Monday, August 8, 2022

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2022-08-12 / 14:00 ~ 15:00
학과 세미나/콜로퀴엄 - PDE 세미나: 인쇄
by 이동현(포스텍)
Global wellposedness and asymptotic stability of the Boltzmann equation with specular reflection boundary condition in 3D non-convex domain is an outstanding open problem in kinetic theory. Motivated by Guo’s L^2-L^\infty theory, the problem was completely solved for general C^3 domain, but it is still widely open for general non-convex domains. The problem was solved in cylindrical domain with analytic non-convex cross section. Generalizing previous work, we study the problem in general solid torus, a solid torus with general analytic convex cross-section. This is the first results for the domain which contains essentially 3D non-convex structure. This is a joint work with Chanwoo Kim and Gyeonghun Ko.
2022-08-10 / 14:30 ~ 15:30
학과 세미나/콜로퀴엄 - 정수론: 인쇄
by ()
The past decade has witnessed a great advancement on the Tate conjecture for varieties with Hodge number $h^{2,0} = 1$. Charles, Madapusi-Pera and Maulik completely settled the conjecture for K3 surfaces over finite fields, and Moonen proved the Mumford-Tate (and hence also Tate) conjecture for more or less arbitrary $h^{2,0} = 1$ varieties in characteristic $0$. In this talk, I will explain that the Tate conjecture is true for mod $p$ reductions of complex projective $h^{2,0} = 1$ varieties when $p \gg 0$, under a mild assumption on moduli. By refining this general result, we prove that in characteristic $p \geq 5$ the BSD conjecture holds for a height $1$ elliptic curve $E$ over a function field of genus 1, as long as $E$ is subject to the generic condition that all singular fibers in its minimal compactification are irreducible. We also prove the Tate conjecture over finite fields for a class of surfaces of general type and a class of Fano varieties. The overall philosophy is that the connection between the Tate conjecture over finite fields and the Lefschetz $(1,1)$-theorem over $C$ is very robust for $h^{2,0} = 1$ varieties, and works well beyond the hyperk\”{a}hler world. This is based on joint work with Paul Hamacher and Xiaolei Zhao.
2022-08-10 / 10:30 ~ 11:30
학과 세미나/콜로퀴엄 - 정수론: 인쇄
by ()
The past decade has witnessed a great advancement on the Tate conjecture for varieties with Hodge number $h^{2,0} = 1$. Charles, Madapusi-Pera and Maulik completely settled the conjecture for K3 surfaces over finite fields, and Moonen proved the Mumford-Tate (and hence also Tate) conjecture for more or less arbitrary $h^{2,0} = 1$ varieties in characteristic $0$. In this talk, I will explain that the Tate conjecture is true for mod $p$ reductions of complex projective $h^{2,0} = 1$ varieties when $p \gg 0$, under a mild assumption on moduli. By refining this general result, we prove that in characteristic $p \geq 5$ the BSD conjecture holds for a height $1$ elliptic curve $E$ over a function field of genus 1, as long as $E$ is subject to the generic condition that all singular fibers in its minimal compactification are irreducible. We also prove the Tate conjecture over finite fields for a class of surfaces of general type and a class of Fano varieties. The overall philosophy is that the connection between the Tate conjecture over finite fields and the Lefschetz $(1,1)$-theorem over $C$ is very robust for $h^{2,0} = 1$ varieties, and works well beyond the hyperk\”{a}hler world. This is based on joint work with Paul Hamacher and Xiaolei Zhao.
2022-08-08 / 15:00 ~ 16:30
학과 세미나/콜로퀴엄 - 기타: Algebraic Surfaces 인쇄
by 금종해 (특별강연)(KMS)

2022-08-09 / 14:00 ~ 16:00
학과 세미나/콜로퀴엄 - 기타: (Undergrad student seminar) Basic properties and structures of Riemann surfaces via Čech cohomology 인쇄
by 김재홍(KAIST)
(학사과정 학생 개별연구 결과 발표 세미나) Čech cohomology is the direct limit of cohomology taken from the cochain complex obtained by an open cover and a sheaf. In this talk we will derive some important results about Riemann surfaces such as Riemann-Roch theorem and Serre Duality, regarding low level Čech cohomologies. We will also discuss some basic structure and properties of Riemann surfaces using these results, focusing on genus and the embeddings.
2022-08-09 / 16:30 ~ 17:30
IBS-KAIST 세미나 - 이산수학: Directed flow-augmentation 인쇄
by 김은정(CNRS, LAMSADE)
We show a flow-augmentation algorithm in directed graphs: There exists a polynomial-time algorithm that, given a directed graph G, two integers $s,t\in V(G)$, and an integer $k$, adds (randomly) to $G$ a number of arcs such that for every minimal st-cut $Z$ in $G$ of size at most $k$, with probability $2^{−\operatorname{poly}(k)}$ the set $Z$ becomes a minimum $st$-cut in the resulting graph. The directed flow-augmentation tool allows us to prove fixed-parameter tractability of a number of problems parameterized by the cardinality of the deletion set, whose parameterized complexity status was repeatedly posed as open problems: (1) Chain SAT, defined by Chitnis, Egri, and Marx [ESA'13, Algorithmica'17], (2) a number of weighted variants of classic directed cut problems, such as Weighted st-Cut, Weighted Directed Feedback Vertex Set, or Weighted Almost 2-SAT. By proving that Chain SAT is FPT, we confirm a conjecture of Chitnis, Egri, and Marx that, for any graph H, if the List H-Coloring problem is polynomial-time solvable, then the corresponding vertex-deletion problem is fixed-parameter tractable. Joint work with Stefan Kratsch, Marcin Pilipczuk, Magnus Wahlström.
Events for the 취소된 행사 포함 모두인쇄
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