고등학교 때 미적분을 처음 접했을 때부터  많은 함수에 대해서 그의 미분은 계산하기가 쉬우나 부정적분은 계산하기가 어렵다는 것을 느끼게 됩니다. 로그함수, 역삼각함수 등을 익히고 나면 임의의 유리식의 부정적분을 어떻게 구하는지  배우게 되는데요, 그러면 유리식이 아닌 여러가지 무리식의 부정적분은 어떻게 구하는 걸까요? 이것은 미적분이 도입된 이 후 상당 기간 수학자들에게 가장 큰 관심사였습니다. 이 문제가 어떻게 연구되어 왔는지, 그리고 대학에 와서 수학을 여러 방면으로 더 깊이 배우게 되는데 더 복잡한 무리식의 부정적분은 언제 배우게 되는 것인지 등등 얘기해봅시다.

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

A web of rational curves on a projective manifold is a family of rational curves on the manifold with trivial normal bundle. Most interesting case is when the projective manifold is Fano of number 1. We report on the progress on the Cartan-Fubini type extension theorem for webs of rational curves on Fano manifolds of Picard number 1.

 Classification of proper holomorphicmaps between bounded symmetric domains is deeply related to the study of locally symmetric spaces. In this talk, we consider rigidity problem of proper holomorphic maps between bounded symmetric domains and related problems in locally symmetric spaces. Then we give an introduction to differential geometric techniques on rigidity problems, based on the similar phenomenon for local CR maps between arbitrary boundary components of two bounded symmetric domains of Cartan type I.

A hypergraph on V is a collection E of a subsets of a ground set V. A transversal in a hypergraph H=(V,E) is a subset T of V that intersects every set in E. We are interested in an output-polynomial algorithm for listing the set (inclusion wise) minimal transversals in a given hypergraph (known as Hypergraph Dualization or Transversal Problem). An enumeration algorithm for a set C is an algorithm that lists the elements of C without repetitions; it is said output-polynomial if it can enumerate the set C in time polynomial in the size of C and the input. The Transversal problem is a fifty-year open problem and until now not so many tractable cases are known and has deep connections with several areas of computer science: dualization of monotone functions, data mining, artificial intelligence, etc.

In this talk I will review some known results. In particular I will show that the Transversal problem is polynomially reduced to the enumeration of minimal dominating sets in co-bipartite graphs. A dominating set in a graph is a subset of vertices that intersect the closed neighborhood of every vertex. This interesting connection, we hope, will help in solving the Transversal problem by bringing structural graph theory into this area. I will also review new graph classes where we obtain polynomial delay algorithm for listing the minimal dominating sets. The talk will emphasize on the known techniques rather than a listing of known tractable cases.

We describe all the factorial double covers of P^3 ramified along nodal quartic surface.

We investigate the birational geometry (in the sense of Mori's program) of the moduli space of rank 2 semistable parabolic vector bundles on a rational curve. We compute the effective cone of the moduli space and show that all birational models obtained by Mori's program are also moduli spaces of parabolic vector bundles with certain parabolic weights. In this talk, we introduce wall-crossings of the moduli space, sl_2-conformal blocks and double sequences that are central techniques for the computation of the effective cone. This is a joint work with Dr. Han-Bom Moon.

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

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

In this talk I will define quasi-homomorphisms from braid groups to the smooth concordance group of knots and examine its properties and consequences of its existence. In particular, I will provide a relation between the stable four ball genus in the concordance group and the stable commutator length in braid groups, and produce examples of infinite families of concordance classes of knots with uniformly bounded four ball genus. I will also provide applications to the geometry of the infinite braid group. In particular, I will show that its commutator subgroup admits a stably unbounded conjugation invariant norm. This answers an open problem posed by Burago, Ivanov and Polterovich. If time permits I will describe an interesting connection between the concordance group of knots and number theory. This work is partially joint with Jarek Kedra.

We consider an initial value problem for a nonlocal differential equation with a bistable nonlinearity in several space dimensions and discuss the large time behavior of the solution. The proof that the solution orbits are relatively compact is based upon rearrangement theory. We also characterise the limit function and prove that it is given by a step function. (This is joint work with Hiroshi Matano, Thanh Nam Nguyen and Hendrik Weber.)

Consider a polytope P with integer vertices, then one can define its Ehrhart polynomial f(t) by counting integer points in t.P. After a change of basis, it becomes a polynomial with positive integer coefficients, called the h*-polynomial. It is then a problem to find the combinatorial meaning of these coefficients for special polytopes. For exampe, the n-dimensional hypercube gives the n-th Eulerian polynomial, counting descents in permutations. The goal of this work is to refine this result by considering slices of hypercube and considering descents and excedences in permutations, that are two different Eulerian statistics.

