The classical Schubert calculus arose from classical enumerative geometric problems, and is concerned with the study of the cohomology ring of complex Grassmannians, or generally, of homogeneous varieties G/P of general Lie types. One of the most central problems in this subject is to find a manifestly positive formula of the structure constants for the cup product of Schubert cohomology classes. On the other hand, a Gelfand-Cetlin polytope is a special convex polytope, occurring in many subjects such as representation theory, toric geometry, mathematical physics, and combinatorics. It turns out to be also closely related with Schubert calculus, as was studied by Kogan and Kiritchenko-Smirnov-Timorin. In these lectures, I will talk about the relationship between both sides. In Lecture I, I will give an introduction to the classical Schubert calculus. In Lecture II, I will review some basic properties of Gelfand-Cetlin polytopes and systems, as well as some relationships between them and Schubert calculus. In Lecutre III, IV, I will talk about toric degeneration of flag varieties, together with the transversal intersection of certain Schubert varieties, based on my joint work with DongSeon Hwang, Hwayoung Lee and Jae-Hyouk Lee.

The classical Schubert calculus arose from classical enumerative geometric problems, and is concerned with the study of the cohomology ring of complex Grassmannians, or generally, of homogeneous varieties G/P of general Lie types. One of the most central problems in this subject is to find a manifestly positive formula of the structure constants for the cup product of Schubert cohomology classes. On the other hand, a Gelfand-Cetlin polytope is a special convex polytope, occurring in many subjects such as representation theory, toric geometry, mathematical physics, and combinatorics. It turns out to be also closely related with Schubert calculus, as was studied by Kogan and Kiritchenko-Smirnov-Timorin. In these lectures, I will talk about the relationship between both sides. In Lecture I, I will give an introduction to the classical Schubert calculus. In Lecture II, I will review some basic properties of Gelfand-Cetlin polytopes and systems, as well as some relationships between them and Schubert calculus. In Lecutre III, IV, I will talk about toric degeneration of flag varieties, together with the transversal intersection of certain Schubert varieties, based on my joint work with DongSeon Hwang, Hwayoung Lee and Jae-Hyouk Lee.

TBA

TBA

 In this talk, I will overview the regularity theory for p(x)-Laplace equation. The p(x)-Laplace equation is denoted by
div(|Du|^{p(x)-2}Du)=0 in Omega,
where p(x):Omega to mr satisfies 1<p_-leq p(x)leq p_+<infty. This equation is a generalization of the p-Laplace equation div(|Du|^{p-2}Du)=0, where p is a constant in (1,infty).
One can expect that the regularity of solutions to p(x)-Laplace equation depends on the one of p(x). So, I will present the conditions on p(x) in order to obtain various regularities of solutions.
In addition, I will briefly introduce Calderon-Zygmund type estimates for elliptic equations in the setting of variable exponent Lebesgue space.

In this talk, we consider nonlinear elliptic equations involving the fractional Laplacian or the pseudo-relativistic Laplacian. We shall be concerned about existence and nonexistence results, and asymptotic profile of the solutions when a parameter of the equations is close to a critical value.

The classical Schubert calculus arose from classical enumerative geometric problems, and is concerned with the study of the cohomology ring of complex Grassmannians, or generally, of homogeneous varieties G/P of general Lie types. One of the most central problems in this subject is to find a manifestly positive formula of the structure constants for the cup product of Schubert cohomology classes. On the other hand, a Gelfand-Cetlin polytope is a special convex polytope, occurring in many subjects such as representation theory, toric geometry, mathematical physics, and combinatorics. It turns out to be also closely related with Schubert calculus, as was studied by Kogan and Kiritchenko-Smirnov-Timorin. In these lectures, I will talk about the relationship between both sides. In Lecture I, I will give an introduction to the classical Schubert calculus. In Lecture II, I will review some basic properties of Gelfand-Cetlin polytopes and systems, as well as some relationships between them and Schubert calculus. In Lecutre III, IV, I will talk about toric degeneration of flag varieties, together with the transversal intersection of certain Schubert varieties, based on my joint work with DongSeon Hwang, Hwayoung Lee and Jae-Hyouk Lee.

