To be updated soon.

Jin-Hwan Cho (National Institute for Mathematical Sciences, NIMS)

• Title: Outlier detection algorithms based on random forest

• Abstract: Outlier detection (또는 anomaly detection)은 희귀하거나(few) 대다수의 데이터와는 다른(different) 성질을 가진 이상치를 찾아내는 기계학습의 한 분야이다. 딥러닝을 위시한 인공지능의 연구가 지금처럼 활발하지 않았던 때에도 많은 연구가 이루어져 왔으며, 특히 자연과학은 물론 산업현장의 다양한 문제를 해결하는데 사용되고 있다. 이 발표에서는 기계학습의 기본 지식이 없더라도 쉽게 이해할 수 있으며, 게다가 강력한 퍼포먼스를 가진 두 가지 알고리즘, Isolation Forest와 Robust Random Cut Forest를 소개한다.

Yunhyung Cho (Sungkyunkwan University)

• Title: Mutations and mirror symmetry

• Abstract: In this talk, I will explain a notion of mutations in various contexts (e.g. polytopes, Laurent polynomials, quivers, etc) and describe how they are compatible with each other. Also I will explain how those phenomena appear in mirror symmetry.

Suyoung Choi (Ajou University)

• Title: Industrial math in civil engineering

• Abstract: In this talk, I will introduce some industrial math projects for NDT(nondestructive testing) technology in civil engineering.

Xin Fu (Ajou University)

• Title: The homotopy classification of four-dimensional toric orbifolds

• Abstract: Quasitoric manifolds are compact, smooth 2n-manifolds with a locally standard T^n-action whose orbit space is a simple polytope. The cohomological rigidity problem in toric topology was firstly posed by Suh and Masuda, which asks whether quasitoric manifolds are distinguished by their cohomology rings. A toric orbifold is a generalized notion of a quasitoric manifold, and there are examples of toric orbifolds that do not satisfy cohomological rigidity. In this talk, we see that certain toric orbifolds in four dimensions, though not cohomologically rigid, are homotopy equivalent if their integral cohomology rings are isomorphic. We achieve this goal by decomposing those spaces up to homotopy. This is joint work with Tseleung So (Regina) and Jongbaek Song (KIAS).

Taekgyu Hwang (Ajou University)

• Title: Cohomological rigidity of Bott manifolds

• Abstract: I will sketch a proof of the cohomological rigidity of Bott manifolds. The talk is based on the joint work with Suyoung Choi and Hyeontae Jang.

Eunjeong Lee (Chungbuk National University)

• Title: Classification of toric Schubert varieties

• Abstract: Let G be a simple Lie group and let B be a Borel subgroup. The homogeneous space G/B becomes a smooth projective variety, called the flag variety. Schubert varieties are some of the most interesting subvarieties of the flag variety. A maximal (complex) torus T acts on the flag variety and these subvarieties are stable under the action. In this talk, we consider toric Schubert varieties (with respect to the action of T) and their isomorphism classes. This talk is based on joint work with Mikiya Masuda and Seonjeong Park.

Jeongseok Oh (Imperial College London)

• Title: Complex Kuranishi spaces

• Abstract: We develop a theory of complex Kuranishi structures on projective schemes. These are sufficiently rigid to be equivalent to weak perfect obstruction theories, but sufficiently flexible to admit global complex Kuranishi charts.
  We apply the theory to projective moduli spaces M of stable sheaves on Calabi-Yau 4-folds. Borisov-Joyce produced a real virtual homology cycle on M using real derived differential geometry. In the prequel to this work we constructed an algebraic virtual cycle on M.
  We prove the cycles coincide in homology after inverting 2 in the coefficients. In particular, when Borisov-Joyce’s real virtual dimension is odd, their virtual cycle is torsion.
  This is a joint work with Richard Thomas.

Soumen Sarkar (Indian Institute of Technology Madras)

• Title: Resolution of singularities of quasitoric orbifolds and equivariant cobordism of quasi-contact toric manifolds

• Abstract: In this talk, we show that there is a resolution of singularities of a quasitoric orbifold. Then we prove that a quasi-contact toric manifold is equivariantly a boundary. This result implies that good contact toric manifolds and generalized lens spaces are equivariantly boundaries. This is a joint work with Koushik Brahma and Subhankar Sau.

Dong-Hwi Seo (Hanyang University)

• Title: Uniqueness results for the critical catenoid

• Abstract: A free boundary minimal surface in the three-dimensional unit ball is a properly immersed minimal surface in the unit ball that meets the unit sphere orthogonally along the boundary of the surface. The topic was initiated by Nitsche in 1985, derived from studies by Gergonne, Schwarz, Courant, and Lewy. Basic examples are the equatorial disk and the critical catenoid. The critical catenoid is the unique portion of the catenoid of the proper size. It is claimed to be the only embedded free boundary minimal annulus in the ball up to congruence. Recently, the problem has been attempted using a relationship with the Steklov eigenvalue problem. In this talk, I will describe previous studies in this direction and explain my uniqueness results for the critical catenoid as the embedded free boundary minimal annuli in the ball under symmetry conditions on the boundaries.

Jongbaek Song (KIAS)

• Title: Double cohomology of a moment angle complex

• Abstract: Given a simplicial complex K, one can define a topological space Z(K) called the moment-angle complex. The cohomology of Z(K) is captured by the Tor-algebra corresponding to the face ring of K. In this talk, we introduce a certain differential the cohomology of Z(K) to make it a chain complex. This leads us to define a double cohomology of Z(K), which is a new combinatorial invariant of K. Then, we discuss how it comes in the standard pipeline of TDA. This is a joint work (in progress) with A. Bahri, I. Limonchenko, T. Panov and D. Stanley.

Mathieu Vallée (Université de Rennes 1)

• Title: On the enumeration of (real) toric manifolds of Picard number 4

• Abstract: Toric varieties (resp., real toric varieties) are classified by fans (resp., mod 2 fans). More generally, (real) toric spaces can be classified by pairs $(K,\lambda)$ consisting of a simplicial complex $K$ and a (mod 2) characteristic map $\lambda$ over $K$. It is known that the space obtained from a pair $(K,\lambda)$ is a smooth manifold if the simplicial complex $K$ is a PL-sphere and $\lambda$ is non-singular. A given $K$ will be said ($\Z_2$-)colorable if there exists a non-singular (mod 2) characteristic map over $K$.
  The classification of smooth (real) toric varieties for Picard number smaller than 4 has been entirely achieved by Batirev [1991] and revisited by Choi and Park [2016]. The wedge operation on simplicial complexes preserves both the PL-sphereness and the Picard number. In addition, Choi and Park [2017] have shown that it also preserves ($\Z_2$-)colorability, with their puzzle method. Simplicial complexes which cannot be described as the wedge of a lower dimensional simplicial complex are called seeds. Choi and Park have also shown that there is only a finite number of ($\Z_2$-)colorable seed PL-spheres of fixed Picard number. We take the next step of this classification by completing the case of Picard number 4 with a twofold approach:

1. We firstly simplify the $\Z_2$-colorable PL-sphere enumeration problem to a linear algebra problem which becomes parallel programming compatible;

2. We secondly use CUDA parallel programming capability's to run the modified algorithm on a regular graphic card instead of a supercomputer.

This work was done jointly with Suyoung Choi and Hyeontae Jang.