# Online seminar in November 2020

We have the following seminar via google meet.

1.

Title: Introduction to Deep Q Learning and its application to finance
Time: November 23th (Monday) 09:30 – 10:10
Speaker: Prof. Chanho Min (Ajou University)
Abstract:
This seminar introduces the Deep Q Learning, one of the most popular methods of reinforcement learning and their application to finance problems. Reinforcement learning is a popular model of the learning problems through trial-and-error interactions in a certain given environment. This seminar will discuss the mathematical formulation of Deep Q learning and how each component plays a crucial role in agent learning. Finally it provides real world application in finance, and shows how reinforcement learning can outperform humans even with limited data.

2.

Title: Hamilton-Jacobi-Bellman equations for maximum entropy optimal control
Time: November 23th (Monday) 10:15 – 10:55
Speaker: Dr. Jeongho Kim (SNU)
Abstract:In this talk, we introduce an entropy-regularized optimal control problem for the deterministic control system. We derive dynamic programming principle and corresponding the Hamilton-Jacobi-Bellman (HJB) equation, which is regularized version of the HJB equation of the classical optimal control problem. After deriving the HJB equation, we provide several mathematical properties of it, including asymptotic convergence. We also provide an explicit example of control-affine problem, in which the optimal control is given as a normal distribution. Finally, we test the maximum entropy optimal control framework to several numerical examples, illustrating the benefit of the maximum entropy framework.

# Online seminar in August 2020

We have the following seminar via google meet.

1.
Title: 출근 지하철 혼잡도 분산을 위한 최적 수도권 지역 분할
Time: August 6th (Thursday) 09:30 – 10:10
Speaker: Dr. Wonse Kim (SNU)
Abstract:
출근 지하철 혼잡도 분산을 위한 최적 수도권 지역 분할본 연구는 수도권 전철 네트워크 데이터와 지하철 승객 승, 하차 빅데이터를 분석하여, 출퇴근 지하철 차내 혼잡도를 낮추기 위한 수도권 지역 최적 분할 방법을 제시한다. 구체적으로, (1) Dijkstra Algorithm 에 기반한 Dial Algorithm 을 사용하여 수도권 전철의 출근시간대 차내 혼잡도를 계산하고 (2) 지하철역 위치정보를 활용하여 출근시간 혼잡 구간을 지나는 승객의 지하철 최초 탑승 지역을 파악한다. (1), (2)의 결과를 바탕으로, 수도권 전철 출근시간 혼잡구간의 혼잡도를 최소화 시키는 수도권 지역 최적 분할을 찾기 위한 손실함수 (loss function)을 새롭게 정의하고, 이를 최적화 시킴으로서 최적 수도권 지역분할을 찾는다. 본 연구의 결과는 2차 코로나 대유행을 앞둔 현 시점에서, 정책 당국자들로 하여금 2부제 재택근무와 같은 사회적 거리두기 방법의 효과를 극대화 시킬 수 있는 구체적인 가이드 라인을 제시할 것으로 기대된다.

2.
Title: Thermodynamic Cucker-Smale ensemble on complete Riemannian manifolds
Time: August 6th (Thursday) 10:15 – 10:55
Speaker: Dr. Woojoo Shim (SNU)
Abstract:
We study emergent collective behaviors of a thermodynamic Cucker-Smale(TCS) ensemble on complete smooth Riemannian manifolds. For this, we extend the TCS model on the Euclidean space to a complete smooth Riemannian manifold by adopting the work for a CS ensemble, and provide a sufficient framework for velocity alignment and thermal equilibrium formulated in terms of a priori assumptions on network topology and the uniform continuity of relative velocities. As a concrete example, we also study emergent dynamics of the TCS model on the unit d-sphere and hyperbolic d-space by removing a uniform continuity assumption on the relative velocities in the proposed sufficient framework for a general setting. In particular, asymptotic dynamics of the proposed TCS model on the unit 2-sphere and hyperbolic plane exhibits a dichotomy, either convergence to zero velocities or approach toward a geodesic.