번역기 중 가장 좋다는 구글번역기에 '비단 골이 전부가 아니다'라는 문장을 넣으면, 'Silk is not the only goal'이라고 번역한다. 이라한 오역의 근원은, 번역을 언어의 구조, 성질, 패턴 연구가 아닌 엉뚱한 통계확률로 접근하기 때문이다. 컴퓨터가 발달하고 인간의 지능을 가진 로봇을 만드려는 인간의 노력은 인간이 사용하는 자연어를 기계언어로 번역(프로그램 용어로 compile)하는 문제를 핵심 과제로 부각시켰고 그 연구에 많은 돈과 인력이 투입되고 있다.

이 발표의 목적은 한글 고유의 조사와 서술어미 변형을 구현하는(representation) 수학적 방법론 제시 및 한글 문장의 구문분석에 응용 프로그램을 시연함으로써, 한글구문분석의 올바른 방향을 제시하고자 위함이다.

issue samples from the same tumor are heterogeneous. They consist of different subclones that can be characterized by differences in DNA nucleotide sequences and copy numbers on multiple loci. Inference on tumor heterogeneity thus involves the identification of the subclonal copy number and single nucleotide mutations at a selected set of loci. We carry out such inference on the basis of a Bayesian feature allocation model. We jointly model subclonal copy numbers and the corresponding allele sequences for the same loci, using three random matrices, L, Z and w to represent subclonal copy numbers (L), the number of sub- clonal variant alleles (Z) and the cellular fractions (w) of subclones in one or more tumor samples, respectively. The unknown number of subclones implies a random number of columns. More than one subclone indicates tumor heterogeneity. Using simulation studies and a real data analysis with next-generation sequencing data, we demonstrate how posterior inference on the subclonal structure is enhanced with the joint modeling of both structure and sequencing variants on subclonal genomes. An R package is available at http://cran.r-project.org/web/packages/ BayClone2/index.html. 

Abstract: issue samples from the same tumor are heterogeneous. They consist of different subclones that can be characterized by differences in DNA nucleotide sequences and copy numbers on multiple loci. Inference on tumor heterogeneity thus involves the identification of the subclonal copy number and single nucleotide mutations at a selected set of loci. We carry out such inference on the basis of a Bayesian feature allocation model. We jointly model subclonal copy numbers and the corresponding allele sequences for the same loci, using three random matrices, L, Z and w to represent subclonal copy numbers (L), the number of sub- clonal variant alleles (Z) and the cellular fractions (w) of subclones in one or more tumor samples, respectively. The unknown number of subclones implies a random number of columns. More than one subclone indicates tumor heterogeneity. Using simulation studies and a real data analysis with next-generation sequencing data, we demonstrate how posterior inference on the subclonal structure is enhanced with the joint modeling of both structure and sequencing variants on subclonal genomes. An R package is available at http://cran.r-project.org/web/packages/ BayClone2/index.html.

Abstract: issue samples from the same tumor are heterogeneous. They consist of different subclones that can be characterized by differences in DNA nucleotide sequences and copy numbers on multiple loci. Inference on tumor heterogeneity thus involves the identification of the subclonal copy number and single nucleotide mutations at a selected set of loci. We carry out such inference on the basis of a Bayesian feature allocation model. We jointly model subclonal copy numbers and the corresponding allele sequences for the same loci, using three random matrices, L, Z and w to represent subclonal copy numbers (L), the number of sub- clonal variant alleles (Z) and the cellular fractions (w) of subclones in one or more tumor samples, respectively. The unknown number of subclones implies a random number of columns. More than one subclone indicates tumor heterogeneity. Using simulation studies and a real data analysis with next-generation sequencing data, we demonstrate how posterior inference on the subclonal structure is enhanced with the joint modeling of both structure and sequencing variants on subclonal genomes. An R package is available at http://cran.r-project.org/web/packages/ BayClone2/index.html.

