Wednesday, October 28, 2020

2020-11-03 / 16:30 ~ 17:30

학과 세미나/콜로퀴엄 - 계산수학 세미나: How do flagellated bacteria swim?: Modeling, Simulations & Analysis

by 임숙경(University of Cincinnati)

Swimming bacteria with helical flagella are self-propelled micro-swimmers in nature, and the swimming strategies of such bacteria vary depending on the number and the position of flagella on the cell body. In this talk, I will introduce some microorganisms such as E. coli, Vibrio A and P putida. The Kirchhoff rod theory is used to model the elastic helical flagella and the cell body is represented by a hollow ellipsoid that can translate and rotate as a neutrally buoyant rigid body interacting with a surrounding fluid. The hydrodynamic interaction between the fluid and the bacteria is described by the regularized version of Stokes flow. I will focus on how bacteria can swim and reorient swimming course for survival and how Mathematics can help to understand the swimming mechanism of such bacteria.

2020-10-28 / 16:00 ~ 17:00

학과 세미나/콜로퀴엄 - PDE 세미나:

by 강문진()

I will present my recent work on uniqueness of Riemann problem consisting of two shocks for 1D isentropic Euler system. The uniqueness is guaranteed in the class of vanishing viscosity limits of solutions to the associate Navier-Stokes system, as the Bianchini-Bressan conjecture. The main idea to achieve this issue is to get a uniform stability of any large perturbations from a composite wave of two viscous shocks to the Navier-Stokes. Especially, I will explain about this main idea in a simpler context, that is, in the case of a single shock. This is based on joint works with Alexis Vasseur.

2020-11-03 / 15:00 ~ 16:30

학과 세미나/콜로퀴엄 - 정수론:

by ()

Let $E$ be an elliptic curve over the rational number field $\mathbb{Q}$. Selmer Groups and Ideal Class Groups are important and widely-studied objects in number theory. Brumer and Kramer studied relations between these two objects in their paper in 1977. They actually found an upper bound for the $2$-Selmer rank of $E$ in terms of the ideal class group of a certain cubic field extension of $\mathbb{Q}$. As an application, they determined the Mordell-Weil ranks of (most) elliptic curves of prime conductor assuming the BSD conjecture. In this talk, we will talk about a generalization of Brumer-Kramer's work to the case of elliptic curves over an arbitary number field. We will give both upper and lower bounds for the $2$-Selmer rank in terms of a (modified) ideal class group, and the bounds turn out to be sharp in many cases. This is joint work with Hwajong Yoo. (If you would like to join the seminar, please let me(Bo-Hae Im) know so that I can send you the Zoom link.)

Events for the 취소된 행사 포함