3.
Title: From the Lohe Tensor Model to the Lohe Hermitian Sphere Model and Emergent Dynamics
Time: August 6th (Thursday) 11:00 – 11:40
Speaker: Hansol Park (SNU)
Abstract:
We study emergent behaviors of the Lohe hermitian sphere (LHS) model which is an aggregation model on $\mathbb C^d$. The LHS model is a complex analogue of the Lohe sphere model on $\mathbb R^d$, and hermitian spheres are invariant sets for the LHS dynamics. For the derivation of the LHS model, we use a top-down approach, namely a reduction from a high-rank aggregation model, the Lohe tensor model. The Lohe tensor model is a first-order aggregation model on the space of tensors with the same rank and sizes, and it was first proposed by the authors in a recent work [J. Stat. Phys., 178 (2020), pp. 1268–1292]. In this work, we study how the LHS model appears as a special case of the Lohe tensor model, and for the proposed model, we provide a cross-ratio-like conserved quantity, a sufficient framework for the complete aggregation, and a uniform $\ell^p$-stability estimate with respect to initial data.

# Online seminar in May 2020

We have the following seminar via google meet.

1.
Title: Geometric formulation of the Wasserstein distance in the optimal transport problem
Time: May 21st (Thursday) 14:00 – 14:40
Speaker: Dr. Gihyun Lee (SNU)
Abstract:
In this survey talk, we introduce the relation between the spectral distance of noncommutative geometry and the notion of Wasserstein distance considered in the optimal transport problem. This relation was first observed by Rieffel (1999), and its proof was given by D’Andrea-Martinetti (2010).

2.
Title: Investigation of ‘Flash Crash” via Topological Data Analysis (TDA)
Time: May 21st (Thursday) 14:45 – 15:25
Speaker: Dr. Wonse Kim (SNU)
Abstract:
There is by now a quite extensive literature on applications of TDA. But there are only a few literatures on applications of TDA to financial data, including the recent result of Gidea-Katz(2018). Interestingly, Gidea-Katz (2018) showed that a stock market crash can be foreseen via TDA by utilizing daily US stock market indices data (e.g., S&P 500, DJIA, NASDAQ, and Russell 2000). However, the Flash Crash on 6 May 2010 showed that the market can be substantially destabilized in as little as about 30 min. Since the Flash Crash, analyses of market crash of the intraday-horizon has also become important parts of the study of market crash. In this talk, I will demonstrate that the TDA methodology based on Gidea-Katz (2018) can be used in forecasting short term market crash such as Flash Crash.

3.
Title: Model Predictive Control with Random Batch Methods for a guiding problem
Time: May 21st (Thursday) 15:30 – 16:10
Speaker: Dr. Dongnam Ko (University of Deusto)
Abstract:
We model, simulate and control the guiding problem for a herd of sheep under the action of shepherd dogs. The problem is formulated in the optimal control framework, which is an open-loop control strategy commonly used for the heat or wave equations. However, simulating a herd of sheep quickly becomes unfeasible from the large number of interactions. To overcome this, we use the Random Batch Method (RBM) for a computationally cheap approximation. Moreover, we follow Model Predictive Control (MPC) to ensure the convergence of the algorithm in a more concrete way, compared to the arguments of Stochastic Gradient Descent (SGD).

# PDE seminar in February 2020

Time: 10th February (Monday) 10:00 – 11:00
Speaker: Dr. Dongnam Ko (University of Deusto)
Place: #701, Natural Science Building, Hanyang University

Title : Dynamics and control for multi-agent networked systems

Abstract:
Starting form the analysis on parabolic equations, we study control properties of the consensus model. The existing techniques for PDE control problems allow us to derive explicit estimates on the controllability and control cost. Our approach shows that the chain or circular network systems have the same properties as the 1D heat equation while we may extend it to the multi-dimensional or fractional type heat equations.