Issue samples from the same tumor are heterogeneous. They consist of different subclones that can be characterized by differences in DNA nucleotide sequences and copy numbers on multiple loci. Inference on tumor heterogeneity thus involves the identification of the subclonal copy number and single nucleotide mutations at a selected set of loci

We carry out such inference on the basis of a Bayesian feature allocation model. We jointly model subclonal copy numbers and the corresponding allele sequences for the same loci, using three random matrices, L, Z and w to represent subclonal copy numbers (L), the number of sub- clonal variant alleles (Z) and the cellular fractions (w) of subclones in one or more tumor samples, respectively. The unknown number of subclones implies a random number of columns. More than one subclone indicates tumor heterogeneity.

Using simulation studies and a real data analysis with next-generation sequencing data, we demonstrate how posterior inference on the subclonal structure is enhanced with the joint modeling of both structure and sequencing variants on subclonal genomes

An R package is available at http://cran.r-project.org/web/packages/ BayClone2/index.html.

 The disk embedding problem is of fundamental importance in the study of topology of dimension four. We will discuss backgrounds on its significance and difficulty, including why dimension four is intrinsically different from other dimensions, and then present some recent advances toward the existence and non-existence of embedded disks.

Primitive (birational) automorphisms of projective manifolds, which are irreducible au-
tomorphisms of manifolds, are natural objects in birational algebraic geometry. They are
also very closely related to complex dynamics of several variables. In fact, the dynamical
degrees of birational automorphisms (a kind of renement of a more classical notion of
topological entropy of automorphisms, tting very well with birational geometry), the relative dynamical degrees (their relative version) and the product formula (a kind of Kunneth type formula), introduced by Dinh-Sibony [DS], Dinh-Nyugen [DN], provide very powerful tools also in studying primitive birational automorphisms of manifolds.
In Lecture 1, I would like to give an overview of the basic notions (entropy, dynamical
degrees, relative dynamical degrees etc) and their basic properties with concrete applications for the study of primitive (birational) automorphisms. This lecture is, in some sense, an updated version of [Og].
In Lectures II, III, I would like to prove the well-denedness and the birational invariance
of dynamical degrees, the most basic property of the dynamical degree. The original proof ([DS]) is transcendental being based on some detailed analysis of currents. Here I explain a new purely algebro-geometric proof due to Truong ([Tr]), which is based on a precise form of Chow's moving lemma ([Ro]).
In Lectures IV, V, I would like to prove the product formula, the most fundamental
and useful property of relative dynamical degrees. Here I explain again an algebraic proof
following a guideline explained in [Tr], which is a modication of original analytic proofs
([DN], [DNT]) into an algebraic one again using a precise form of Chow's moving lemma.

References

[DS] Dinh, T.-C., Sibony, N., Une borne superieure de l'entropie topologique d'une application rationnelle, Ann. of Math., 161 (2005) 1637{1644. arXiv:math/0303271.

[DN] Dinh, T.-C., Nguyen V.-A., Comparison of dynamical degrees for semi-conjugate meromorphic maps, Comment. Math. Helv. 86 (2011) 817{840. arXiv:0903.2621.

[DNT] Dinh, T.-C., Nguyen V.-A., Truong, T.-T., On the dynamical degrees of meromorphic maps preserving a bration, Commun. Contemp. Math. 14 (2012) 18pp, arXiv: 1108.4792.

[Og] Oguiso, K., Some aspects of explicit birational geometry inspired by complex dynamics, Proceedings of the International Congress of Mathematicians, Seoul 2014 (Invited Lectures) Vol.II (2015), 695{721. arXiv:1404.2982.

[Ro] Roberts, J., Chow's moving lemma, in Algebraic geometry, Oslo 1970, F. Oort (ed.), WoltersNoordhoff, Publ. Groningnen (1972), 89{96.

[Tr] Truong, T.T., (Relative) dynamical degrees of rational maps over an algebraic closed eld, arXiv:1501.01523.

