DSpace Community: KAIST Dept. of Mathematical Sciences
http://hdl.handle.net/10203/527
KAIST Dept. of Mathematical SciencesThu, 10 Oct 2019 19:34:57 GMT2019-10-10T19:34:57Zl-adic étale cohomology of Shimura varieties of Hodge type with non-trivial coefficients
http://hdl.handle.net/10203/251897
Title: l-adic étale cohomology of Shimura varieties of Hodge type with non-trivial coefficients
Authors: Hamacher, Paul; Kim, Wansuhttp://hdl.handle.net/10203/251897A logarithmic chemotaxis model featuring global existence and aggregation
http://hdl.handle.net/10203/264321
Title: A logarithmic chemotaxis model featuring global existence and aggregation
Authors: Desvillettes, Laurent; Kim, Yong-Jung; Trescases, Ariane; Yoon, Changwook
Abstract: The global existence of a chemotaxis model for cell aggregation phenomenon is obtained. The model system belongs to the class of logarithmic models and takes a Fokker-Planck type diffusion for the equation of cell density. We show that weak solutions exist globally in time in dimensions n is an element of {1, 2, 3} and for large initial data. The proof covers the parameter regimes that constant steady states are linearly stable. It also partially covers the other parameter regimes that constant steady states are unstable. We also find the sharp instability condition of constant steady states and provide numerical simulations which illustrate the formation of aggregation patterns. (C) 2019 Elsevier Ltd. All rights reserved.Sun, 01 Dec 2019 00:00:00 GMThttp://hdl.handle.net/10203/2643212019-12-01T00:00:00ZThe transcendence of zeros of canonical basis elements of the space of weakly holomorphic modular forms for Gamma(0)(2)
http://hdl.handle.net/10203/264323
Title: The transcendence of zeros of canonical basis elements of the space of weakly holomorphic modular forms for Gamma(0)(2)
Authors: Choi, SoYoung; Im, Bo-Hae
Abstract: We consider the canonical basis elements f(k,m)(epsilon) for the space of weakly holomorphic modular forms of weight k for the Hecke congruence group Gamma(0)(2) and we prove that for all m >= c(k) for some constant c(k), if z(0) in a fundamen- tal domain for Gamma(0)(2) is a zero of f(k,m)(epsilon), then either z(0) is in {i/root 2, - 1/2 + i/2, 1/2 + i/2, -1+i root 7/4, 1+i root 7/4} or z(0) is transcendental. (C) 2019 Elsevier Inc. All rights reserved.Fri, 01 Nov 2019 00:00:00 GMThttp://hdl.handle.net/10203/2643232019-11-01T00:00:00ZThe regularity of partial elimination ideals, Castelnuovo normality and syzygies
http://hdl.handle.net/10203/263727
Title: The regularity of partial elimination ideals, Castelnuovo normality and syzygies
Authors: Ahn, Jeaman; Kwak, Sijong
Abstract: Let X be a reduced closed subscheme in P-n, pi : X -> pi(X) subset of Pn-1 be a projection from a point outside X and Z(i) (X) subset of pi(X) be the closed subscheme defined by the i-th partial elimination ideal K-i(I-x), which is supported on the (i + 1)-th multiple points of pi. In this paper, motivated from projection methods to prove Eisenbud-Goto conjecture on regularity in many cases, we describe the syzygetic behaviors and Castelnuovo normality of the projection with a viewpoint of the regularity of the partial elimination ideal K-i(I-X), i >= 1 (or that of the multiple locus Z(i) (X) of pi). We also give some applications to the syzygies and Castelnuovo normality of successive projections, which recover and generalize some known results in [1,3,15,16]. (C) 2019 Published by Elsevier Inc.Sun, 01 Sep 2019 00:00:00 GMThttp://hdl.handle.net/10203/2637272019-09-01T00:00:00Z