DSpace Community: KAIST Dept. of Mathematical SciencesKAIST Dept. of Mathematical Scienceshttp://hdl.handle.net/10203/5272017-03-30T10:42:58Z2017-03-30T10:42:58ZInterlacing of zeros of certain weakly holomorphic modular forms for Gamma(+)(0)(2)Choi, SoYoungIm, Bo-Haehttp://hdl.handle.net/10203/2208442017-03-28T06:49:08Z2017-05-01T00:00:00ZTitle: Interlacing of zeros of certain weakly holomorphic modular forms for Gamma(+)(0)(2)
Authors: Choi, SoYoung; Im, Bo-Hae
Abstract: We prove that zeros of each basis element of the space of weakly holomorphic modular forms of weight k for the Fricke group Gamma(+)(0)(2) of level 2 interlace, extending the result for SL2(Z) of Jenkins and Pratt [4].
(c) 2016 Elsevier Inc. All rights reserved.2017-05-01T00:00:00ZCLASSIFICATION OF REAL BOTT MANIFOLDS AND ACYCLIC DIGRAPHSChoi, SuyoungMasuda, MikiyaOum, Sang-ilhttp://hdl.handle.net/10203/2204322017-03-24T08:25:29Z2017-04-01T00:00:00ZTitle: CLASSIFICATION OF REAL BOTT MANIFOLDS AND ACYCLIC DIGRAPHS
Authors: Choi, Suyoung; Masuda, Mikiya; Oum, Sang-il
Abstract: We completely characterize real Bott manifolds up to affine diffeomorphism in terms of three simple matrix operations on square binary matrices obtained from strictly upper triangular matrices by permuting rows and columns simultaneously. We also prove that any graded ring isomorphism between the cohomology rings of real Bott manifolds with Z/2 coefficients is induced by an affine diffeomorphism between the real Bott manifolds.
Our characterization can also be described in terms of graph operations on directed acyclic graphs. Using this combinatorial interpretation, we prove that the decomposition of a real Bott manifold into a product of indecomposable real Bott manifolds is unique up to permutations of the indecomposable factors. Finally, we produce some numerical invariants of real Bott manifolds from the viewpoint of graph theory and discuss their topological meaning. As a byproduct, we prove that the toral rank conjecture holds for real Bott manifolds.2017-04-01T00:00:00ZCHOW GROUPS OF PRODUCTS OF SEVERI-BRAUER VARIETIES AND INVARIANTS OF DEGREE 3Baek, Sanghoonhttp://hdl.handle.net/10203/2204452017-03-24T08:26:07Z2017-03-01T00:00:00ZTitle: CHOW GROUPS OF PRODUCTS OF SEVERI-BRAUER VARIETIES AND INVARIANTS OF DEGREE 3
Authors: Baek, Sanghoon
Abstract: We study the semi-decomposable invariants of a split semisimple group and their extension to a split reductive group by using the torsion in the codimension 2 Chow groups of a product of Severi-Brauer varieties. In particular, for any n >= 2 we completely determine the degree 3 invariants of a split semisimple group, the quotient of (SL2)(n) by its maximal central sub-group, as well as of the corresponding split reductive group. We also provide an example illustrating that a modification of our method can be applied to find the semi-decomposable invariants of a split semisimple group of type A.2017-03-01T00:00:00ZColoring graphs without fan vertex-minors and graphs without cycle pivot-minorsChoi, IlkyooKwon, O-JoungOum, Sang-ilhttp://hdl.handle.net/10203/2204332017-03-22T02:52:34Z2017-03-01T00:00:00ZTitle: Coloring graphs without fan vertex-minors and graphs without cycle pivot-minors
Authors: Choi, Ilkyoo; Kwon, O-Joung; Oum, Sang-il
Abstract: A fan F-k is a graph that consists of an induced path on k vertices and an additional vertex that is adjacent to all vertices of the path. We prove that for all positive integers q and k, every graph with sufficiently large chromatic number contains either a clique of size q or a vertex-minor isomorphic to F-k. We also prove that for all positive integers q and k >= 3, every graph with sufficiently large chromatic number contains either a clique of size q or a pivot-minor isomorphic to a cycle of length k. (C) 2016 Elsevier Inc. All rights reserved.2017-03-01T00:00:00Z