Primitive (birational) automorphisms of projective manifolds, which are irreducible au-
tomorphisms of manifolds, are natural objects in birational algebraic geometry. They are
also very closely related to complex dynamics of several variables. In fact, the dynamical
degrees of birational automorphisms (a kind of renement of a more classical notion of
topological entropy of automorphisms, tting very well with birational geometry), the relative dynamical degrees (their relative version) and the product formula (a kind of Kunneth type formula), introduced by Dinh-Sibony [DS], Dinh-Nyugen [DN], provide very powerful tools also in studying primitive birational automorphisms of manifolds.
In Lecture 1, I would like to give an overview of the basic notions (entropy, dynamical
degrees, relative dynamical degrees etc) and their basic properties with concrete applications for the study of primitive (birational) automorphisms. This lecture is, in some sense, an updated version of [Og].
In Lectures II, III, I would like to prove the well-denedness and the birational invariance
of dynamical degrees, the most basic property of the dynamical degree. The original proof ([DS]) is transcendental being based on some detailed analysis of currents. Here I explain a new purely algebro-geometric proof due to Truong ([Tr]), which is based on a precise form of Chow's moving lemma ([Ro]).
In Lectures IV, V, I would like to prove the product formula, the most fundamental
and useful property of relative dynamical degrees. Here I explain again an algebraic proof
following a guideline explained in [Tr], which is a modication of original analytic proofs
([DN], [DNT]) into an algebraic one again using a precise form of Chow's moving lemma.

References

[DS] Dinh, T.-C., Sibony, N., Une borne superieure de l'entropie topologique d'une application rationnelle, Ann. of Math., 161 (2005) 1637{1644. arXiv:math/0303271.

[DN] Dinh, T.-C., Nguyen V.-A., Comparison of dynamical degrees for semi-conjugate meromorphic maps, Comment. Math. Helv. 86 (2011) 817{840. arXiv:0903.2621.

[DNT] Dinh, T.-C., Nguyen V.-A., Truong, T.-T., On the dynamical degrees of meromorphic maps preserving a bration, Commun. Contemp. Math. 14 (2012) 18pp, arXiv: 1108.4792.

[Og] Oguiso, K., Some aspects of explicit birational geometry inspired by complex dynamics, Proceedings of the International Congress of Mathematicians, Seoul 2014 (Invited Lectures) Vol.II (2015), 695{721. arXiv:1404.2982.

[Ro] Roberts, J., Chow's moving lemma, in Algebraic geometry, Oslo 1970, F. Oort (ed.), WoltersNoordhoff, Publ. Groningnen (1972), 89{96.

[Tr] Truong, T.T., (Relative) dynamical degrees of rational maps over an algebraic closed eld, arXiv:1501.01523.

Primitive (birational) automorphisms of projective manifolds, which are irreducible au-
tomorphisms of manifolds, are natural objects in birational algebraic geometry. They are
also very closely related to complex dynamics of several variables. In fact, the dynamical
degrees of birational automorphisms (a kind of renement of a more classical notion of
topological entropy of automorphisms, tting very well with birational geometry), the relative dynamical degrees (their relative version) and the product formula (a kind of Kunneth type formula), introduced by Dinh-Sibony [DS], Dinh-Nyugen [DN], provide very powerful tools also in studying primitive birational automorphisms of manifolds.
In Lecture 1, I would like to give an overview of the basic notions (entropy, dynamical
degrees, relative dynamical degrees etc) and their basic properties with concrete applications for the study of primitive (birational) automorphisms. This lecture is, in some sense, an updated version of [Og].
In Lectures II, III, I would like to prove the well-denedness and the birational invariance
of dynamical degrees, the most basic property of the dynamical degree. The original proof ([DS]) is transcendental being based on some detailed analysis of currents. Here I explain a new purely algebro-geometric proof due to Truong ([Tr]), which is based on a precise form of Chow's moving lemma ([Ro]).
In Lectures IV, V, I would like to prove the product formula, the most fundamental
and useful property of relative dynamical degrees. Here I explain again an algebraic proof
following a guideline explained in [Tr], which is a modication of original analytic proofs
([DN], [DNT]) into an algebraic one again using a precise form of Chow's moving lemma.

