Wednesday, August 2, 2023

2023-08-04 / 14:00 ~ 16:00

by ()

The well-known Internal Model Principle (IMP) is a cornerstone of modern control theory. It stipulates the necessary conditions for asymptotic robustness of disturbance-prone dynamical systems by asserting that such a system must embed a subsystem in a feedback loop, and this subsystem must be able to reduplicate the dynamic disturbance using only the regulated variable as the input. The insights provided by IMP can help in both designing suitable controllers and also in analysing the regulatory mechanisms in complex systems. So far the application of IMP in biology has been case-specific and ad hoc, primarily due to the lack of generic versions of the IMP for biomolecular reaction networks that model biological processes. In this short article we highlight the need for an IMP in biology and discuss a recently developed version of it for biomolecular networks that exhibit maximal Robust Perfect Adaptation (maxRPA) by being robust to the maximum number of disturbance sources.

2023-08-08 / 10:00 ~ 11:00

SAARC 세미나 - SAARC 세미나:

by ()

We consider the nonlinear Schrödinger equation and the nonlinear wave equation with initial data decaying slower than L^2 functions. However, the L^p-spaces for p \neq 2 are not invariant under the linear propagation. We consider function spaces, which allow for decay like in L^p, p > 2, and which are invariant under the linear propagation. We show L^p-smoothing estimates using \ell^2-decoupling due to Bourgain-Demeter. The results on nonlinear wave equations are joint work with Jan Rozendaal (IMPAN).

2023-08-03 / 14:00 ~ 15:00

학과 세미나/콜로퀴엄 - 정수론:

by 문용석()

Let X be a semistable p-adic formal scheme. In this talk, we will discuss a prismatic description of semistable local systems on the generic fiber of X. A main new ingredient is a purity result. This is based on a joint work with Heng Du, Tong Liu, Koji Shimizu.

2023-08-02 / 16:30 ~ 17:30

IBS-KAIST 세미나 - 이산수학: High chromatic common graphs

by Daniel Kráľ(Masaryk University)

Ramsey’s Theorem guarantees for every graph H that any 2-edge-coloring of a sufficiently large complete graph contains a monochromatic copy of H. As probabilistic constructions often provide good bounds on quantities in extremal combinatorics, we say that a graph H is common if the random 2-edge-coloring asymptotically minimizes the number of monochromatic copies of H. This notion goes back to the work of Erdős in the 1960s, who conjectured that every complete graph is common. The conjecture was disproved by Thomason in the 1980s, however, a classification of common graphs remains one of the most intriguing problems in extremal combinatorics. Sidorenko’s Conjecture (if true) would imply that every bipartite graph is common, and in fact, no bipartite common graph unsettled for Sidorenko’s Conjecture is known. Until Hatami et al. showed that a 5-wheel is common about a decade ago, all graphs known to be common had chromatic number at most three. The existence of a common graph with chromatic number five or more has remained open for three decades. We will present a construction of (connected) common graphs with arbitrarily large chromatic number. At the end of the talk, we will also briefly discuss the extension of the notion to more colors and particularly its relation to Sidorenko’s Conjecture. The main result presented in the talk is based on joint work with Jan Volec and Fan Wei.

2023-08-04 / 16:00 ~ 18:00

학과 세미나/콜로퀴엄 - 위상수학 세미나:

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We review constructions of Manolescu’s Floer homotopy type, which gives a homotopical refinement of monopole Floer homology. Based on it, we will introduce some homology cobordism/ knot concordance invariant. Using these invariants, we provide relative versions of 10/8 inequalities for 4-manifolds with boundary or surfaces in 4-manifolds. In particular, I’ll explain Manolescu’s relative 10/8 inequality, real 10/8 inequality, and Montague’s 10/8 inequality.

2023-08-09 / 11:00 ~ 12:30

SAARC 세미나 - SAARC 세미나:

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In this lecture series, I will discuss rigidity in the long time dynamics of some evolution equation. The specific equation to be paid attention to is the self-dual Chern-Simons-Schrödinger equation (CSS) within equivariant symmetry. (CSS) is a gauged 2D cubic nonlinear Schrödinger equation that has pseudoconformal invariance and solitons. However, two distinguished features of (CSS), the self-duality and non-locality, make the long time dynamics of (CSS) surprisingly rigid. For instance, (i) any finite energy spatially decaying solutions to (CSS) decompose into at most one modulated soliton and a radiation. Moreover, (ii) in the high equivariance case (i.e., the equivariance index ≥ 1), any smooth finite-time blow-up solutions even have a universal blow-up speed, namely, the pseudoconformal one. We will explore this rigid dynamics using modulation analysis, combined with the self-duality and non-locality of the problem, in detail.

2023-08-08 / 11:00 ~ 12:30

SAARC 세미나 - SAARC 세미나:

by ()

2023-08-09 / 16:30 ~ 17:30

IBS-KAIST 세미나 - 이산수학: Intersection patterns of convex sets

by Amzi Jeffs(Carnegie Mellon University)

How can one arrange a collection of convex sets in d-dimensional Euclidean space? This guiding question is fundamental in discrete geometry, and can be made concrete in a variety of ways, for example the study of hyperplane arrangements, embeddability of simplicial complexes, Helly-type theorems, and more. This talk will focus on the classical topic of d-representable complexes and its more recent generalization to convex codes. We will show how these frameworks differ, share some novel Helly-type results, and offer several tantalizing open questions.

Events for the 취소된 행사 포함