<<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
セミナー
立命館大学幾何学セミナー（2022年6月24日（金））
2022.06.13 Mon up
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
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>>
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.
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
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.)
Math-Fi seminar on 21 Apr.
2022.04.20 Wed up
- Date: 21 Apr. (Thu.)
- Place: W.W. 6th-floor, Colloquium Room and on the Web (Zoom)
- Time: 17:00-18:00
- Speaker: Jiro Akahori (Ritsumeikan University)
- Title: Variational approach to optimal stopping problems revisited
- Abstract:
After reviewing besoussan-lions’s variational approach, I will discuss its applications to numerical problems; discretization error, deep solver, and so on. The talk will be in English.
Math-Fi seminar on 14 Apr.
2022.04.14 Thu up
- Date: 14 Apr. (Thu.)
- Place: On the Web
- Time: 17:00-18:30
- Speaker: Umut Cetin (London School of Economics)
- Title: Speeding up the Euler scheme for killed diffusions
- Abstract:
Let X be a linear diffusion taking values in (l,r) and consider the standard Euler discretisation to compute the fair price of a Barrier option written on X that becomes worthless if X hits one of the barriers before the maturity date T. It is well-known since Gobet’s work that the presence of killing introduces a loss of accuracy and reduces the weak convergence rate to N^{-1/2} with N being the number of discretisatons. We introduce a drift-implicit Euler method to bring the convergence rate back to 1/N, i.e. the optimal rate in the absence of killing, using the theory of recurrent transformations. Although the current setup assumes a one-dimensional setting, multidimensional extension is within reach as soon as a systematic treatment of recurrent transformations is available in higher dimensions.
Math-Fi seminar on 7 Apr.
2022.04.11 Mon up
- Date: 7 Apr. (Thu.)
- Place: On the Web
- Time: 16:30-18:00
- Speaker: Andrey Pilipenko (Ukraine National Academy of Sciences)
- Title: Limit behavior of perturbed random walks
- Abstract:
A particle moves randomly over the integer points of the real line. Jumps of the particle outside the membrane (a fixed “locally perturbating set”) are i.i.d., have zero mean and finite variance, whereas jumps of the particle from the membrane have other distributions with finite means which may be different for different points of the membrane; furthermore, these jumps are mutually independent and independent of the jumps outside the membrane. We prove that the weak scaling limit of the particle position is a skew Brownian motion.
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