the
computational aspects of the Selberg trace formula for GL(2) for
general levels and applications towards the Selberg eigenvalue
conjecture and classification of 2-dimensional Artin representations
of small conductor.
This is a joint work with Andrew Booker and Andreas Strömbergsson.

Host: 임보해     영어     2017-03-02 11:08:35

Imagine you want to present your collection of n coins on a shelf, taking as little space as possible – how should you arrange the coins?

 
More precisely, we are given n circular disks of different radii, and we want to place them in the plane so that they touch the x-axis from above, such that no two disks overlap. The goal is to minimize the length of the range from the leftmost point on a disk to the rightmost point on a disk.
 
On this seemingly innocent problem we will meet a wide range of algorithmic concepts: An efficient algorithm for a special case, an NP-hardness proof, an approximation algorithm with a guaranteed approximation factor, APX-hardness, and a quasi-polynomial time approximation scheme.

 

Host: 엄상일     미정     2017-03-29 15:18:29