References

[DS] Dinh, T.-C., Sibony, N., Une borne superieure de l'entropie topologique d'une application rationnelle, Ann. of Math., 161 (2005) 1637{1644. arXiv:math/0303271.

[DN] Dinh, T.-C., Nguyen V.-A., Comparison of dynamical degrees for semi-conjugate meromorphic maps, Comment. Math. Helv. 86 (2011) 817{840. arXiv:0903.2621.

[DNT] Dinh, T.-C., Nguyen V.-A., Truong, T.-T., On the dynamical degrees of meromorphic maps preserving a bration, Commun. Contemp. Math. 14 (2012) 18pp, arXiv: 1108.4792.

[Og] Oguiso, K., Some aspects of explicit birational geometry inspired by complex dynamics, Proceedings of the International Congress of Mathematicians, Seoul 2014 (Invited Lectures) Vol.II (2015), 695{721. arXiv:1404.2982.

[Ro] Roberts, J., Chow's moving lemma, in Algebraic geometry, Oslo 1970, F. Oort (ed.), WoltersNoordhoff, Publ. Groningnen (1972), 89{96.

[Tr] Truong, T.T., (Relative) dynamical degrees of rational maps over an algebraic closed eld, arXiv:1501.01523.

변화하는 상황 속에서 인과관계를 유추하고 빠르게 학습하는 능력은 인간과 같은 고등 생명체의 고유한 특성이다. 그러나, 이러한 인간의 일반지능(general intelligence)의 뇌 과학적 원리는 밝혀져 있지 않다. 본 세미나에서는 다양한 수학적 모델을 뇌 과학 연구에 접목시켜 학습 및 추론 과정을 조절하는 인간의 인지 제어 프로세스를 이해하는 인공지능-뇌과학 융합 연구를 소개하고, 산업, 공학,정신의학 분야로의 적용 가능성을 모색하고자 한다.

Primitive (birational) automorphisms of projective manifolds, which are irreducible au-
tomorphisms of manifolds, are natural objects in birational algebraic geometry. They are
also very closely related to complex dynamics of several variables. In fact, the dynamical
degrees of birational automorphisms (a kind of renement of a more classical notion of
topological entropy of automorphisms, tting very well with birational geometry), the relative dynamical degrees (their relative version) and the product formula (a kind of Kunneth type formula), introduced by Dinh-Sibony [DS], Dinh-Nyugen [DN], provide very powerful tools also in studying primitive birational automorphisms of manifolds.
In Lecture 1, I would like to give an overview of the basic notions (entropy, dynamical
degrees, relative dynamical degrees etc) and their basic properties with concrete applications for the study of primitive (birational) automorphisms. This lecture is, in some sense, an updated version of [Og].
In Lectures II, III, I would like to prove the well-denedness and the birational invariance
of dynamical degrees, the most basic property of the dynamical degree. The original proof ([DS]) is transcendental being based on some detailed analysis of currents. Here I explain a new purely algebro-geometric proof due to Truong ([Tr]), which is based on a precise form of Chow's moving lemma ([Ro]).
In Lectures IV, V, I would like to prove the product formula, the most fundamental
and useful property of relative dynamical degrees. Here I explain again an algebraic proof
following a guideline explained in [Tr], which is a modication of original analytic proofs
([DN], [DNT]) into an algebraic one again using a precise form of Chow's moving lemma.

References

[DS] Dinh, T.-C., Sibony, N., Une borne superieure de l'entropie topologique d'une application rationnelle, Ann. of Math., 161 (2005) 1637{1644. arXiv:math/0303271.

[DN] Dinh, T.-C., Nguyen V.-A., Comparison of dynamical degrees for semi-conjugate meromorphic maps, Comment. Math. Helv. 86 (2011) 817{840. arXiv:0903.2621.

[DNT] Dinh, T.-C., Nguyen V.-A., Truong, T.-T., On the dynamical degrees of meromorphic maps preserving a bration, Commun. Contemp. Math. 14 (2012) 18pp, arXiv: 1108.4792.

[Og] Oguiso, K., Some aspects of explicit birational geometry inspired by complex dynamics, Proceedings of the International Congress of Mathematicians, Seoul 2014 (Invited Lectures) Vol.II (2015), 695{721. arXiv:1404.2982.