In view of scheme language, we start from the beginning of the theory of elliptic curves and geometric modular forms, and further cover the topics about Jacobians and Galois representation as well as modularity problems.

In this talk, we will survey the article "Modular forms and projective invariants - J.Igusa(1967)".

In this talk, we will survey the article "Class fields over real quadratic fields and Hecke operators - G.Shimura(1972)".

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

In this series of lectures I will give an overview to the status of explicit birational geometry of algebraic 3-folds. First I explain the idea to classify the weighted basket of 3-folds. Then I provide two applications of the basket theory to 3-folds of general type as well as to Q-Fano 3-folds (very new results). Finally I will introduce the status of 3-dimensional geography — Noether’s inequality and so on.

신용상품에는 크게 국가 및 회사은행개인의 신용을 거래하는 금융 상품으로 크게는 채권과 Credit Default Swap 및 옵션이 있습니다. 이 시간에는 첫번째로 각각의 상품의 개요와 미국 신용 상품 거래 시장이 어떻게 발전해 왔는지에 대해서 개략적으로 설명하겠습니다. 두번째로는 2008년 금융 위기 이후에 새로 바뀐 제도적 규제가 신용상품 거래 시장에 어떠한 영향을 미쳤는 지를 설명하겠습니다. 마지막으로 이 규제로 인해 현재 은행 및 투자자들이 당면한 문제들과 어떻게 이것을 해결할 방법이 있는지에 대해서 알아 보는 시간을 가지겠습니다.

In this series of lectures I will give an overview to the status of explicit birational geometry of algebraic 3-folds. First I explain the idea to classify the weighted basket of 3-folds. Then I provide two applications of the basket theory to 3-folds of general type as well as to Q-Fano 3-folds (very new results). Finally I will introduce the status of 3-dimensional geography — Noether’s inequality and so on.

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

We generate ring class fields of imaginary quadratic fields in terms of the special values of certain eta-quotients, which are related to the relative norm of Siegel-Ramachandra invariants. These give us minimal polynomials with relatively small coefficients from which we are able to solve certain quadratic Diophantine equations concerning non-convenient numbers.

In this series of lectures I will give an overview to the status of explicit birational geometry of algebraic 3-folds. First I explain the idea to classify the weighted basket of 3-folds. Then I provide two applications of the basket theory to 3-folds of general type as well as to Q-Fano 3-folds (very new results). Finally I will introduce the status of 3-dimensional geography — Noether’s inequality and so on.

In this series of lectures I will give an overview to the status of explicit birational geometry of algebraic 3-folds. First I explain the idea to classify the weighted basket of 3-folds. Then I provide two applications of the basket theory to 3-folds of general type as well as to Q-Fano 3-folds (very new results). Finally I will introduce the status of 3-dimensional geography — Noether’s inequality and so on.

In view of scheme language, we start from the beginning of the theory of elliptic curves and geometric modular forms, and further cover the topics about Jacobians and Galois representation as well as modularity problems.

In this talk, we will survey the article "Modular forms and projective invariants - J.Igusa(1967)".

In this talk, we will survey the article "Class fields over real quadratic fields and Hecke operators - G.Shimura(1972)".

내용: 강연을 통해 괴델의제1, 제 2 불완전성정리의내용과의미를살펴보려합니다.

          이의증명과튜링머신개념의  연관성에대해서도소개하려합니다.   

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

LG화학과 LG화학 R&D에 대한 일반적 현황을 소개하고, 미래 기술 혁신의 방향에 대해 논의해 보고자 한다. 미래 기술 혁신을 위한 First Mover 전략의 중요성을 LG화학에서 개발한 제품과 기술의 사례들을 통해 설명하고자 한다. First Mover 제품 창출과 바람직한 연구 조직 운영을 위한 조직문화 구축 측면에서 LG화학기술연구원에서 진행하고 있는 노력들을 소개하면서 미래 지향적 조직 문화에 대한 개인적 견해를 피력하고자 한다.

Let A and B be finite nonempty subsets of a multiplicative group G, and consider the product set AB = { ab | a in A and b in B }. When |G| is prime, a famous theorem of Cauchy and Davenport asserts that |AB| is at least the minimum of {|G|, |A| + |B| - 1}. This lower bound was refined by Vosper, who characterized all pairs (A,B) in such a group for which |AB| < |A| + |B|. Kneser generalized the Cauchy-Davenport theorem by providing a natural lower bound on |AB| which holds in every abelian group. Shortly afterward, Kemperman determined the structure of those pairs (A,B) with |AB| < |A| + |B| in abelian groups. Here we present a further generalization of these results to arbitrary groups. Namely we generalize Kneser’s Theorem, and we determine the structure of those pairs with |AB| < |A| + |B| in arbitrary groups.

