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Information Center for Mathematical Science

세미나

Information Center for Mathematical Science

세미나

CMS-KIAS Seminar

This talk will illustrate a geometric and probabilistic approach of Asymptotic Geometric Analysis to several high-dimensional phenomena described by a large class of random matrices. Those include Gaussian and +1/-1 matrices, more generally, subgaussian matrices, and also matrices determined by subsets of bounded orthogonal systems. We shall consider random embeddings of normed spaces (notably, of the Euclidean space) and some properties of combinatorial flavor of random 0/1 polytops. These phenomena are intimately connected to probabilistic inequalities for singular numbers of a wide class of random matrices.

서울대학교 수학강연회
  • Title : Group Bargaining Theory
  • Speaker : 채수찬
  • Data : 2008-10-28 16:00:00
  • Host : 서울대학교 수리과학부
  • Place :

일정 :
* 제1강 : 10월 28일(화) 오후4-6시 Game Theoretical Preliminaries
* 제2강 : 10월 29일(수) 오후4-6시 Two-Person Bargaining Theory
* 제3강 : 11월 4일(화) 오후4-6시 N-Person Bargaining Theory
* 제4강 : 11월 5일(수) 오후4-6시 Group Bargaining Theory
* 제5강 : 11월 11일(화) 오후4-6시 Group Power

한국고등과학원 세미나

This talk will illustrate a geometric and probabilistic approach of Asymptotic Geometric Analysis to several high-dimensional phenomena described by a large class of random matrices. Those include Gaussian and +1/-1 matrices, more generally, subgaussian matrices, and also matrices determined by subsets of bounded orthogonal systems. We shall consider random embeddings of normed spaces (notably, of the Euclidean space) and some properties of combinatorial flavor of random 0/1 polytops. These phenomena are intimately connected to probabilistic inequalities for singular numbers of a wide class of random matrices.

한국고등과학원 세미나

Free probability theory provides concepts and tools for the treatment of many random matrix models in the limit that the size of the matrix tends to infinity. In particular, Gaussian random matrices, with independent and normal entries, are described by semicircular elements; the understanding of the latter is intimately connected with the combinatorics of non-crossing pairings. It seems that more general Gaussian random matrices, where one allows correlations between the entries, cannot be treated nicely within free probabily theory. However, it turns out that they fit well into the frame of a more general, 'operator-valued', free probability theory, and can be described by operator-valued semicircular elements. For the understanding of those, the combinatorics of non-crossing pairings becomes even more prominent. In my talk, I will explain these connections and also point out how the understanding of operator-valued semicircular elements is related to solving special quadratic matrix equations under some positivity constraint.

한국고등과학원 세미나

In this talk I will recall facts about finite groups which act freely on spheres and how they can be extended to products of spheres under certain conditions. A key ingredient is the geometric characterization of spaces with periodic cohomology.

한국고등과학원 세미나

한국고등과학원 세미나

The principal aim of this series of my lectures is to provide my audience with an overview of the most fascinating development in the theory of the Riemann zeta-function that was made in the last decade. I shall start with a brief history of the study of the zeta-function and the distribution of prime numbers, with which I shall try to explain why and how we are lead to the study of mean values of the zeta and L- functions. Thus this part can also be regarded as an introduction to the very core of modern Analytic Number Theory. With this, I shall begin an account of the spectral theory of real analytic automorphic forms, with minimum prerequisites. My argument is completely 'classic' and no heavy preparation from representation theory is assumed. Then I shall give the spectral theory of sums of Kloosterman sums that was created by Bruggeman and Kuznetsov, and that caused a fundamental change in Analytic Number Theory. Lastly as an application of results so far delivered I shall give a beautiful/mysterious spectral expansion of a moment of the Riemann zeta-function. The result will be viewed from several angles including the Riemann Hypothesis.

한국고등과학원 세미나

The principal aim of this series of my lectures is to provide my audience with an overview of the most fascinating development in the theory of the Riemann zeta-function that was made in the last decade. I shall start with a brief history of the study of the zeta-function and the distribution of prime numbers, with which I shall try to explain why and how we are lead to the study of mean values of the zeta and L- functions. Thus this part can also be regarded as an introduction to the very core of modern Analytic Number Theory. With this, I shall begin an account of the spectral theory of real analytic automorphic forms, with minimum prerequisites. My argument is completely 'classic' and no heavy preparation from representation theory is assumed. Then I shall give the spectral theory of sums of Kloosterman sums that was created by Bruggeman and Kuznetsov, and that caused a fundamental change in Analytic Number Theory. Lastly as an application of results so far delivered I shall give a beautiful/mysterious spectral expansion of a moment of the Riemann zeta-function. The result will be viewed from several angles including the Riemann Hypothesis.