[Ro] Roberts, J., Chow's moving lemma, in Algebraic geometry, Oslo 1970, F. Oort (ed.), WoltersNoordhoff, Publ. Groningnen (1972), 89{96.

[Tr] Truong, T.T., (Relative) dynamical degrees of rational maps over an algebraic closed eld, arXiv:1501.01523.

The study of laminar groups was motivated by the Thurston's universal circle theory. We show that certain laminar groups act on S^1 or S^2 as a convergence group, and discuss the connection to the Cannon's conjecture.

Primitive (birational) automorphisms of projective manifolds, which are irreducible au-
tomorphisms of manifolds, are natural objects in birational algebraic geometry. They are
also very closely related to complex dynamics of several variables. In fact, the dynamical
degrees of birational automorphisms (a kind of renement of a more classical notion of
topological entropy of automorphisms, tting very well with birational geometry), the relative dynamical degrees (their relative version) and the product formula (a kind of Kunneth type formula), introduced by Dinh-Sibony [DS], Dinh-Nyugen [DN], provide very powerful tools also in studying primitive birational automorphisms of manifolds.
In Lecture 1, I would like to give an overview of the basic notions (entropy, dynamical
degrees, relative dynamical degrees etc) and their basic properties with concrete applications for the study of primitive (birational) automorphisms. This lecture is, in some sense, an updated version of [Og].
In Lectures II, III, I would like to prove the well-denedness and the birational invariance
of dynamical degrees, the most basic property of the dynamical degree. The original proof ([DS]) is transcendental being based on some detailed analysis of currents. Here I explain a new purely algebro-geometric proof due to Truong ([Tr]), which is based on a precise form of Chow's moving lemma ([Ro]).
In Lectures IV, V, I would like to prove the product formula, the most fundamental
and useful property of relative dynamical degrees. Here I explain again an algebraic proof
following a guideline explained in [Tr], which is a modication of original analytic proofs
([DN], [DNT]) into an algebraic one again using a precise form of Chow's moving lemma.

References

[DS] Dinh, T.-C., Sibony, N., Une borne superieure de l'entropie topologique d'une application rationnelle, Ann. of Math., 161 (2005) 1637{1644. arXiv:math/0303271.

[DN] Dinh, T.-C., Nguyen V.-A., Comparison of dynamical degrees for semi-conjugate meromorphic maps, Comment. Math. Helv. 86 (2011) 817{840. arXiv:0903.2621.

[DNT] Dinh, T.-C., Nguyen V.-A., Truong, T.-T., On the dynamical degrees of meromorphic maps preserving a bration, Commun. Contemp. Math. 14 (2012) 18pp, arXiv: 1108.4792.

[Og] Oguiso, K., Some aspects of explicit birational geometry inspired by complex dynamics, Proceedings of the International Congress of Mathematicians, Seoul 2014 (Invited Lectures) Vol.II (2015), 695{721. arXiv:1404.2982.

[Ro] Roberts, J., Chow's moving lemma, in Algebraic geometry, Oslo 1970, F. Oort (ed.), WoltersNoordhoff, Publ. Groningnen (1972), 89{96.

[Tr] Truong, T.T., (Relative) dynamical degrees of rational maps over an algebraic closed eld, arXiv:1501.01523.

A toric variety, which arose in the field of algebraic geometry, of dimension n is a normal algebraic variety with an algebraic action of a complex torus (ℂ*)n having a dense orbit.

For a given toric variety X, the subset consisting of points with real coordinates of X is called a real toric variety Xℝ. In particular, if Xℝ is compact and smooth, it is called a real toric manifold.

The formula for the integral cohomology ring of toric varieties (and their generalizations) have been well established. Interestingly, the formula is quite simple; according to the formula, the ring is obtained as a quotient of a polynomial ring generated by only degree 2 elements, and it has no torsion.

Nevertheless, only little is known about the topology of real toric manifolds.

The topological structures of real toric manifolds are more complicated than those of toric manifolds.