√ Lecture 4

Advanced Topics (time permits): numeraire pairs and change of numeraire, growth optimal portfolios.

  In this talk, I will present two different topics; minimax lower bound in normal mixtures, and global rates of convergence in a log-concave shape-constrained estimation.
  The first half (part of my Ph.D. thesis, accepted in Bernoulli, 2013) deals with minimax rates of convergence for estimation of density functions on the real line. The densities are assumed to be location mixtures of normals, a global regularity requirement that creates subtle difficulties for the application of standard minimax lower bound methods. Using novel Fourier and Hermite polynomial techniques, we determine the minimax optimal rate|slightly larger than the parametric rate|under squared error loss.
  In the second half, I will present recent results in log-concave density estimation (joint work with Richard Samworth, submitted to the Annals of Statistics, 2014). We study the performance of log- concave density estimators with respect to global (e.g. squared Hellinger) loss functions, and adopt a minimax approach....

Matt DeVos

Simon Franser U.
 

Lecture 4) 9. 23(Tue) PM 4:00 ~ 6:00  E6-1  Rm 1409

Graphs and Sumsets (Schrijver-Seymour)
 

Abstract: I intend to give an introduction to some of the wonderful topics in the world of additive combinatorics. This is a broad subject which features numerous different tools and techniques, and is presently a hotbed of exciting research. My focus will be on the combinatorics, and I will keep things as basic as possible (I will assume nothing more than a basic background in combinatorics). I’ll begin the tour with some of the classical theorems like Cauchy-Davenport and Erdos-Ginzburg-Ziv and I will exhibit some very clean proofs of these and other results such as the Theorems of Schrijver-Seymour, Green-Ruzsa, Dvir, and Elekes. We will also discuss (but not prove) some more recent results like the Breulliard-Green-Tao Theorem.

Multi-Asset Model: Margrabe formula, probabilistic method and hedging, cross-currency options, currency-protected options.

Let a 3-dimensional smooth and bounded domain be given. We compare two problems arising in kinetic theory: the Vlasov-Poisson system and the Fokker-Planck equation. In the Vlasov-Poisson case, the existence of regular solutions is determined according to whether the boundary of the domain is convex or not. But, in the Fokker-Planck case, there is a smoothing effect due to the random force, solutions are expected to be more regular.

For each smooth del Pezzo surface S, we find ample divisors A on the surface S

such that S admits an A-polar cylinder and we present an eff ective divisor D that is Q-linearly

equivalent to A and such that the open set , the complement of Supp(D) is a cylinder. 

Moreover using similar construction of cylinders, we prove that affine cones over any ample polarization of 

del Pezzo surfaces with degree 4 are flexible. 

√ Lecture 2

Black-Scholes World: self-financing, original proof of BS equation, martingale derivation of BS formula, dividend, hedging, robustness.

The square $G^2$ of a graph G is the graph defined on V(G) such that two vertices u and v are adjacent in $G^2$ if the distance between u and v in G is at most 2. Let $chi(H)$ and $chi_{ell}(H)$ be the chromatic number and the list chromatic number of H, respectively. A graph H is called chromatic-choosable if $chi_{ell} (H) = chi(H)$. It is an interesting problem to find graphs that are chromatic-choosable.

In view of scheme language, we start from the beginning of the theory of elliptic curves and geometric modular forms, and further cover the topics about Jacobians and Galois representation as well as modularity problems.

Matt DeVos

Simon Franser U.

Lecture 3) 9. 18(Thu) PM 4:00 ~ 6:00   E6-1  Rm 3433

Sums and Products (Elekes and Dvir)

Abstract: I intend to give an introduction to some of the wonderful topics in the world of additive combinatorics. This is a broad subject which features numerous different tools and techniques, and is presently a hotbed of exciting research. My focus will be on the combinatorics, and I will keep things as basic as possible (I will assume nothing more than a basic background in combinatorics). I’ll begin the tour with some of the classical theorems like Cauchy-Davenport and Erdos-Ginzburg-Ziv and I will exhibit some very clean proofs of these and other results such as the Theorems of Schrijver-Seymour, Green-Ruzsa, Dvir, and Elekes. We will also discuss (but not prove) some more recent results like the Breulliard-Green-Tao Theorem.

√ Lecture 1

Advanced Stochastic Calculus: linear SDE, change of measures, Girsanov theorem, martingale representation, Feynman-Kac theorem.

