ニュース＆イベント

Math-Fi seminar on 23 Jun.

2022.06.23 Thu up
  • Date: 23 Jun. (Thu.)
  • Place: W.W. 6th-floor, Colloquium Room and on the Web (Zoom)
  • Time: 16:30-18:00
  • Speaker: Kosuke Yamato (Kyoto University)
  • Title: A unifying approach to non-minimal quasi-stationary distributions for one-dimensional diffusions
  • Abstract:
In the present talk, we consider convergence to non-minimal quasi-stationary distributions for one-dimensional diffusions. I will explain a method of reducing the convergence to the tail behavior of the lifetime via a property which we call the first hitting uniqueness. We apply the results to Kummer diffusions with negative drifts and give a class of initial distributions converging to each non-minimal quasi-stationary distribution.
 

Math-Fi seminar on 16 Jun.

2022.06.14 Tue up
  • Date: 16 Jun. (Thu.)
  • Place: W.W. 6th-floor, Colloquium Room and on the Web (Zoom)
  • Time: 16:30-18:30

  • Speaker 1: Tomoyuki Ichiba (University of California, Santa Barbara)
  • Title: Stochastic Differential Games on Random Directed Trees
  • Abstract:
We consider stochastic differential games on a random directed tree with mean-field interactions, where the network of countably many players is formulated randomly in the beginning and each player in the network attempts to minimize the expected cost over a finite time horizon. Here, the cost function is determined by the random directed tree. Under the setup of the linear quadratic stochastic game with directed chain graph, we solve explicitly for an open-loop Nash equilibrium for the system, and we find that the dynamics under the equilibrium is an infinite-dimensional Gaussian process associated with a Catalan Markov chain. We extend it to the random directed tree structures and discuss convergence results.
 
  • Speaker 2: Noriyoshi Sakuma (Nagoya City University)
  • Title: Selfsimilar free additive processes and freely selfdecomposable distributions
  • Abstract:
In the paper by Fan(2006), he introduced the marginal selfsimilarity of non-commutative stochastic processes and proved the marginal distributions of selfsimilar processes with freely independent increments are freely selfdecomposable. In this talk, we, first, give a short introduction of free probability. Then we introduce a new definition of selfsimilarity via linear combinations of non-commutative stochastic processes and prove the converse of Fan’s result, to complete the relationship between selfsimilar free additive processes and freely selfdecomposable distributions. Furthermore, we construct stochastic integrals with respect to free additive processes for constructing the background driving free L{\’e}vy processes of freely selfdecomposable distributions. A relation in terms of their free cumulant transforms is also given and several examples are also discussed. This talk is based on a joint work arXiv:2202.11848 with Makoto Maejima.
 

立命館大学幾何学セミナー（2022年6月24日（金））

2022.06.13 Mon up
<<立命館大学幾何学セミナー>>

日時： 2022年6月24日（金） 18:00～19:00

タイトル： Jacobi構造とRiemann計量の整合性

講演者： 中村 友哉 （工学院大学）

アブストラクト：
こちらのPDFファイルをご覧ください．
開催方法：Zoom配信での開催です．

問い合わせ先：立命館大学理工学部数理科学科 多羅間 大輔

Math-Fi seminar on 9 Jun.

2022.06.08 Wed up
  • Date: 9 Jun. (Thu.)
  • Place: On the Web
  • Time: 16:30-18:00
  • Speaker: Toshiyuki Nakayama (MUFG, Bank, Ltd.)
  • Title: Distance between closed sets and the solutions to SPDEs
  • Abstract: 
The goal of this talk is to clarify when the solutions to stochastic partial differential equations stay close to a given subset of the state space for starting points which are close as well. This includes results for deterministic partial differential equations. As an example, we will consider the situation where the subset is a finite dimensional submanifold with boundary. We also discuss applications to mathematical finance, namely the modeling of the evolution of interest rate curves. This talk is based on a co-authored paper with Stefan Tappe “Distance between closed sets and the solutions to stochastic partial differential equations”, arXiv:2205.00279v1, 30 Apr 2022 (https://arxiv.org/abs/2205.00279).

Math-Fi seminar on 2 Jun.

2022.06.01 Wed up
  • Date: 2 Jun. (Thu.)
  • Place: W.W. 6th-floor, Colloquium Room & On the Web
  • Time: 16:30-18:00
  • Speaker: Kiyoiki Hoshino (Osaka Metropolitan University)
  • Title: Extraction of random functions from the stochastic Fourier coefficients by the process with quadratic variation
  • Abstract: 
Let V_t be a real stochastic process with quadratic variation. Our concern is whether and how a noncausal type stochastic differential dX_t:=a(t) dV_t+b(t) dt is determined from its stochastic Fourier coefficients (SFCs for short) with respect to a CONS B of L^2[0,L]. In this talk, we use the notion of stochastic derivative to show the following: (i) when B is the Haar system, any stochastic differential dX is determined from its SFCs, (ii) when B is composed of functions of bounded variation, dX is determined from its SFCs under a certain continuity, where dX is defined by an arbitrary stochastic integral which is the inverse of the stochastic derivative.