For instance, every real toric manifold is not a simply connected while every toric manifold is simply connected.

Hence, in general, it is difficult to compute topological invariants of real toric manifolds.

Only the formula of ℤ2-cohomology ring has been established by Davis-Januszkiewicz.

In this talk, we introduce the notion of real toric space as a generalization of a real toric manifold. We provide a formula of the rational cohomology ring of real toric spaces, and discuss the existence of arbitrary torsion in the integral cohomology. Furthermore, we propose several topological classification problems for real toric spaces.

A graph is (d₁, …, d_r)-colorable if its vertex set can be partitioned into r sets V₁, …, V_r where the maximum degree of the graph induced by V_i is at most d_i for each i in {1, …, r}.

Time Reversal and Cross Correlation Techniques for Inverse
Source Problems

Abdul Wahab
Department of Bio & Brain Engineering
Korea Advanced Institute of Science and Technology

Abstract. We present time reversal and cross correlation based mathematical techniques
to resolve inverse source problems, where the aim is to nd the spatial support of radiating
sources from boundary wave measurements. We rst deal with temporally localized acoustic,
elastic and electromagnetic sources and present time reversal algorithms for their resolution.
Then, we localize stationary Gaussian noise sources using cross-correlation based statistical
tools. Both spatially correlated and uncorrelated noise sources will be considered. For
correlated sources, we sketch a procedure for retrieving their correlation structure. The
eciency and robustness of the developed algorithms are substantiated through numerical
illustrations.
Joint work. This research has been jointly conducted with Prof. H. Ammari (ETH-Zurich),
Dr. E. Bretin (INSA-Lyon), Prof. J. Garnier (Paris VII), Prof. T. Hayat (QAU, Islamabad),
Dr. R. Nawaz (CIIT, Islamabad), and Dr. A. Rasheed (LUMS, Lahore).
References
[1] H. Ammari, E. Bretin, J. Garnier and A. Wahab, Time reversal in attenuating acoustic
media, in Mathematical and Statistical Methods for Imaging, Contemporary Mathematics,
vol. 548, AMS, (2011), 151{163.
[2] H. Ammari, E. Bretin, J. Garnier and A.Wahab, Time reversal algorithms in viscoeastic
media, European Journal of Applied Mathematics, 24(4):(2013), 565{600.
[3] H. Ammari, E. Bretin, J. Garnier and A.Wahab, Noise source localization in an attenuating
medium, SIAM Journal of Applied Mathematics, 72(1):(2012), 317{336.
[4] H. Ammari, E. Bretin, J. Garnier, H. Kang, and H. Lee and A.Wahab, Mathematical
Methods in Elasticity Imaging, Princeton Series in Applied Mathematics, Princeton
University Press, NJ, USA, 2015.
[5] A. Wahab, A. Rasheed, T. Hayat and R. Nawaz, Electromagnetic time reversal algorithms
and source localization in lossy dielectric media, Communications in Theoretical
Physics, 62(6):(2014), 779-789

Algebraic varieties over finite fields have their associated zeta functions. André Weil conjectured that these functions have a list of properties, including an analogue of the Riemann hypothesis, and these Weil conjectures were proved by Pierre Deligne in the 1970s. Deligne used the so-called l-adic étale cohomology theory, but it is told as a folklore that Alexander Grothendieck was not fully satisfied by this Fields Prize winning work of Deligne for not having proven the conjectures using algebraic cycles.

In this talk, I will first roughly sketch the above historical background, and then talk about how one could revisit the Weil conjectures through algebraic cycles, via 40 years' modern mathematical developments from the late 1970s to now, spanning from higher algebraic K-theory, crystalline cohomology, motivic cohomology, intersection theory, triangulated categories of motives, by Daniel Quillen, Pierre Berthelot, Spencer Bloch, Luc Illusie, Vladimir Voevodsky, Kiran Kedlaya, Hélène Esnault, etc. The main theorem is my joint work with Amalendu Krishna of the Tata Institute of Fundamental Research.

