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Information Center for Mathematical Science

### 세미나

Information Center for Mathematical Science

#### 세미나

##### 2019 서울대학교 수리과학부 세미나

The Calder´on-Zygmund theory of elliptic equations with discontinuous coecients has been extensively studied in the last fifty years. In this talk, I will review some work in this direction. And I mainly introduce our recent work about the L^p(x)-estimate and variable Lorentz estimate for the elliptic problems.

##### 2019 서울대학교 수리과학부 세미나
• Title : Root numbers I
• Speaker : 한겨울
• Data : 2019-01-24 14:00:00
• Host : SNU
• Place :

A root number is one of the important notions in number theory. I will introduce several ways to define root numbers and the relations among them.

##### 2019 서울대학교 수리과학부 세미나

We consider the numerical approximation for two types of optimal control problems governed by elliptic interface equations. We adopt the variational discretization concept to discretize the optimal control problems, and apply extended finite element methods for the elliptic equations to discretize the corresponding state and adjoint equations. Optimal error estimates are derived for the optimal state, co-state and control. Numerical results verify the theoretical results. This is a joint work with Tao Wang and Chaochao Yang.

##### 한국고등과학원 세미나

In algebraic combinatorics, a central area of study is Schur functions. These functions were introduced early in the last century with respect to representation theory, and since then have become important in other areas such as quantum physics and algebraic geometry. These functions also form a basis for the algebra of symmetric functions, which is a subalgebra of the algebra of quasisymmetric functions that appear in areas such as category theory and card shuffling. Despite this strong connection, the existence of a natural quasisymmetric refinement of Schur functions was considered unlikely for many years. In this short course we will introduce quasisymmetric functions and Schur functions. Then we will introduce quasisymmetric Schur functions. We will see how these quasisymmetric Schur functions refine Schur function properties, with combinatorics that strongly reflects the classical case such as diagrams. This course needs no knowledge of any of the above terms. Everything will be defined, and illustrated with examples.

##### 한국고등과학원 세미나

In algebraic combinatorics, a central area of study is Schur functions. These functions were introduced early in the last century with respect to representation theory, and since then have become important in other areas such as quantum physics and algebraic geometry. These functions also form a basis for the algebra of symmetric functions, which is a subalgebra of the algebra of quasisymmetric functions that appear in areas such as category theory and card shuffling. Despite this strong connection, the existence of a natural quasisymmetric refinement of Schur functions was considered unlikely for many years. In this short course we will introduce quasisymmetric functions and Schur functions. Then we will introduce quasisymmetric Schur functions. We will see how these quasisymmetric Schur functions refine Schur function properties, with combinatorics that strongly reflects the classical case such as diagrams. This course needs no knowledge of any of the above terms. Everything will be defined, and illustrated with examples.

##### 한국고등과학원 세미나

It is known that a flag domain, which is an open orbit on a flag manifold, is either holomorphic convex or pseudoconcave. Pseudoconcavity of flag domains is equivalent to cycle-connectivity. In this talk, we discuss one-connectivity, which is a kind of strong cycle-connectivity, of flag domains.

##### 한국고등과학원 세미나

In this survey talk, I will start by explaining the original idea and some of the motivations of Deligne (1984) that there should exist an "irregular Hodge filtration" sharing some properties with the usual one, on a vector bundle on a curve with connection having irregular singularities at infinity. I will then describe the present status of the development of this idea as an irregular Hodge theory, and the various applications to arithmetic, mirror symmetry and confluent hypergeometric differential equations, that can be made with this theory. The main example developed will be that of the twisted de Rham complex associated to a regular function on a smooth complex quasi-projective variety, extending the construction of Deligne in his article ‘Hodge II’ (1972).

##### 한국고등과학원 세미나

I will present an inductive algorithm to compute the bulk-deformed potentials for toric Fano surfaces via wall-crossing techniques and a tropical-holomorphic correspondence for holomorphic discs. As an application, we find an explicit relation between the oscillatory integrals of the bulk-deformed potentials and log descendant Gromov-Witten invariants, which recovers the previous result of Gross for P^2. This is a joint work with Yu-Shen Lin and Jingyu Zhao.

##### 한국고등과학원 세미나

We discuss the formation of singularity for the compressible Euler equations. To this end, we first review some fundamental properties of the hyperbolic system of conservation laws including shock waves, rarefaction waves and Riemann invariants. Then we shall go over the existing results on C^1 blow-up for 1d p-system that is obtained from the compressible Euler equations via the Lagrangian coordinates. If time permits, we will discuss some related problems arising in the Euler-Poisson system.

##### 한국고등과학원 세미나

Statistical dynamics of a system of collisionless particles in the gravitational field they generate is described by a Vlasov-Poisson system. By quantizing it, we get a Hartree system which describes statistical dynamics of a system of bosons. It has been an one of central problems of mathematical physics to rigorously prove the convergence of the semiclassical limit between IVP from Hatree systems to Vlasov-Poisson systems. In this talk, we turn to semiclassical limits of solitons between them. We will see that the semiclassical problems for solitons are independent of problems for IVP so completely different approaches, for example, variational approaches are required to prove it.

##### 한국고등과학원 세미나

We discuss the super string theory for mathematicians for one semester. We cover 1.Brief review of mechanics(classical and quantum) and field theory(classical and quantum) 2. Bosonic and super string theory 3. D-branes(Dirichlet branes) 4. AdS(anti de Sitter) and CFT(conformal field theory)

##### 한국고등과학원 세미나

We discuss the super string theory for mathematicians for one semester. We cover 1.Brief review of mechanics(classical and quantum) and field theory(classical and quantum) 2. Bosonic and super string theory 3. D-branes(Dirichlet branes) 4. AdS(anti de Sitter) and CFT(conformal field theory)

##### 한국고등과학원 세미나

We discuss the super string theory for mathematicians for one semester. We cover 1.Brief review of mechanics(classical and quantum) and field theory(classical and quantum) 2. Bosonic and super string theory 3. D-branes(Dirichlet branes) 4. AdS(anti de Sitter) and CFT(conformal field theory)

##### 한국고등과학원 세미나

We discuss the super string theory for mathematicians for one semester. We cover 1.Brief review of mechanics(classical and quantum) and field theory(classical and quantum) 2. Bosonic and super string theory 3. D-branes(Dirichlet branes) 4. AdS(anti de Sitter) and CFT(conformal field theory)

##### 한국고등과학원 세미나

We discuss the super string theory for mathematicians for one semester. We cover 1.Brief review of mechanics(classical and quantum) and field theory(classical and quantum) 2. Bosonic and super string theory 3. D-branes(Dirichlet branes) 4. AdS(anti de Sitter) and CFT(conformal field theory)

##### 한국고등과학원 세미나

We discuss the super string theory for mathematicians for one semester. We cover 1.Brief review of mechanics(classical and quantum) and field theory(classical and quantum) 2. Bosonic and super string theory 3. D-branes(Dirichlet branes) 4. AdS(anti de Sitter) and CFT(conformal field theory)