Saturday, October 9, 2021

2021-10-15 / 10:00 ~ 11:00

SAARC 세미나 - SAARC 세미나:

by 김건우(포항공과대학교 수학과)

Partial differential equations such as heat equations have traditionally been our main tool to study physical systems. However, physical systems are affected by randomness (noise). Thus, stochastic partial differential equations have gained popularity as an alternative. In this talk, we first consider what “noise” means mathematically and then consider stochastic heat equations perturbed by space-time white noise such as parabolic Anderson model and stochastic reaction-diffusion equations (e.g., KPP or Allen-Cahn equations). Those stochastic heat equations have similar properties as heat equations, but exhibit different behavior such as intermittency and dissipation, especially as time increases. We investigate in this talk how the long-time behaviors of the stochastic heat equations are different from heat equations.

2021-10-15 / 16:00 ~ 17:00

학과 세미나/콜로퀴엄 - PDE 세미나:

by 이기암(서울대학교)

In this talk, we are going to discuss boundary regularities of various degenerate local equation and nonlocal equations. Diffusion rates deform undefined geometry related to diffusion and the corresponding distance function makes important role in the theory of regularity. And then we will also discuss the possible applications.

2021-10-13 / 10:00 ~ 12:00

학과 세미나/콜로퀴엄 - 위상수학 세미나: Random walks on SL_2(C)

by Lucas Kauffman(IBS, Center for Complex Geometry)

Given a sequence of random i.i.d. 2 by 2 complex matrices, it is a classical problem to study the statistical properties of their product. This theory dates back to fundamental works of Furstenberg, Kesten, etc. and is still an active research topic. In this talk, I intend to show how methods from complex analysis and analogies with holomorphic dynamics offer a new point of view to this problem. This is used to obtain several new limit theorems for these random processes, often in their optimal version. This is based on joint works with T.-C. Dinh and H. Wu.

2021-10-12 / 16:30 ~ 17:30

IBS-KAIST 세미나 - 이산수학: Majority dynamics on sparse random graphs

by 이준경(한양대)

Majority dynamics on a graph $G$ is a deterministic process such that every vertex updates its $\pm 1$-assignment according to the majority assignment on its neighbor simultaneously at each step. Benjamini, Chan, O'Donnell, Tamuz and Tan conjectured that, in the Erd\H{o}s--R\'enyi random graph $G(n,p)$, the random initial $\pm 1$-assignment converges to a $99\%$-agreement with high probability whenever $p=\omega(1/n)$. This conjecture was first confirmed for $p\geq\lambda n^{-1/2}$ for a large constant $\lambda$ by Fountoulakis, Kang and Makai. Although this result has been reproved recently by Tran and Vu and by Berkowitz and Devlin, it was unknown whether the conjecture holds for $p< \lambda n^{-1/2}$. We break this $\Omega(n^{-1/2})$-barrier by proving the conjecture for sparser random graphs $G(n,p)$, where $\lambda' n^{-3/5}\log n \leq p \leq \lambda n^{-1/2}$ with a large constant $\lambda'>0$.

2021-10-14 / 16:15 ~ 17:15

학과 세미나/콜로퀴엄 - 콜로퀴엄: Brain’s solutions to temporal credit assignment

by 이상완(KAIST 바이오및뇌공학과)

The temporal credit assignment, the problem of determining which actions in the past are responsible for the current outcome (long-term cause and effect), is difficult to solve because one needs to backpropagate the error signal through space and time. Despite its computational challenges, humans are very good at solving this problem. Our lab uses reinforcement learning theory and algorithms to explore the nature of computations underlying the brain’s ability to solve the temporal credit assignment. I will outline two-fold approaches to this issue: (1) training a computational model from human behavioral data without underfitting and overfitting (Brain → AI) and (2) using the trained model to manipulate the way the human brain solves the temporal credit assignment problem (AI → brain).

Events for the 취소된 행사 포함