Title & Abstract
강은주(호남대)
Title: A Weierstrass semigroup as a generalized flex on a plane curve
Abstract: We consider a Weierstrass semigroup at a generalized flex on a smooth plane curve. We find the candidates of a Weierstrass semigroup at a 2-flex of higher multiplicity on a smooth plane curve of degree d ≥ 5, and give some examples to show the existence of them.
김순영(서강대)
Title: The cyclic group scheme of order p and Godeaux surfaces
Abstract: Over an algebraically closed field of characteristic p, there are 3 group schemes ℤ_p, μ_p and α_p. The Tate-Oort group scheme 𝔾_p puts these together in one family in characteristic zero. We study some constructions related to 𝔾_p and apply it to give a uniform construction of the Godeaux surfaces with Pic^{τ} of order 5. This is joint work in progress with Miles Reid.
김신영(IBS CGP)
Title: Characterizations of smooth projective horospherical varieties of Picard number one
Abstract: Smooth projective horospherical varieties of Picard number one are classified as five different types. Among those types, we focused on the variety of minimal rational tangents (VMRTs) at a general point of the type B and of the type F_4 which have rarely been explored.
Moreover, we characterize smooth projective horospherical varieties of Picard number one of the type B and of the type F_4 by its projectively equivalent VMRTs in the category of uniruled projective manifolds of Picard number one up to biholomorphism. This is joint work with Jaehyun Hong.
김호성(IBS CCG)
Title: The total VMRT associated to minimal rational component and bigness of tangent bundle
Abstract: In this talk, I will introduce the Total Variety of Minimal tangents and show its application on studying bigness of tangent bundle based on the joint work with Jeong-Seop Kim and Yongnam Lee.
문지연(서울대)
Title: On the space of anti-symplectic involutions of rational symplectic 4-manifolds
Abstract: J-holomorphic curves, introduced by Gromov in 1985, have been used in the study of various aspects of symplectic manifolds. Foliations by J-holomorphic curves can be used to study the symplectomorphism group and the topology of Lagrangian submanifolds in the complex projective plane and the product of 2-spheres. In this talk, we explore the space of anti-symplectic involutions of those rational symplectic 4-manifolds.
박선정(전주대)
Title: c_1-cohomological rigidity on Fano generalized Bott manifolds
Abstract: A smooth Fano variety is a smooth projective variety X whose anti-canonical divisor -K_X is ample. In this talk, we consider the conjecture that two smooth Fano toric varieties are isomorphic if there exists a c_1-preserving isomorphism between their integral cohomology rings. I will introduce a partial affirmative result to the conjecture on Fano generalized Bott manifolds.
양윤정(충남대)
Title: A Survey of the Trends of Recent Studies for the Keum-Naie surface
Abstract: In this talk, we explore the space of anti-symplectic involutions of those rational symplectic 4-manifolds.In this talk, I will introduce what the original Keum-Naie surface is and my research, and I will also introduce recent trends related to the Keum-Naie surface.
First of all, I will briefly introduce the definition of the Keum-Naie surface, and talk about how I constructed the Keum-Naie surface in another way. Finally, I will conclude this lecture by introducing the recent studies related to this.
천은주(경상대, 건국대)
Title: Codes and finite geometry
Abstract: In this talk, we explore the connection between linear codes and finite geometry. For a linear code C, there are important parameters length n, dimension k and minimum distance d, we call C an [n, k, d]_q linear code. In coding theory, it is an interesting problem to find some good codes which have small n (for fast transmission), large k (for a wide variety of messages) and large d (to correct many errors).
We construct linear codes using geometrical objects in projective space over the finite fields and investigate their parameters, and hence we note those codes gives optimal one.
홍재현(IBS CCG)
Title: Cohomology spaces of regular semisimple Hessenberg varieties
Abstract: Hessenberg varieties are subvarieties of the ag variety G/B parameterized by the Lie algebra of G and the set of B-submodules of the Lie algebra of G. Examples include Springer fibers, Peterson varieties, and permutohedral varieties. In general they are singular but those corresponding to regular semisimple elements in the Lie algebra of G, called regular semisimple Hessenberg varieties, are smooth. In these cases, the maximal torus of G acts on them, which induces an action of the Weyl group of G on their cohomology spaces. When G is of type A, one of the interesting questions originated from combinatorics is whether this cohomology space is isomorphic to a direct sum of permutation modules.
In this talk we describe the action of the symmetric group in terms of the basis obtained from the Bianlyicki-Birular decomposition and explain how to express the cohomology space as a sum of permutation modules, which is a direct sum in some special cases. This is joint work with S. Cho and E. Lee.
(강연자는 가나다순 정리)