News&Events

Math-Fi seminar on 28 May

2020.05.28 Thu up
Date: 28 May (Thu.)
Place: On the Web
Time: 16:30-18:00
Speaker: Takafumi Amaba (Fukuoka University)
Title: Bayesian CNNとTsirelson-Vershikによる黒色雑音の構成について
 

Math-Fi seminar on 7 May

2020.05.07 Thu up
  • Date: 7 May (Thu.)
  • Place: On the Web
  • Time: 16:30-18:00
  • Speaker: Takuya Nakagawa (Ritsumeikan University)
  • Title: On a Monte Carlo scheme for a stochasticquantity of SPDEs with discontinuous initial conditions
  • Abstract:
The aim of this seminar is to study the simulation of an expectation of a stochastic quantity $\e[f(u(t,x))]$ for a solution of stochastic partial differential equation driven by multiplicative noise with a non-smooth coefficients and a boundary condition: $Lu(t,x)=h(t,x) \dot{W}(t,x)$.
We first define a Monte Carlo scheme $P_{t}^{(N,M,L)}f(x)$ for $P_{t}f(x):=\e[f(u(t,x))]$, where $f$ is a bounded measurable function $f$ and $u(t,x)$ is a solution of stochastic partial differential equation given by Duhamel’s formula, and then we prove the convergence of the Monte Carlo scheme $P_{t}^{(N,M,L)}f(x)$ to $P_{t}f(x)$ and  the rate of weak error.
In addition, we introduce results of numerical experiments about the convergence error and the Central limit theorem for the scheme.

Math-Fi seminar on 23 Apr.

2020.04.23 Thu up
  • Date:  23 Apr. (Thu.)
  • Place: On the Web
  • Time: 16:30-18:00
  • Speaker: Dai Taguchi (Okayama University)
  • Title: Multi-dimensional Avikainen’s estimates
  • Abstract:
Avikainen provided a sharp upper bound of the expectation of |f(X)-f(Y)|^{q} by the expectation of |X-Y|^{p}, for any one-dimensional random variables X with bounded density and Y, and function of bounded variation f. In this talk, we consider multi-dimensional analogues of this estimate for any function of bounded variation in R^{d}, Orlicz–Sobolev spaces, Sobolev spaces with variable exponents or fractional Sobolev spaces.

We apply main statements to the numerical analysis on irregular functional of a solution to stochastic differential equations based on the Euler–Maruyama scheme and the multilevel Monte Carlo method, and L^{2}-time regularity of decoupled forward–backward stochastic differential equations with irregular terminal conditions.

This is joint work with Akihiro Tanaka (Osaka university) and Tomooki Yuasa (Ritsumeikan University).

Math-Fi seminar on 9 Apr.

2020.04.09 Thu up
  • Date: 9 Apr. (Thu.)
  • Place: On the Web
  • Time: 16:30-18:00
  • Speaker: Pierre Bras (École normale supérieure Paris)
  • Title: Acceleration of stochastic optimization algorithms
  • abstract: 
I will introduce stochastic algorithms to solve optimization problems, arising in machine learning or mathematical finance. Then, starting with the basic stochastic gradient algorithm, we will see how one can modify it so that to accelerate the convergence towards the optimal solution.
 

Math-Fi seminar on 26 Mar.

2020.04.09 Thu up
  • Date: 26 Mar. (Thu.)
  • Place: On the Web
  • Time: 16:30-18:00
  • Speaker: Shin Harase (Ritsumeikan University)
  • Title: マルコフ連鎖モンテカルロ（MCMC）法の準モンテカルロ法化

Math-Fi seminar on 27 Feb.

2020.02.07 Fri up
  • Date: 27 Feb. (Thu.)
  • Place: W.W. 6th-floor, Colloquium Room
  • Time: 16:30-18:00
  • Speaker: Pierre Bras (École normale supérieure Paris)
  • Title: Bayesian inference and Metropolis-Hastings algorithms (provisional title)
  • Abstract:
​Markov chains Monte Carlo (MCMC) methods are simulation methods for sampling from a probability distribution from which direct sampling is difficult, and are particulary used in bayesian learning. The Metropolis-Hastings algorithm is one of the most popular. I will present the algorithm, then prove convergence results, and present the adaptation of the algorithm to stochastic optimization problems. Please come and join us.
 

