Intensive lectures on quantum information theory

We have the following lectures via google meet.

Title: Quantum information theory
April 26th (Monday) 13:00 – 14:00
May 4th (Tuesday) 13:00 – 14:00
May 11th (Tuesday) 13:00 – 14:00

Speaker: Prof. Soojoon Lee (Kyung Hee University)
우선, 직관적으로 이해할 수 있는 고전정보이론의 기초를 설명하고, 그와 대응되는 양자정보이론의 기초를 설명한다. 이를 통해, 고전정보와 양자정보의 유사점과 차이점에 대해서 알아본다.

Seminar in April 2021

Time: 8th April (Thursday) 13:00 – 14:00
Speaker: Dr. Jinwook Jung (Seoul National Univertisy)
Place: #702, Natural Science Building, Hanyang University

Title : On the pressureless damped Euler-Riesz equations

In this talk, we analyze the pressureless damped Euler–Riesz equations posed in either the whole space or periodic domain. We construct the global-in-time existence and uniqueness of classical solutions for the system around a constant background state. We also establish large-time behaviors of classical solutions showing the solutions towards the equilibrium as time goes to infinity. In the whole space case, we first show the algebraic decay rate of solutions under additional assumptions on the initial data compared to the existence theory. We then refine the argument to have the exponential decay rate of convergence even in the whole space. In the case of the periodic domain, without any further regularity assumptions on the initial data, we provide the exponential convergence of solutions.

Online seminar in February 2021

We have the following seminar via google meet.


Title: Convergence of first-order consensus-based global optimization algorithms
Time: February 17th (Wednesday) 10:00 – 10:40
Speaker: Dr. Doheon Kim (KIAS)
Recently, consensus-based optimization (in short CBO) methods have been introduced as gradient-free optimization methods capable of tackling non-convex objective functions. Until recently, the convergence study for CBO methods was carried out only on their corresponding mean-field limits, Fokker-Planck equations, which do not imply the convergence of the CBO method per se. In this talk, we study convergence analysis for first-order CBO methods, without resorting to the corresponding mean-field models.



Title: A singular limit of the Chern-Simons-Higgs model
Time: February 17th (Wednesday) 10:45 – 11:25
Speaker: Dr. Bora Moon (Seoul National University)
In this talk, we consider the singular limit of the Cauchy problem for Chern-Simons-Higgs model that suggests a correspondence between the model of Chern-Simons-Higgs and Chern-Simons-Schrodinger. More precisely, we prove that when the velocity of light goes to infinity (the so-called ‘non-relativistic limit’), a class of time-dependent solutions of the modulated Chern-Simons-Higgs system converges to the corresponding solution of the Chern-Simons-Schrodinger system globally in time under the assumption of suitable initial data.

Online seminar in January 2021

We have the following seminar via google meet.


Title: Uniform-in-time continuum limit of the lattice Winfree model and emergent dynamics
Time: January 13th (Wednesday) 10:00 – 10:40
Speaker: Myeongju Kang (Seoul National University)
Abstract: We study a uniform-in-time continuum limit of the lattice Winfree model(LWM) and its asymptotic dynamics which depends on system functions such as natural frequency function and coupling strength function. The continuum Winfree model(CWM) is an integro-differential equation for the temporal evolution of Winfree phase field. The LWM describes synchronous behavior of weakly coupled Winfree oscillators on a lattice lying in a compact region. For bounded measurable initial phase field, we establish a global well-posedness of classical solutions to the CWM under suitable assumptions on coupling function, and we also show that a classical solution to the CWM can be obtained as a $L^1$-limit of a sequence of lattice solutions.



Title: Emergence of consensus on the Stiefel manifold
Time: January 13th (Wednesday) 10:45 – 11:25
Speaker: Dr. Dohyun Kim (Seoul National University)
Abstract: In this talk, we introduce first-order and second-order high-dimensional Kuramoto models on the Stiefel manifold which extend the previous consensus models on Riemannian manifolds including several matrix Lie groups. For the proposed models, sufficient frameworks leading to complete and practical consensus are provided in terms of the initial data and system parameters. On the other hand, we propose a consensus-based algorithm for nonconvex optimization on the Stiefel manifold. For a given objective (or target) function on the Stiefel manifold, we construct a stochastic interacting particle system for sample points which are expected to converge to a single point, which is close enough to a global minimizer.