A Noetherian ring is called quasi-Gorenstein if the ring is (locally) isomorphic to a canonical module. A Gorenstein ring is a Cohen-Macaulay quasi-Gorenstein ring. In general, a quasi-Gorenstein ring is not Gorenstein. In this talk, we show that certain classes of quasi-Gorenstein extended Rees algebras are Gorenstein.

Matt DeVos

Simon Franser U

Lecture 2)  9. 16(Tue) PM 4:00 ~ 6:00  E6-1  Rm 1409

Rough Structure (Green-Ruzsa)

Abstract: I intend to give an introduction to some of the wonderful topics in the world of additive combinatorics. This is a broad subject which features numerous different tools and techniques, and is presently a hotbed of exciting research. My focus will be on the combinatorics, and I will keep things as basic as possible (I will assume nothing more than a basic background in combinatorics). I’ll begin the tour with some of the classical theorems like Cauchy-Davenport and Erdos-Ginzburg-Ziv and I will exhibit some very clean proofs of these and other results such as the Theorems of Schrijver-Seymour, Green-Ruzsa, Dvir, and Elekes. We will also discuss (but not prove) some more recent results like the Breulliard-Green-Tao Theorem.

In view of scheme language, we start from the beginning of the theory of elliptic curves and geometric modular forms, and further cover the topics about Jacobians and Galois representation as well as modularity problems.

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

In this talk, we will survey the article "Modular forms and projective invariants - J.Igusa(1967)".

In this talk, we will survey the article "Class fields over real quadratic fields and Hecke operators - G.Shimura(1972)".

In this talk, we will survey the article "Class fields over real quadratic fields and Hecke operators - G.Shimura(1972)".

Graph immersion is a natural containment relation like graph minors. However, until recently, graph immersion has received relatively little attention. In this talk we shall describe some recent progress toward understanding when a graph does not immerse a certain subgraph. Namely, we detail a rough structure theorem for graphs which do not have K_t as an immersion, and we discuss the precise structure of graphs which do not have K_{3,3} as an immersion. Then we turn our attention to a special class of digraphs, those forwhich every vertex has both indegree and outdegree equal to 2. Thesedigraphs have special embeddings in surfaces where every vertex has alocal rotation in which the inward and outward edges alternate. Itturns out that the nature of these embeddings relative to immersion isquite closely related to the usual theory of graph embedding and graphminors. Here we describe the complete list of forbidden immersionsfor (special) embeddings in the projective plane. These results are joint with various coauthors including Archdeacon,Dvorak, Fox, Hannie, Malekian, McDonald, Mohar, and Scheide.

Given a curve in a plane, we construct a factorization of a polynomial multiplied by an identity matrix into the product of two matrices, by counting certain polygons in a plane. Such correspondences between geometric objects (curves, polygons) and algebraic objects (matrix factorizations of a polynomial) are instances of homological mirror symmetry. We explain the generalization of the construction to higher dimensions, and its application to the proof of homological mirror symmetry conjecture for certain spaces.

 Sidorenko's conjecture states that for every bipartite graph H on {1,...,k} $$ int prod_{(i,j)in E(H)} h(x_i, y_j) dmu^{|V(H)|} ge left( int h(x,y) ,dmu^2 right)^{|E(H)|} $$ holds, where $mu$ is the Lebesgue measure on [0,1] and h is a bounded, non-negative, symmetric, measurable function on [0,1]^2. An equivalent discrete form of the conjecture is that the number of homomorphisms from a bipartite graph H to a graph G is asymptotically at least the expected number of homomorphisms from H to the Erdos-Renyi random graph with the same expected edge density as G.In this talk, we will give an overview on known results and new approaches to attack Sidorenko's conjecture. This is a joint work with Jeong Han Kim and Choongbum Lee.

Matt DeVos

Simon Franser U.

Lecture 1)  9. 2(Tue) PM 4:00 ~ 6:00  E6-1  Rm 1409

Sumsets and Subsequence Sums (Cauchy-Davenport, Kneser, and Erdos-Ginzburg-Ziv)

Abstract: I intend to give an introduction to some of the wonderful topics in the world of additive combinatorics. This is a broad subject which features numerous different tools and techniques, and is presently a hotbed of exciting research. My focus will be on the combinatorics, and I will keep things as basic as possible (I will assume nothing more than a basic background in combinatorics). I’ll begin the tour with some of the classical theorems like Cauchy-Davenport and Erdos-Ginzburg-Ziv and I will exhibit some very clean proofs of these and other results such as the Theorems of Schrijver-Seymour, Green-Ruzsa, Dvir, and Elekes. We will also discuss (but not prove) some more recent results like the Breulliard-Green-Tao Theorem.