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구글 Calendar나 iPhone 등에서 구독하면 세미나 시작 전에 알림을 받을 수 있습니다.

심사위원장 : 강 완 모, 심 사 위 원 : 황강욱, 김동환, 윤세영(AI대학원), 조경현(뉴욕대 전산학과)
한국어     2020-05-13 16:25:56
In this penultimate talk of the Graphon Seminar, we investigate the method of sampling from a graph as a method of gathering information about very large, dense graphs. We will talk about this method in the context of graphons and introduce the concept of a W-random graph for a graphon W. This talk is based on chapter 10 of the book "Large networks and graph limits" by Lászlo Lovász.
Host: 폴정     Contact: 이슬기 (042-350-8111)     영어     2020-05-25 16:09:46
In this final talk of the Graphon Seminar, we take a closer look at how graphons arise as the limit of convergent sequences of dense graphs. This talk is based on chapter 11 of the book "Large networks and graph limits" by Lászlo Lovász.
Host: 폴정     Contact: 이슬기 (042-350-8111)     영어     2020-05-25 16:23:51
심사위원장 : 정 연 승, 심 사 위 원 : 김성호, 황강욱, 전현호, 이은지(충남대 통계학과)
한국어     2020-05-13 17:10:52
Let $E$ be an elliptic curve over $\mathbb{Q}$ with discriminant $\Delta_E$. For primes $p$ of good reduction, let $N_p$ be the number of points modulo $p$ and write $N_p=p+1-a_p$. In 1965, Birch and Swinnerton-Dyer formulated a conjecture which implies $$\lim_{x\to\infty}\frac{1}{\log x}\sum_{\substack{p\leq x\\ p\nmid \Delta_{E}}}\frac{a_p\log p}{p}=-r+\frac{1}{2},$$ where $r$ is the order of the zero of the $L$-function $L_{E}(s)$ of $E$ at $s=1$, which is predicted to be the Mordell-Weil rank of $E(\mathbb{Q})$. We show that if the above limit exits, then the limit equals $-r+1/2$. We also relate this to Nagao's conjecture. This is a recent joint work with M. Ram Murty. (If you would like to join this online seminar, please email me (Bo-Hae Im) to get a link.)
Host: Bo-Hae Im     미정     2020-05-26 11:25:26