김명호 (경희대학교)
- 제목: g-vectors of the dual canonical basis
- 초록: The dual canonical basis (also called the upper global basis) is a distinguished basis of the half of the quantum group which enjoys several nice properties. The half of a quantum group equips with a cluster algebra structure and the set of cluster monomials forms a subset of the dual canonical basis. Recently, N. Fujita and H. Oya constructed certain Newton–Okounkov polytopes for seeds in the cluster pattern. The integral points of each polytope are the g-vectors of dual canonical basis associated with the seed. In this talk, we will review basic facts on the dual canonical basis and their g-vectors associated with a seed.

김신영 (기초과학연구원 기하학 수리물리 연구단)
- 제목: Some properties of symmetric homogeneous spaces and their completions
- 초록: An irreducible symmetric homogeneous space is spherical, which is roughly given by a Lie group and an involution. We review some well-known properties of symmetric homogeneous spaces and their completions. And then, we will describe the VMRTs of smooth symmetric varieties of Picard number one by marking on the Kac diagrams. This talk is based on the work with K.-D. Park.

김유식 (부산대학교)
- 제목: Mirror symmetry of partial flag manifolds of classical type
- 초록: In this talk, I will discuss mirror symmetry of partial flag manifolds from symplectic perspective. After explaining a general picture, I will talk about difficulties and ideas how to overcome them.

박경동 (고등과학원)
- 제목: Kähler–Einstein metrics on smooth Fano toroidal symmetric varieties of type AIII
- 초록: Symmetric varieties are normal equivarient open embeddings of symmetric homogeneous spaces, and they are interesting examples of spherical varieties. In this talk, we discuss the existence of Kähler–Einstein metrics on the wonderful compactifications X_m of symmetric homogeneous spaces of type AIII(2, m) and their blow-ups along the (unique) closed orbit. Using a combinatorial criterion for K-stability of smooth Fano spherical varieties obtained by Delcroix, we prove that whereas all wonderful compactifications X_m admit Kähler–Einstein metrics, the blow-up of X_m along the closed orbit admit Kähler–Einstein metrics if and only if m = 4, 5. This is a joint with Kyusik Hong and DongSeon Hwang.

서애령 (경북대학교)
- 제목: Complex analyticity of totally geodesic isometric embeddings between bounded symmetric domains
- 초록:

유성민 (기초과학연구원 복소기하학 연구단)
- 제목: Limits of Bergman kernels on a tower of coverings of compact Kähler manifolds
- 초록: A famous theorem by Kazhdan states that a tower of coverings of a compact Riemann surface converging to the universal covering is Bergman stable. Recently, Baik, Shokrieh and Wu generalized this theorem where the universal cover is replaced with any infinite Galois cover. In this talk, we prove a generalized version of this theorem, where compact Riemann surfaces are replaced with compact Kähler manifolds. We also discuss its application to the projectivity of manifolds. This is a joint work with Jihun Yum (IBS-CCG).

이경석 (Miami 대학교)
- 제목: Birational geometry and Cox rings of spherical varieties
- 초록: Cox ring is an important tool in modern birational geometry and several other branches of mathematics. In this talk, I will discuss birational geometry and Cox rings of spherical varieties.

이재혁 (이화여자대학교)
- 제목: Polygon spaces and Spin representations
- 초록: In this talk, we discuss the geometry of the polygons in Euclidean spaces and identifications in dimension 2, 3 and 5. We explain fundamental issues of the geometry of polygons along the chamber structures according to moment maps and related polytopes, and introduce an approach with spin action to characterize polygons in 5-dimensional Euclidean space as an extention of the identifications between Grassmannians and polygons in dimension 2 and 3. This is a joint with Eunjeong Lee.

정승조 (전북대학교)
- 제목: Higher du Bois singularities and higher log canonical singularities
- 초록: This talk briefly introduces Deligne–Du Bois complexes and the notion of higher du Bois singularities. Via the minimal exponent, which is the maximal root of the reduced Bernstein–Sato polynomial for hypersurface singularities, we can define higher log canonical singularities. In this talk, we prove that the two notions are equivalent. This is based on joint work with I.-K.  Kim, M. Saito and Y. Yoon.

조윤형 (성균관대학교)
- 제목: Construction of monotone Lagrangian tori in flag varieties via toric degenerations
- 초록: A monotone symplectic manifold is a symplectic analogue of a smooth Fano variety and it provides an important classes of objects, called monotone Lagrangian tori, in view of mirror symmetry. In this talk, I will explain a way of producing monotone Lagrangian tori in a given smooth Fano variety using toric degeneration. Using this technique, we prove that there exist infinitely many monotone Lagrangian tori not Hamiltonian isotopic to each other in a full flag variety. This is based on ongoing joint work with Myungho Kim, Yoosik Kim, Jaehoon Kwon, and Euiyong Park at Center for Quantum Structures in Modules and Spaces (QSMS).

최인송 (건국대학교)
- 제목: Orthogonal bundles of low rank over an algebraic curve
- 초록: We give an explicit description on the orthogonal bundles of low rank over an algebraic curve which arise from the canonical isomorphisms between Lie groups of low dimension. This enables us to understand delicate issues: Stiefel–Whitney class, irreducibility of the moduli space and the quot schemes. This is based on a joint work with George H. Hitching.

홍규식 (전주대학교)
- 제목: On Factoriality of 3-folds with isolated singularities
- 초록: For a given commutative ring, it is an interesting question to decide weather it is UFD or not. 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. In most of cases, the factoriality of projective varieties can be expressed in terms of topological data and can be proved by using powerful tools of topology such as the Lefschetz theorem and the Poincare duality. Algebraic surfaces, i.e., algebraic varieties of complex dimension two, are usually not factorial. For most of complex projective 3-folds, i.e., algebraic varieties of complex dimension three, the factoriality simply means that its topology is trivial outside of the cycles of real dimension three. For example, every smooth 3-fold hypersurface is factorial by the Lefschetz theorem and the Poincare duality. For 3-folds with isolated singularities, we still can use the Lefschetz theorem, but the Poincare duality usually fails. For example, every smooth 3-fold hypersurface is factorial if and only if the Poincare duality does not fail for it. For a wide class of singular 3-folds, 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 (isolated, ordinary multiple points). This problem can be studied by methods of commutative algebra, topology, differential geometry and algebraic geometry. We expect to obtain new and interesting results in this direction.

홍재현 (기초과학연구원 복소기하학 연구단)
- 제목: Characterization of smooth horospherical varieties of Picard number one
- 초록: A homogeneous space G/H is said to be horospherical if G is reductive and H contains the unipotent radical of a Borel subgroup of G. In this case the normalizer P of H in G is parabolic and the morphism from G/H to G/P is a torus bundle over a rational homogeneous variety. A horospherical variety is a normal G-variety having an open dense G-orbit which is horospherical. Examples include rational homogeneous varieties, toric varieties, and odd symplectic Grassmannians. Pasquier classified smooth projective horospherical varieties of Picard number one, and one of the interesting questions is whether they can be characterized by the variety of minimal rational tangents at a general point, as in the case of rational homogeneous varieties of Picard number one. Hwang and Li confirm this characterization holds for odd symplectic Grassmannians, and recently for smooth horospherical variety of type G_2. In this talk, focusing on those of type B_n and of type F_4, we explain how to apply the prolongation method to get the characterization by the variety of minimal rational tangents. This is joint work with Shin-Young Kim.