한국고등과학원 세미나

The principal aim of this series of my lectures is to provide my audience with an overview of the most fascinating development in the theory of the Riemann zeta-function that was made in the last decade. I shall start with a brief history of the study of the zeta-function and the distribution of prime numbers, with which I shall try to explain why and how we are lead to the study of mean values of the zeta and L- functions. Thus this part can also be regarded as an introduction to the very core of modern Analytic Number Theory. With this, I shall begin an account of the spectral theory of real analytic automorphic forms, with minimum prerequisites. My argument is completely 'classic' and no heavy preparation from representation theory is assumed. Then I shall give the spectral theory of sums of Kloosterman sums that was created by Bruggeman and Kuznetsov, and that caused a fundamental change in Analytic Number Theory. Lastly as an application of results so far delivered I shall give a beautiful/mysterious spectral expansion of a moment of the Riemann zeta-function. The result will be viewed from several angles including the Riemann Hypothesis.

한국고등과학원 세미나

Uncoordinated individuals in human society pursuing their personally optimal strategies do not always achieve the social optimum, the most beneficial state to the society as a whole. Instead, strategies form Nash equilibria, which are, in general, socially suboptimal. Society, therefore, has to pay a price of anarchy for the lack of coordination among its members, which is often difficult to quantify in engineering, economics and policymaking. Here, we report on an assessment of this price of anarchy by analyzing the road networks of Boston, New York, and London as well as complex model networks, where one's travel time serves as the relevant cost to be minimized. Our simulation shows that uncoordinated drivers possibly spend up to 30% more time than they would in socially optimal traffic, which leaves substantial room for improvement. Counterintuitively, simply blocking certain streets can partially improve the traffic condition to a measurable extent based on our result. One-sentence summaries: Traffic in transportation networks often substantially suboptimal due to a lack of coordination among users can be guided to the social optimum without directly controlling individual behavior by adjusting the underlying network structure appropriately.

한국고등과학원 세미나

The principal aim of this series of my lectures is to provide my audience with an overview of the most fascinating development in the theory of the Riemann zeta-function that was made in the last decade. I shall start with a brief history of the study of the zeta-function and the distribution of prime numbers, with which I shall try to explain why and how we are lead to the study of mean values of the zeta and L- functions. Thus this part can also be regarded as an introduction to the very core of modern Analytic Number Theory. With this, I shall begin an account of the spectral theory of real analytic automorphic forms, with minimum prerequisites. My argument is completely 'classic' and no heavy preparation from representation theory is assumed. Then I shall give the spectral theory of sums of Kloosterman sums that was created by Bruggeman and Kuznetsov, and that caused a fundamental change in Analytic Number Theory. Lastly as an application of results so far delivered I shall give a beautiful/mysterious spectral expansion of a moment of the Riemann zeta-function. The result will be viewed from several angles including the Riemann Hypothesis.

한국고등과학원 세미나

2009 will be the 30th anniversary of the first discovery of cosmic gravitational lens. Since the first gravitaionally lensed double quasars Q0957+561, a variety of gravitaional lens systems such as rings, arcs, microlenses, and weak lenses have been discovered over the years. I will briefly review these systems, and discuss the promises that the gravitational lenses were hoped to deliver and the realities that we had learned so far.

한국고등과학원 세미나

Giant elliptical galaxies are usually composed of trillion stars. Their origin and the path of evolution have been a subject of heated debates ever since their discovery. Their preference to dwell in the cluster centres and hosting the largest central black holes all make the mystery even more fascinating. I present the current status on this issue and the progress made in my group lately.

POSTEC Math Colloquium

POSTEC Math Colloquium

POSTEC Math Colloquium

POSTEC Math Colloquium

POSTEC Math Colloquium

POSTEC Math Colloquium

POSTEC Math Colloquium
  • Title : Graph Braid Groups
  • Speaker : 고기형
  • Data : 2008-09-06 16:00:00
  • Host : 포항수학연구소(PMI), 포스텍 BK21 수학사업단
  • Place :