Friday, September 13, 2024

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2024-09-20 / 14:00 ~ 16:00
IBS-KAIST 세미나 - 수리생물학: 인쇄
by ()
In this talk, we discuss the paper “Achieving Occam’s razor: Deep learning for optimal model reduction” by Botond B. Antal et.al., PLOS Computational Biology, 2024.
2024-09-13 / 14:00 ~ 16:00
IBS-KAIST 세미나 - 수리생물학: 인쇄
by 김현(IBS 의생명수학그룹)
In this talk, we discuss the paper “Deep learning linking mechanistic models to single-cell transcriptomics data reveals transcriptional bursting in response to DNA damage” by Zhiwei Huang, et. al., bioRxiv, 2024.
2024-09-13 / 10:30 ~ 12:30
학과 세미나/콜로퀴엄 - 대수기하학: 인쇄
by ()
I will describe recent joint work with Keller VandeBogert on constructing pure free resolutions over quadric hypersurface rings. Along the way I will describe some connections between total positivity and Koszul algebras and some conjectures regarding the homotopy Lie algebra and its "fattened" versions.
2024-09-20 / 11:30 ~ 13:00
학과 세미나/콜로퀴엄 - 대수기하학: 인쇄
by 김영락(부산대)
An Ulrich bundle E on an n-dimensional projective variety (X, O(1)) is a vector bundle whose module of twisted global sections is a maximal Cohen-Macaulay module having the maximal number of generators in degree 0. It was once studied by commutative algebraists, but after Eisenbud and Schreyer introduced its geometric viewpoint, many people discovered several important applications in wide areas of mathematics. In this motivating paper, Eisenbud-Schreyer asked a question whether a given projective variety has an Ulrich bundle, and what is the minimal possible rank of an Ulrich bundle if exists. The answer is still widely open for algebraic surfaces and higher dimensional varieties. Thanks to a number of studies, the answer for the above question is now well-understood for del Pezzo threefolds. In particular, a del Pezzo threefold V_d of (degree d≥3) has an Ulrich bundle of rank r for every r at least 2. The Hartshorne-Serre correspondence translates the existence of rank-3 Ulrich bundle into the existence of an ACM curve C in V_d of genus g=2d+4 and degree 3d+3. In this talk, we first recall a construction of rank-3 Ulrich bundle on a cubic threefold by Geiss and Schreyer, by showing that a "random" curve of given genus and degree lies in a cubic threefold and satisfies the whole conditions we needed. We also discuss how this problem is related to the unirationality of the Hurwitz space H(k, 2g+2k-2) and the moduli of curves M_g. An analogous construction works for d=4, however, for d=5 a general curve of genus 14 and degree 18 does not belong to V_5. We characterize geometric conditions when does such a curve can be embedded into V_5 using the vanishing resonance. This is a joint work with Marian Aprodu.
2024-09-20 / 14:00 ~ 16:00
학과 세미나/콜로퀴엄 - 위상수학 세미나: 인쇄
by ()
We give L^2-signature obstructions to embedding closed 3-manifolds with infinite cyclic first homology in closed 4-manifolds with infinite cyclic fundamental group preserving first homology. From the obstructions, we obtain lower bounds on the double slice genus of a knot, and give examples of algebraically doubly slice knots with vanishing Casson-Gordon invariants whose double slice genera are arbitrarily large. This is a joint work with Taehee Kim.
2024-09-20 / 11:05 ~ 12:00
학과 세미나/콜로퀴엄 - 응용 및 계산수학 세미나: 인쇄
by 이진실()
We propose a collocation method based on multivariate polynomial splines over triangulation or tetrahedralization for numerical solution of partial differential equations. We start with a detailed explanation of the method for the Poisson equation and then extend the study to other PDEs. We shall show that the numerical solution can approximate the exact PDE solution very well. Then we present a large amount of numerical experimental results to demonstrate the performance of the method over the two- and three-dimensional settings.
2024-09-19 / 10:30 ~ 11:30
학과 세미나/콜로퀴엄 - 대수기하학: 인쇄
by ()
The lecture series gives a view on computational methods and their some applications to existence and classfication problems. In the first lectures I will introduce Groebner basis and their basic applications in commutative algebra such as computing kernel and images of morphism between finitely presented modules over polynomial rings. As a theoretical application of Groebner basis I will give Petri's analysis of the equations of a canonical curve. The second topic will be Computer aided existence and unirationality proofs of algebraic varieties and their moduli spaces. In case of curves liaison theory is needed, which will be developed. For existence proofs random searches over finite fields is a technique that has not been exploited very much. I will illustrate this technique in a number of examples, in particular for the construction of certain surfaces. Classification of non-minimal surfaces uses adjunction theory. We will discuss this from a computational point of view.
Events for the 취소된 행사 포함 모두인쇄
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