# 세미나 및 콜로퀴엄

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

It is a common theme in algebraic geometry that many constructions have only been done for schemes and morphisms of finite type. However, in arithmetic geometry one would also like to work with infinite objects, as for example infinite level modular curve. In my talk I motivate and define schemes and morphism satisfying a weaker finiteness property, which contain many examples from arithmetic geometry. The aim of this talk is to extend the definition of cohomology with compact support to them; in fact, we even obtain Grothendieck's six operations for this class of morphism.

Host: 김완수     영어     2019-09-19 09:04:26
Support vector machine (SVM) is a very popular technique for classification. A key property of SVM is that its discriminant function depends only on a subset of data points called support vectors. This comes from the representation of the discriminant function as a linear combination of kernel functions associated with individual cases. Despite the direct relation between each case and the corresponding coefficient in the representation, the influence of cases and outliers on the classification rule has not been examined formally. Borrowing ideas from regression diagnostics, we define case influence measures for SVM and study how the classification rule changes as each case is perturbed. To measure case sensitivity, we introduce a weight parameter for each case and reduce the weight from one to zero to link the full data solution to the leave-one-out solution. We develop an efficient algorithm to generate case-weight adjusted solution paths for SVM. The solution paths and the resulting case influence graphs facilitate evaluation of the influence measures and allow us to examine the relation between the coefficients of individual cases in SVM and their influences comprehensively. We present numerical results to illustrate the benefit of this approach.
Host: 정연승     한국어     2019-09-19 22:39:29

Synchronization phenomenon is ubiquitous in an ensemble of coupled oscillators, e.g., hand clapping in opera and musical halls, flashing of fireflies and heart beating of pacemaker cells, etc. In the last forty years, the Kuramoto model served as a prototype model for describing such synchronization phenomena. In particular, we will consider the Kuramoto model under the stochastic noise. As the number of oscillators tends to infinity, we can derive the kinetic

equation for the Kuramoto model by using the standard BBGKY hierarchy. In this talk, we will consider the asymptotic behavior for the kinetic Kuramoto models under the stochastic noise, and talk about their large time behaviors.

Host: 권순식     Contact: 최은아 (8111)     미정     2019-09-09 11:59:25
Regularization methods for modeling and prediction are popular in statistics and machine learning. They may be viewed as the procedures that modify the maximum likelihood principle or empirical risk minimization. In particular, methods of regularization defined in reproducing kernel Hilbert spaces (known as kernel methods) provide versatile tools for statistical learning. Primary examples include smoothing splines and support vector machines. I will describe kernel methods focusing on these two examples and discuss some relevant statistical and computational issues. Further I will provide a general description of kernel methods covering mathematical elements and results underlying the methods. Part I: Smoothing Splines (September 30, Monday) Part II: Support Vector Machines (October 2, Wednesday and October 4, Friday) Part III: Kernel Methods (October 8, Tuesday)
Host: 정연승     미정     2019-09-23 13:13:45
Regularization methods for modeling and prediction are popular in statistics and machine learning. They may be viewed as the procedures that modify the maximum likelihood principle or empirical risk minimization. In particular, methods of regularization defined in reproducing kernel Hilbert spaces (known as kernel methods) provide versatile tools for statistical learning. Primary examples include smoothing splines and support vector machines. I will describe kernel methods focusing on these two examples and discuss some relevant statistical and computational issues. Further I will provide a general description of kernel methods covering mathematical elements and results underlying the methods. Part I: Smoothing Splines (September 30, Monday) Part II: Support Vector Machines (October 2, Wednesday and October 4, Friday) Part III: Kernel Methods (October 8, Tuesday)
Host: 정연승     미정     2019-09-23 13:15:40
A diffusion equation is one of most famous partial differential equations. Lots of generalized diffusion equations have appeared on the basis of scientific meaning. Equations describing degenerate or unbounded diffusion including stochastic noises are some of them. In this talk, we are going to discuss change of regularity of solutions depending on degeneracy and unboundedness of diffusion and stochastic noise.
Host: 폴정     영어     2019-09-19 15:40:02
Regularization methods for modeling and prediction are popular in statistics and machine learning. They may be viewed as the procedures that modify the maximum likelihood principle or empirical risk minimization. In particular, methods of regularization defined in reproducing kernel Hilbert spaces (known as kernel methods) provide versatile tools for statistical learning. Primary examples include smoothing splines and support vector machines. I will describe kernel methods focusing on these two examples and discuss some relevant statistical and computational issues. Further I will provide a general description of kernel methods covering mathematical elements and results underlying the methods. Part I: Smoothing Splines (September 30, Monday) Part II: Support Vector Machines (October 2, Wednesday and October 4, Friday) Part III: Kernel Methods (October 8, Tuesday)
Host: 정연승     미정     2019-09-23 13:17:45

This is joint work with Sławomir Kołodziej. We show that the complex m-Hessian
operator of a Holder continuous m-subharmonic function is well dominated by the corresponding capacity. As consequence we obtain the Holder continuous subsolution theorem for the complex m-Hessian equation.

