세미나 및 콜로퀴엄

2021-01
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2021-02
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구글 Calendar나 iPhone 등에서 구독하면 세미나 시작 전에 알림을 받을 수 있습니다.

We consider the Cauchy problem of the self-dual Chern-Simons-Schrödinger equation (CSS) under equivariance symmetry. It is $L^2$-critical, has the pseudoconformal symmetry, and admits a soliton $Q$ for each equivariance index $m \geq 0$. An application of the pseudoconformal transform to $Q$ yields an explicit finite-time blow-up solution $S(t)$ which contracts at the pseudoconformal rate $|t|$. In the high equivariance case $m \geq 1$, the pseudoconformal blow-up for smooth finite energy solutions in fact occurs in a codimension one sense; it is stable under a codimension one perturbation, but also exhibits an instability mechanism. In the radial case $m=0$, however, $S(t)$ is no longer a finite energy blow-up solution. Interestingly enough, there are smooth finite energy blow-up solutions, but their blow-up rates differ from the pseudoconformal rate by a power of logarithm. We will explore these interesting blow-up dynamics (with more focus on the latter) via modulation analysis. This talk is based on my joint works with Soonsik Kwon and Sung-Jin Oh.
Host: 강문진     미정     2021-01-19 00:31:42
In the context of Voevodsky’s triangulated category of motives, we will describe a tower of triangulated functors which induce a finite filtration on the Chow groups. For smooth projective varieties, this finite filtration is a good candidate for the (still conjectural) Bloch-Beilinson filtration.
Zoom ID: 352 730 6970, PW: 9999 All time is in Korean Standard Time KST= UTC+9h.
Host: 박진현     Contact: 박진현 (2734)     영어     2021-01-20 19:01:32
We will discuss recent work, where we study the properties of the spectral sequence induced by the birational tower introduced in the 1st talk. In particular, we will show that this spectral sequence is strongly convergent.
Zoom ID: 352 730 6970, PW: 9999 All times are in Korean Standard Time KST = UTC+9
Host: 박진현     Contact: 박진현 (2734)     영어     2021-01-20 19:08:33
A famous theorem of Green and Tao says there are arbitrarily long arithmetic progressions consisting of prime numbers. In that 2008 paper, they predicted that similar statements should hold for prime elements of other number fields and the case of the Gaussian integers $Z[i]$ was subsequently settled by Tao. In the first of my two talks, I would like to share my (limited) knowledge about the background and history underlying their work.
Zoom ID : 352 730 6970, PW: 9999 All times in KST = UTC+9. This is also identical to the Japan Standard Time.
Host: 박진현     Contact: 박진현 (2734)     영어     2021-01-25 23:26:07
In the latter one hour, I will explain our generalization of their work to the general number fields based on my joint work with my Tohoku collegues Masato Mimura, Akihiro Munemasa, Shin-ichiro Seki and Kiyoto Yoshino (arxiv:2012.15669). Time permitting, I will also touch upon its positive characteristic analog (arxiv:2101.00839). The case of the polynomial rings had also been conjectured by Green-Tao in the same paper and settled by Lê in 2011.
Zoom ID : 352 730 6970, PW: 9999 All times in KST = UTC+9. This is also identical to the Japan Standard Time.
Host: 박진현     Contact: 박진현 (2734)     영어     2021-01-25 23:28:22
*Zoom Link: https://zoom.us/j/8456734198?pwd=eWJVSWFUS3psSldGUTdwYWNzWlhMQT09
[Zoom Meeting Information] Meeting ID: 845 673 4198, Password: 9999
Host: 곽시종     Contact: 김윤옥 (5745)     미정     2021-01-09 19:09:16
*Zoom Link: https://zoom.us/j/8456734198?pwd=eWJVSWFUS3psSldGUTdwYWNzWlhMQT09
[Zoom Meeting Information] Meeting ID: 845 673 4198, Password: 9999
Host: 곽시종     Contact: 김윤옥 (5745)     미정     2021-01-09 19:06:57