# 세미나 및 콜로퀴엄

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

The circle is the only connected closed 1-dimensional manifold, and maybe that's why it has so many interesting features. In this talk, we would like to emphasize that there are many things we still do not know about this one of the simplest manifolds. We will survey many interesting recent results around the circle in the context of low-dimensional topology.

2017 제4회 정오의 수학산책

강연자: 양성덕 (고려대)

일시: 2017년 6월 2일(금) 12:00 ~ 13:15

장소: 카이스트 자연과학동 E6-1 3435호

제목: 고차원 공간의 계량과 곡률

내용: TBA

등록: 2017년 5월 31일(수) 오후 3시까지

https://goo.gl/forms/ol819KdGNA5SdGSr2

문의: hskim@kias.re.kr / 내선:8545

The interactions between particles and

uid have received a bulk of attention

due to a number of their applications in the eld of, for example, biotechnol-

ogy, medicine, and in the study of sedimentation phenomenon, compressibility

of droplets of the spray, cooling tower plumes, and diesel engines, etc. In this

talk, we present coupled kinetic-

uid equations. The proposed equations consist

of Vlasov-Fokker-Planck equation with local alignment forces and the incom-

pressible Navier-Stokes equations. For the equations, we establish the global

existence of weak solutions, hydrodynamic limit, and large-time behavior of

solutions. We also remark on blow-up of classical solutions in the whole space.

Hyperrings and hyperfields are algebraic structures which generalize commutative rings and fields. In this talk, we aim to introduce these exotic structures and also provide examples which illustrate how hyperrings and hyperfields show up in algebraic geometry and combinatorics following the idea of Baker and Bowler on `matroids over hyperfields'.

The discrepancy of a sequence f(1), f(2), ... of numbers is defined to be the largest value of |f(d) + f(2d) + ... + f(nd)| as n,d range over the natural numbers. In the 1930s, Erdos posed the question of whether any sequence consisting only of +1 and -1 could have bounded discrepancy. In 2010, the collaborative Polymath5 project showed (among other things) that the problem could be effectively reduced to a problem involving completely multiplicative sequences. Finally, using recent breakthroughs in the asymptotics of completely multiplicative sequences by Matomaki and Radziwill, as well as a surprising application of the Shannon entropy inequalities, the Erdos discrepancy problem was solved in 2015. In this talk I will discuss this solution and its connection to the Chowla and Elliott conjectures in number theory.

2017 CMC Distinguished Lecture Series by Terence Tao

####
Fusion Hall(1F), KI Bldg.(#E4), KAIST, Daejeon
해외 석학 특별 강연 시리즈
Terrence Tao (UCLA)
Finite time blowup constructions for supercritical equations

Many basic PDE of physical interest, such as the three-dimensional Navier-Stokes equations, are "supercritical" in that the known conserved or bounded quantities for these equations allow the nonlinear components of the PDE to dominate the linear ones at fine scales. Because of this, almost none of the known methods for establishing global regularity for such equations can work, and global regularity for Navier-Stokes in particular is a notorious open problem. We present here some ways to show that if one allows some modifications to these supercritical PDE, one can in fact construct solutions that blow up in finite time (while still obeying conservation laws such as conservation of energy). This does not directly impact the global regularity question for the unmodified equations, but it does rule out some potential approaches to establish such regularity.

2017 CMC Distinguished Lecture Series by Terence Tao