Host: 권순식     Contact: 최은아 (8111)     미정     2019-09-17 10:49:37
(This is a reading seminar for graduate students.) Recall that there is a spectral sequence strongly converging to the connective $K$-groups whose second page is given by the Zariski cohomology of connective $K$-theory sheaf. In the proof of this result by Quillen, the localization theorem is the most important ingredient. We prove an analogous statement for non-connective $K$-theory with both Zariski and Nisnevich cohomology for noetherian schemes of finite Krull dimension. This theorem is usually phrased as \"non-connective algebraic $K$-theory satisfies Zariski and Nisnevich descent\". It is known that non-connective algebraic $K$-theory does not satisfy étale descent.
Host: 박진현     Contact: 박진현 (2734)     한국어     2019-09-21 21:31:56
Regularization methods for modeling and prediction are popular in statistics and machine learning. They may be viewed as the procedures that modify the maximum likelihood principle or empirical risk minimization. In particular, methods of regularization defined in reproducing kernel Hilbert spaces (known as kernel methods) provide versatile tools for statistical learning. Primary examples include smoothing splines and support vector machines. I will describe kernel methods focusing on these two examples and discuss some relevant statistical and computational issues. Further I will provide a general description of kernel methods covering mathematical elements and results underlying the methods. Part I: Smoothing Splines (September 30, Monday) Part II: Support Vector Machines (October 2, Wednesday and October 4, Friday) Part III: Kernel Methods (October 8, Tuesday)
Host: 정연승     미정     2019-09-23 13:19:26
A well-known Ramsey-type puzzle for children is to prove that among any 6 people either there are 3 who know each other or there are 3 who do not know each other. More generally, a graph G arrows a graph H if for any coloring of the edges of G with two colors, there is a monochromatic copy of H. In these terms, the above puzzle claims that the complete 6-vertex graph K_6 arrows the complete 3-vertex graph K_3. We consider sufficient conditions on the dense host graphs G to arrow long paths and even cycles. In particular, for large n we describe all multipartite graphs that arrow paths and cycles with 2n edges. This implies a conjecture by Gyárfás, Ruszinkó, Sárkőzy and Szemerédi from 2007 for such n. Also for large n we find which minimum degree in a (3n-1)-vertex graph G guarantees that G arrows the 2n-vertex path. This yields a more recent conjecture of Schelp. This is joint work with Jozsef Balogh, Mikhail Lavrov and Xujun Liu. (*Joint Colloquium between KAIST Mathematical Sciences and IBS Discrete Mathematics Group)
Host: 엄상일     영어     2019-09-20 13:21:20

The Boussinesq abcd system was originally derived by Bona, Chen and Saut [J. Nonlinear. Sci. (2002)] as a rst order 2-wave approximations of the incompressible and irrotational, two dimensional water wave equations in the shallow water wave regime. Among many particular regimes, the Hamiltonian generic regime is characterized by the setting b = d > 0 and a; c < 0. It is known that the system in this regime is globally well-posed for small data in the energy space H1 H1 by Bona, Chen and Saut [Nonlinearity (2004)]. In this talk, we are going to discuss about the decay of small solutions to abcd system in three directions: First, for a weakly dispersive abcd systems (characterized only in terms of parameters a; b and c), all small solutions must decay to zero, locally strongly in the energy space, in proper subset of the light cone jxj jtj. Second, for every ray x = vt, jvj < 1 inside the light cone, small solutions to suciently dispersive system (smallness and dispersion are characterized by v) decay to zero, in proper subset along the ray. Last, small solutions decay to zero in exterior regions jxj jtj under suitable conditions of parameters (a; b; c). All results rule out, among other things, the existence of zero or nonzero speed or super-luminical small solitary waves in each regime where decay is present.

This is joint work with Claudio Munoz.

