이준호

(목포대)

On the units of algebraic number fields

The arithmetic of units in number fields provides rich insights into the fields themselves.

Dirichlet’s unit theorem offers a clear description of the structure of units in orders of number fields.

In this talk, we focus on obtaining explicit expressions for these units.
We will review known results, present several conjectures concerning units, and discuss our recent progress in this direction.

변성수

(서울대)

q-deformations in random matrix theory

The concept of q-deformation provides a powerful framework for constructing quantised analogues of classical mathematical structures. In this talk, I will introduce q-deformed random matrix models and describe how their probabilistic and analytic features emerge in the large-system limit.

배영진

(인천대)

Legendrian knots, Lagrangian fillings, and cluster structure.

In this talk, I will introduce Legendrian knots in 3-dimensional contact space.
After introducing the classical invariants of Legendrian knots, I will discuss the idea of constructing more advanced invariants.
We consider the space of Lagrangian fillings of the Legendrian knot, and how cluster structure enters this setup.

이상욱

(숭실대)

Kodaira-Spencer maps for elliptic orbispheres as isomorphisms of Frobenius algebras

Given a mirror pair of a symplectic manifold $X$ and a Landau-Ginzburg potential $W$, we are interested in whether the quantum cohomology of $X$ and the Jacobian algebra of $W$ are isomorphic. Since those can be equipped with Frobenius algebra structures, we might ask whether they are isomorphic as Frobenius algebras. We show that the Kodaira-Spencer map gives a Frobenius algebra isomorphism for elliptic orbispheres, under the Floer theoretic modification of the residue pairing.

곽시종

(KAIST)

 고등과학원과 함께 한 나의 연구 생활 

 저는 고등과학원(KIAS)이 1996년 10월에 설립되어 문을 열었을 때  김인강 교수님과 함께 처음 참여했던 연구원 중 한 명으로  2000년 초까지 재직했습니다.  당시의 소중한 경험과 연구원들과의 추억을 돌아보고 그 이후로도 고등과학원 방문을 통해 학문적 에너지와 즐거움을 만끽하였던  귀한 시간들의  의미를 되짚어 보고자 합니다. 

덤으로 사영대수기하학 분야에서 지금까지 얻은 나름의 연구 성과도 소개합니다.