Friday, October 29, 2021

2021-11-01 / 16:00 ~ 17:00

학과 세미나/콜로퀴엄 - PDE 세미나: Hydrodynamic limits of the Schrodinger equation with gauge fields

by 김정호(한양대학교 수학과)

In this talk, we present the hydrodynamic limits of the Schrodinger equation, affected by different gauge fields. Precisely, we first present the hydrodynamic limit of the Schrodinger equation with the Chern-Simons gauge fields (Chern-Simons-Schrodinger equation), toward to the Euler-Chern-Simons equation on the two-dimensional state space. Then, we consider the hydrodynamic limit of the Schrodinger equation with the Maxwell gauge fields (Maxwell-Schrodinger equation), toward to the Euler-Maxwell equation on the three-dimensional state space. Both estimate use the estimate on the modulated energy functionals.

2021-11-02 / 16:30 ~ 17:30

IBS-KAIST 세미나 - 이산수학: Maximal 3-wise intersecting families

by Ben Lund(IBS 이산수학그룹)

A family F of subsets of {1,2,…,n} is called maximal k-wise intersecting if every collection of at most k members from F has a common element, and moreover, no set can be added to F while preserving this property. In 1974, Erdős and Kleitman asked for the smallest possible size of a maximal k-wise intersecting family, for k≥3. We resolve this problem for k=3 and n even and sufficiently large. This is joint work with Kevin Hendrey, Casey Tompkins, and Tuan Tran.

2021-11-05 / 09:30 ~ 16:20

SAARC 세미나 - SAARC 세미나:

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2021-11-04 / 09:30 ~ 16:20

SAARC 세미나 - SAARC 세미나:

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2021-11-03 / 09:30 ~ 16:20

SAARC 세미나 - SAARC 세미나:

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2021-11-01 / 16:00 ~ 17:30

학과 세미나/콜로퀴엄 - 박사논문심사: 조건부 기댓값을 이용한 이색 옵션의 가격 산정

by 김민석 (KAIST)()

심사위원장 최건호, 심사위원 곽도영, 권순식, 김동석(경영공학부), 김완수

2021-10-29 / 10:30 ~ 11:20

학과 세미나/콜로퀴엄 - 해외 석학 특별 강연 시리즈: Algorithmic and mathematical issues in deep learning

by George Karniadakis(Brown University)

KAIX 석학강연

2021-10-29 / 09:30 ~ 10:20

학과 세미나/콜로퀴엄 - 해외 석학 특별 강연 시리즈: Physics-informed learning for diverse applications in science and engineering

by George Karniadakis(Brown University)

KAIX 석학 강연

2021-11-01 / 16:30 ~ 17:30

학과 세미나/콜로퀴엄 - 대수기하학:

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First, I will say a few words about Galois descent in the particular case of a projective variety embedded into a projective space. Then I will recall the definintion of a torsor and will explain how to construct the quotient of a torsor of a simple simply connected split algebraic group modulo a Borel subgroup. Finally, I will prove that the Picard group of such a quotient does not change for one particular finite Galois extension of the base field, and then, if there is enough time, for any extension of the base field.

2021-11-04 / 14:00 ~ 15:30

학과 세미나/콜로퀴엄 - 위상수학 세미나:

by 박기호(고등과학원)

We will survey recent development in subadditive thermodynamic formalism for matrix cocycles. In particular, in the setting of locally constant cocycles as well as fiber-bunched cocycles, we will discuss sufficient conditions for the norm potentials of such cocycles to have unique equilibrium states. If time permitting, we will also discuss ergodic properties of such equilibrium states as well as some applications.

2021-11-05 / 15:00 ~ 16:00

학과 세미나/콜로퀴엄 - 대수기하학: Twisted equivalences in spectral algebraic geometry I

by 조창연(서울대학교 QSMS)

Derived equivalence has been an interesting subject in relation to Fourier-Mukai transform, Hochschild homology, and algebraic K-theory, just to name a few. On the other hand, the attempt to classify schemes by their derived categories twisted by elements of Brauer groups is very restrictive as we have a positive answer only for affines. I'll talk about how we can extend this result to a broader class of algebro-geometric objects in the setting of derived/spectral algebraic geometry at the expense of a stronger notion of twisted equivalences than that of ordinary twisted derived equivalences. I'll convince you that the new notion is not only reasonable, but also indispensable from this point of view. The first talk will be mainly devoted to giving brief expository accounts of some background materials needed to understand the notion of twisted derived equivalence in the setting of derived/spectral algebraic geometry; in particular, some familiarity with ordinary algebraic geometry will be enough for the talk.

2021-10-29 / 16:00 ~ 17:00

학과 세미나/콜로퀴엄 - PDE 세미나:

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The purpose of this talk is to mathematically investigate the formation of a plasma sheath, and to analyze the Bohm criterions which are required for the formation. Bohm derived originally the (hydrodynamic) Bohm criterion from the Euler–Poisson system. Boyd and Thompson proposed the (kinetic) Bohm criterion from kinetic point of view, and then Riemann derived it from the Vlasov–Poisson system. We study the solvability of boundary value problems of the Vlasov–Poisson system. On the process, we see that the kinetic Bohm criterion is a necessary condition for the solvability. The argument gives a simpler derivation of the criterion. Furthermore, the hydrodynamic criterion can be derived from the kinetic criterion. It is of great interest to find the relation between the solutions of the Vlasov–Poisson and Euler–Poisson systems. To clarify the relation, we also investigate the hydrodynamic limit of solutions of the Vlasov–Poisson system.

2021-11-04 / 16:15 ~ 17:15

학과 세미나/콜로퀴엄 - 콜로퀴엄: On a conjecture of Coleman concerning Euler systems

by 서수길(연세대학교)

We introduce a distribution-theoretic conjecture of Roert Coleman of the 1980's and prove the conjecture in a recent joint work with Burns and Daoud. This accordingly gives an explicit description of the complete set of Euler systems for the multiplicative group over Q together with a connection to other conjectures in number theory.

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