立命館大学幾何学セミナー（2022年6月13日（月））

2022.05.31 Tue up
日時：2022年6月13日（月） 16:30–18:00
タイトル： 有限集合上の最適輸送問題の凸緩和について
講演者： 高津 飛鳥氏 （都立大学）
アブストラクト：
有限集合上の最適輸送問題は線形計画問題の一種であり、具体的には有界な閉凸多面体上で線形関数を最小化する変分問題である。線形計画問題では最小化因子が閉凸多面体の境界に現れ、このことは応用上好ましくない。そこで線形関数に凸関数を加え、緩和する方法がある。実際、最適輸送問題は、Kullback–Leibler divergence による緩和が成功を収めている。本講演では、Kullback–Leibler divergence を含むクラスである Bregman divergenceによる緩和を考え、その数理構造について説明をする。
 
開催方法： 
Zoomによる配信です．下記のURLより6月12日（日）までにご登録ください．
ご登録いただいた方に当日昼頃にZoomミーティングの情報をお送りします．
 
また、2022年6月14日(火)10:00–12:00に同Zoomミーティングにて高津飛鳥氏にWasserstein幾何の入門セミナーを行っていただきます．ぜひご参加ください．
 
問い合わせ先：野澤 啓（立命館大学理工学部数理科学科）
　　　　　　

立命館大学幾何学セミナー（2022年6月3日（金））

2022.05.23 Mon up
<<立命館大学幾何学セミナー>>

日時： 2022年6月3日（金） 18:00～19:00

タイトル： Conformal differential symmetry breaking operators for (O(n+1,1), O(n,1)) for differential forms

講演者： 久保利久 （龍谷大学）

アブストラクト：
こちらのPDFファイルをご覧ください．
開催方法：Zoom配信での開催です．

問い合わせ先：立命館大学理工学部数理科学科 多羅間 大輔

立命館大学数理工学セミナー（2022年5月26日（木））

2022.05.19 Thu up
<<立命館大学幾何学セミナー>>

日時：2022年5月26日（木） 16:30～18:00

タイトル：On the role and the design of loss functions in machine learning

講演者： Nguyen Tien Zung (Institut de Mathématiques de Toulouse)

アブストラクト：
Most people who are doing machine learning use some “standard” loss functions, such as the cross entropy and the mean square loss. However, for the same machine learning problem, one may use many different loss functions, and some of them may turn out to work much better than the “standard” ones. In this talk I want to discuss some simple general ideas about the loss functions, how do they affect the machine learning programs, and how to design them. I’ll try to use some examples from what we’re doing at Torus AI (https://torus.ai) for illustration.

開催方法：Zoom配信での開催です．

問い合わせ先：立命館大学理工学部数理科学科 多羅間 大輔

数理科学科談話会 （2022/5/19）

2022.05.16 Mon up
日時：5月19日(木) 16:30-17:30
開催方法：対面とオンラインのハイブリッド開催
場所：ウエストウイング 6階 談話会室（対面）および Zoom
講師：福泉麗華（東北大学）
講演題目：A nonlinear Kronig-Penney model
講演概要：
We consider the 1D nonlinear Schroedinger equation with focusing nonlinearities concentrated at some points.
In the linear model, there are many studies on the spectrum properties of the Schrodinger operator depending on the position of those points (quasi-periodic, random, etc).
In this talk we address the asymptotic behavior of the global solution for the nonlinear model, and its applications. The main argument we use is due to Kenig-Merle, but it is required to make use of an appropriate function space (not Strichartz space) according to the smoothing properties of the associated integral equation.


問い合せ先：立命館大学理工学部数理科学科　平良晃一　
 
オンライン参加の方は平良 ktaira@fc.ritsumei.ac.jp までご連絡いただけたら，談話会当日にzoomのアドレスをお送りいたします．

Math-Fi seminar on 28 Apr.

2022.04.27 Wed up
  • Date: 28 Apr. (Thu.)
  • Place: On the Web
  • Time: 17:00-18:30
  • Speaker:  Arturo Kohatsu-Higa (Ritsumeikan University)
  • Title:   Simulation of Reflected Brownian motion on two dimensional wedges
  • Abstract: 
We study Brownian motion in two dimensions, which is reflected, stopped or killed in a wedge represented as the intersection of two half-spaces. First, we provide explicit density formulas, hinted by the method of images. These explicit expressions rely on infinite oscillating sums of Bessel functions and may demand computationally costly procedures. We propose suitable recursive algorithms for the simulation of the laws of reflected and stopped Brownian motion which are based on generalizations of the reflection principle in two dimensions. We study and give bounds for the complexity of the proposed algorithms. (Joint with P. Bras.)

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