In this talk we discuss a utility-deviation risk portfolio selection problem. By considering the first order condition for the objective function, we derive a primitive static problem, called Nonlinear Moment Problem, subject to a set of constraints involving nonlinear functions of “mean-field terms”, to completely characterize the optimal terminal wealth. Under a mild assumption on utility, we establish the existence of the optimal solutions for both utility-downside-risk and utility-strictly-convex-risk problems, their positive answers have long been missing in the literature. In particular, the existence result in utility-downside-risk problem is in contrast with that of mean-downside-risk problem considered in Jin-Yan-Zhou (2005) in which they prove the non-existence of optimal solution instead and we can show the same non-existence result via the corresponding Nonlinear Moment Problem. (Joint work with K.C. Wong and S.C.P. Yam)

In this talk, we consider the optimal dividend payment strategy for an insurance company, having two collaborating business lines. The surpluses of the business lines are modelled by diffusion processes. The collaboration between the two business lines permits that money can be transferred from one line to another with or without transaction costs while money must be transferred from one line to another to help both business lines keep running before simultaneous ruin of the two lines eventually occur. (Joint work with J.W. Gu and M. Steffensen)

Brain can be divided into several regions based on its functions or structures. And these regions are functionally connected with each other. Fibre tracking on the white-matter from diffusion-tensor image is one of approaches to study brain connectivity. This presentation will introduce static brain connectivity and discuss its clinical applications.

폐에는 매우 복잡하고 고도로 조직화된 형상이 들어있다. 이러한 형상이 다양한 이유로 변형되면서 만성폐쇄성폐질환(COPD)과 같은 질환이 나타나게 된다. 하지만 폐의 형상 변화에 있어서 기체교환면이 줄어들거나 기관지 벽이 두꺼워지는 것 이상의 어떤 '질서'또는 '필수 정보'가 손상되는 것이 궁극적으로 폐기능 저하로 이어지게 되는지는 여전히 잘 설명하지 못하고 있으며, 그것을 어떻게 측정하거나 평가해야 할 지 힌트가 부족한 상황이다. 이와 같은 질문에 답하기 위해서는 다학제간 연구가 통합적으로 필요하다. 이번에는 특히 폐 형상에서 질서를 계량화하고 비교하는 데 쓸 수 있는 수학적 도구를 찾아보고, 질문을 구체적인 수학적 문제로서 정의하는 데 초점을 맞추려 한다.

Heart and Lung have intrinsic motions to fulfill their own functionalities. Physically, these organ's motions are generated from physical potentials and mass distribution composing them. Thus in reverse, physically and mathematically relevant modeling for their genuine motions may lead us to better understanding about key clinical features in need. 3 case studies will be presented to discuss possible improvements on physical modelings under current clinical circumstances.

We define and study grid diagrams for singular links.

A face of an oriented knot diagram on the two sphere is called a coherent (resp. incoherent) region if the orientation of its boundary is coherent (resp. incoherent). In this talk, we investigate the number of the coherent faces and incoherent faces of an oriented knot diagram, and give some relations between the number of the incoherent regions and the canonical genus of a knot. This is a joint work with Kokoro Tanaka (Tokyo Gakugei University)

The canonicai genus of a Whitehead double of a knot is less than or equal to its crossing number. Tripp observed that the equality holds for 2-braid knots and conjectured that the equality holds for all knots. However, Jang and Lee found counterexamples for this conjecture. In this talk, we discuss this conjecture for non-prime alternating knots.

In this talk, I attempt to provide a comprehensive introduction to the matroid properties that hold for almost all matroids.

One of the most prominent subjects which is widely adopted in fintech area is machine learning. One can analyze big data to classify and predict various objects using machine learning techniques. Especially, machine learning shows strong applicability in credit valuation. In this talk, we introduce some methods of machine learning and illustrate how to value credits.

LIBOR is one of the most important floating interest rates, since it is widely used as the underlying of the swap contract. Recently, however, there are some attempts to replace LIBOR with another benchmark rate due to some drawbacks of LIBOR. In this talk, we investigate the flaws of LIBOR and introduce overnight index swap(OIS) as an alternative.