Host: 권순식     Contact: 최은아 (8111)     미정     2019-09-17 10:53:00
We would give a characterization of those motivic spectra for which the associated slice spectral sequence converges strongly. The characterization is given in terms of the birational covers introduced by the author in order to study the Bloch-Beilinson filtration.
Host: 박진현     Contact: 박진현 (2734)     영어     2019-09-20 13:50:53
In this talk, we present the notion of Stark units in function field arithmetic. This notion was first introduced for investigations on the construction of certain units from the L-function of Drinfeld modules, i.e. log-algebraicity identities. More generally, to a Drinfeld module of higher dimension defined over a function field, we can associate its module of Stark units. We give basic properties of this object and state its connection with Taelman\'s class formula. Then we will describe the module of Stark units attached to the Carlitz module and its power tensors defined over certain abelian extensions of function fields.
Host: Bo-Hae Im     영어     2019-09-23 14:22:17

Stochastic heat equations usually refer to heat equations perturbed by noise. Depending on noise, stochastic heat equations have similar properties as heat equations such as strict positivity or properties which cannot be seen from heat equations such as intermittency. We consider various properties of stochastic heat equations in this talk. (This talk will be a survey talk and should be accessible to all graduate students.)

Host: 권순식     Contact: 최은아 (8111)     미정     2019-09-09 11:52:13

Let F and H be graphs. The subgraph counting function ex(n,H,F) is defined as the maximum possible number of subgraphs H in an n-vertex F-free graph. This function is a direct generalization of the Turán function as ex(n,F)=ex(n,K2,F). The systematic study of ex(n,H,F) was initiated by Alon and Shikhelman in 2016 who generalized several classical results in extremal graph theory to the subgraph counting setting. Prior to their paper, a number of individual cases were investigated; a well-known example is the question to determine the maximum number of pentagons in a triangle-free graph. In this talk we will survey results on the function ex(n,H,F) including a number of recent papers. We will also discuss this function’s connection to hypergraph Turán problems.

Host: 엄상일     영어     2019-09-11 07:17:25

Given a graph GG, we define exc(G)exc(G) to be the minimum value of tt for which there exists a constant N(t,G)N(t,G) such that every tt-connected graph with at least N(t,G)N(t,G) vertices contains GG as a minor. The value of exc(G)exc(G) is known to be tied to the vertex cover number τ(G)τ(G), and in fact τ(G)≤exc(G)≤312(τ(G)+1)τ(G)≤exc(G)≤312(τ(G)+1). We give the precise value of exc(G)exc(G) when GG is a forest. In particular we find that exc(G)≤τ(G)+2exc(G)≤τ(G)+2 in this setting, which is tight for infinitely many forests.

영어     2019-09-04 16:56:32

In this talk we consider a reaction-diffusion model for the spreading of farmers in Europe, which was occupied by hunter-gatherers; this process is known as the Neolithic agricultural revolution. The spreading of farmers is modelled by a nonlinear porous medium type diffusion equation which coincides with the singular limit of another model for the dispersal of farmers as a small parameter tends to zero. From the ecological viewpoint, the nonlinear diffusion takes into account the population density pressure of the farmers on their dispersal. The interaction between farmers and hunter-gatherers is of the Lotka-Volterra prey-predator type. We show the existence and uniqueness of a global in time solution and study its asymptotic behaviour as time tends to infinity.

미정     2019-09-02 14:07:13

After the discovery of algebraic $K$-theory of schemes by Quillen, it was anticipated that algebraic cycles would play a fundamental role in computing the $K$-groups of schemes. These groups are usually very hard to compute even as they contain a lot of information about the underlying scheme. For smooth schemes, the problem of describing $K$-theory by algebraic cycles was satisfactorily settled by works of several mathematicians, spanned over many years.

However, solving this problem under the presence of singularities is still a very challenging task.

The theory of additive Chow groups and the Chow groups with modulus were invented to address this problem.

Even if it is not yet clear if these Chow groups will finally solve the problem, I shall present some positive results in this direction in my talk. In particular, I shall show that the additive Chow groups do completely describe the $K$-theory of infinitesimal neighborhoods of the origin in the affine line. This was the initial motivation of the discovery of additive Chow groups by Bloch and Esnault. This talk is based on a joint work with Rahul Gupta.

Host: 박진현     영어     2019-09-02 15:56:42

After the discovery of algebraic $K$-theory of schemes by Quillen, it was anticipated that algebraic cycles would play a fundamental role in computing the $K$-groups of schemes. These groups are usually very hard to compute even as they contain a lot of information about the underlying scheme. For smooth schemes, the problem of describing $K$-theory by algebraic cycles was satisfactorily settled by works of several mathematicians, spanned over many years.

However, solving this problem under the presence of singularities is still a very challenging task.

The theory of additive Chow groups and the Chow groups with modulus were invented to address this problem.

Even if it is not yet clear if these Chow groups will finally solve the problem, I shall present some positive

results in this direction in my talk. In particular, I shall show that the additive Chow groups do completely describe the $K$-theory of infinitesimal neighborhoods of the origin in the affine line. This was the initial motivation of the discovery of additive Chow groups by Bloch and Esnault. This talk is based on a joint work with Rahul Gupta.

Host: 박진현     영어     2019-09-02 16:09:56