이기암 (서울대학교)

- Title: Nonlinear Partial Differential Equation: a journey to understand social or natural phenomena

- Abstract: In this talk, we are going to discuss recent progress to understand the relationship between nonlinear partial differential equations and social or natural phenomena. At first, we will try to understand synchronization, domination, mixing and etc among offsprings in terms of the system of nonlinear partial differential equations. And then we try to discuss the relationship among observed data, distribution, and nonlinear partial differential equations.

김준태 (서강대학교)

- Title: Entropy of symplectic automorphisms

- Abstract: The topological entropy measures the complexity of a diffeomorphism in terms of the volume growth of submanifolds. It is then natural to ask whether the topological entropy is positive. If we restrict ourselves to symplectic automorphisms of symplectic manifolds, then we can define the Floer theoretic entropy. We will give geometric ideas why a positive Floer theoretic entropy implies a positive topological entropy. This is joint work in progress with Myeonggi Kwon.

최우철 (성균관대학교)

- Title: An introduction to optimization and control problems for mechanical engineering

- Abstract: Optimization and control problems are widely studined in connection with Mechanical engineering. In particular, one has to use highly efficient algorithms in optimization and control theory to develop intelligent robots and machines. In this talk, I will introduce the mathematical aspects of the optimization and control problems in connection with applications to intelligent robots and machines. An important concept is the model predictive control which solves the optimal control problem repeatedly in real-time applications. I will explain related constrained optimizations problems and various algorithms for solving such constrained optimization.

홍규식 (전주대학교)

- Title: Points set in projective spaces and some applications

- Abstract: Assume that S is a finite set of points in n-dimensional space. In algebraic geometry, it is interesting to ask when the points of the set S impose independent linear conditions on polynomials of degree at most d. The most basic and useful is to take points in n-dimensional complex projective space and to ask about homogeneous forms of degree d instead of polynomials of degree at most d. In commutative algebra, a unique factorization domain is a commutative ring in which every element can be uniquely written as a product of prime elements, analogous to the fundamental theorem of arithmetic for the integers. Most rings familiar from elementary mathematics are UFDs: the integers, the polynomial rings over a field, the ring of functions in a fixed number of complex variables holomorphic at the origin etc. However, most factor rings of a polynomial ring are not UFDs. An affine algebraic variety is called factorial if its coordinate ring is UFD. For a projective algebraic variety, one can define the factoriality in a similar way. For a 3-fold with mild singularities, the factoriality problem was investigated by Clemens. He showed that the factoriality of many singular 3-folds can be expressed in terms of the number of independent linear conditions that their singular points impose on the homogeneous forms of certain degree. We plan to investigate how the factoriality of singular 3-folds depends on the number of singular points. This problem can be studied by methods of commutative algebra, topology, differential geometry and algebraic geometry.

김장수 (성균관대학교)

- Title: Affine Gordon-Bender-Knuth identities for cylindric Schur functions 

- Abstract: The Gordon-Bender-Knuth identities are determinant formulas for the sum of Schur functions of partitions with bounded height, which have interesting combinatorial consequences such as connections between standard Young tableaux of bounded height, lattice walks in a Weyl chamber, and noncrossing matchings. In this talk we give an affine analog of the Gordon-Bender-Knuth identities, which are determinant formulas for the sum of cylindric Schur functions. We also consider combinatorial aspects of these identities. As a consequence we obtain an unexpected connection between cylindric standard Young tableaux and r-noncrossing and s-nonnesting matchings. This is joint work with JiSun Huh, Christian Krattenthaler, and Soichi Okada.

김선광 (충북대학교)

- Title: The norm attaining function theory on Banach space

- Abstract: It is very well known that the continuity of a function implies the attainment of its maximum on compact space. Our aim in the theory of norm attaining operators is to consider a continuous linear functional or operator on the unit ball of Banach space. In general, the unit ball is not compact, and so it is not true that the continuity implies the norm attainment. We will see some brief history on this and interesting characterization of Banach spaces by norm attaining maps.

팽성훈 (건국대학교)

- Title: Willmore-type inequality and distance to minimal surface

- Abstract: We study the Willmore-type inequality. With the estimate of the integral norm of the mean curvature, we study the distance to the minimal surface in an asymptotically flat manifold.

박철 (UNIST)

- Title: Introduction to the weight part of Serre's conjecture

- Abstract: The weight part of Serre's conjecture is considered as a firrst step towards mod-p Langlands program in which it is believed that one can attach mod-p smooth representations to mod-p Galois representations in a natural way. In this talk, we introduce the weight part of Serre's conjecture, together with a few problems that give some evidences of the weight part of Serre's conjecture.

김민훈 (경북대학교)

- Title: Cappell-Shaneson homotopy 4-spheres

- Abstract: In 1976, Cappell and Shaneson constructed an infinite family of smooth homotopy 4-spheres, called Cappell-Shaneson homotopy 4-spheres. Cappell-Shaneson homotopy 4-spheres are the most notable potential counterexamples to the smooth 4-dimensional Poincare conjecture and they are related to other important conjectures including the Gluck, Schoenflies, slice-ribbon conjectures. In this talk, I would like to give a survey on Cappell-Shaneson homotopy 4-spheres.

금종해 (고등과학원)

- Title: Algebraic Surfaces

- Abstract: Recent progress on algebraic surfaces will be presented, with some not-so-old results. Topics will be K3 surfaces and their automorphisms, elliptic surfaces, and general type surfaces such as fake projective planes. I will also explain why the theory of algebraic surfaces is richer and more complicated than the theory of algebraic curves (Riemann surfaces). For non-experts, basic notions and examples will be mentioned.