Math-Fi seminar on 13 Feb.

2020.02.07 Fri up
  • Date: 13 Feb. (Thu.)
  • Place: W.W. 6th-floor, Colloquium Room
  • Time: 16:30-18:00
  • Speaker: Pierre Bras (École normale supérieure Paris)
  • Title: Stochastic optimization and neural networks
  • Abstract: 
Stochastic algorithms aim to solve optimization problems by randomly exploring the state space. They appear in machine learning and in financial mathematics, and are the main tool used for calibrating neural networks. I will demonstrate some convergence properties, and present the gradient descent in the framework of neural networks.
 

Math-Fi seminar on 17 Jan.

2020.01.14 Tue up
  • Date: 17 Jan. (Fri.)
  • Place: W.W. 6th-floor, Colloquium Room
  • Time: 16:30-18:40


  • First Speaker: Yushi Hamaguchi (Kyoto University)
  • Time: 16:30-17:30
  • Title: Time-inconsistent consumption-investment problems in incomplete markets
 
  • Second Speaker: Yuki Ueda (Hokkaido University) 
  • Time: 17:40-18:40
  • Title: Introduction to free probability theory and infinitely divisible distributions

Math-Fi seminar on 9 Jan.

2020.01.07 Tue up
  • Date: 9 Jan. (Thu.)
  • Place: W.W. 6th-floor, Colloquium Room
  • Time: 16:00-19:00


  • First Speaker: Katsushi Nakajima (Ritsumeikan Asia Pacific University)
  • Time: 16:00-17:30
  • Title: TBA

  • Second Speaker: Koya Sakakibara (Kyoto University)
  • Time: 17:30-19:00
  • Title: Numerical analysis of interface problem
  • Abstract:
​ The interface appears in several problems, such as fluid dynamics between two different liquids. To study its evolution and dynamics forms the basis of the research in natural science. Although there are several mathematical studies for interfacial phenomena, they are, in general, so difficult, and numerical study becomes an essential tool in this field.
 In this talk, I will talk about the numerical analysis of interface problem, and especially consider two issues: The Hele-Shaw problem and grain boundary. The Hele-Shaw problem describes the motion of viscous fluid in a quasi-two-dimensional space, which started from a short paper by Henry Selby Hele-Shaw (1854–1941). It is now recognized as a basic mathematical model to study the fingering phenomena (also known as the Saffman–Taylor instability), and several researchers have studied this problem; however, there are still several open questions. A problem on the grain boundary appears in the field of material science. A grain boundary is an interface between two grains, or crystallites, in a polycrystalline material. It is the two-dimensional defect in the crystal structure. The study of grain boundaries and their effects on the mechanical, electrical, and other properties of materials forms an essential topic in material science. My study aims to understand the mechanism of grain boundaries from mathematical and numerical points of view.
 In the first half of this talk, I will explain this problem and construct some efficient numerical scheme based on the method of fundamental solutions and the asymptotic uniform distribution method. I will also briefly survey the geometric numerical integration, which aims to construct a numerical scheme which inherits properties of the original problem in some discrete sense. In the second half of this talk, I will move on to the problem on grain boundaries and consider manifold-valued total variation flows. I will introduce spatially discretized total variation flow and construct a numerical scheme using the exponential map of the manifold. I will also present an energy dissipation property and convergence result.

Ritsumeikan University Geometry Seminar (16/December/2019)

2019.12.10 Tue up
<<Ritsumeikan University Geometry Seminar>>

Date: 16/December/2019, Monday, 16:30-18:00

Title: Semitoric systems in geometry and dynamics

Speaker: Sonja Hohloch (University of Antwerp)

Abstract: PDF-file

Room: Ritsumeikan University, Biwako-Kusatsu Campus, Westwing, 6th floor, Colloquium Room

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