セミナー

Math-Fi seminar on 24 Apr.

2025.04.22 Tue up
  • Date: 24 Apr. (Thu.) 
  • Place: West Wing, 6th floor, Colloquium Room and on the Web (zoom)
  • Time: 13:10–19:00


  • Speaker 1: Dima Ivanenko (Taras Shevchenko National University of Kyiv)
  • Time: 13:10–14:10
  • Title: ON APPROXIMATION OF SOME LÉVY PROCESSES <4>
  • Abstract:
A Levy process X(t) has the structure X(t) = at + σW(t) + J(t) where W(t) is standard
Brownian motion (BM) and J(t) an independent pure jump process. This class of processes
has been used in numerous application areas, of which we in particular mention nance
and queueing. Calculations for a Levy process are, however, in general more dicult than
for BM, and an abundance of expressions that are explicit for BM are not so even in the
most popular parametric Levy models. Simulation of X(t) is therefore one of the main
computational tools.
A Levy process has countably many jumps on any interval [0, T] and nitely many jumps
of size bigger than some xed ε > 0. In order to simulate Z, we need to take nitely many
jumps of Z, which gives an adequate description of Z. Apart from some particular cases,
e.g. Brownian motion, Gamma process, α-stable process, simulation of the Levy process
with a given triplet is not an easy task.
Usually, the distribution function of a Levy process is unknown or has a rather compli-
cated form, which makes the simulation rather perplex. For the methods of generating
innitely divisible random variables (r.v.’s) and Levy processes (e.g. methods of Khinchin,
Fergusson-Klass, Bondesson, LePage, Rosinski) we refer to Rosinski (2001) and propose
our own method. We also would like to mention that the Damien-Laud-Smith algorithm
from Damien, Laud, and Smith (1995) gives a way to simulate an (approximation of)
an arbitrary onedimensional innitely divisible r.v., which allows us to simulate a Levy
process. On the other hand, it was observed by Bondesson (1982) and later by Asmussen
and Rosinski (2001), that under some conditions small jumps can be substituted by an
(arithmetic) Brownian motion.
The series of seminars includes a general theory of Levy processes, an overview of known
methods for modeling such processes, and a comparison of these methods with our own.
 
 
  • Speaker 2: Oleksii Kulik　 (Wroclaw University of Science and Technology)
  • Time: 14:20-15:20
  • Title: A moments respecting explicit simulation scheme for L´evy driven SDEs, II: Simulation methods for SDEs with super-linearly dissipative drifts.
  • Abstract:
This is the first of two lectures devoted to the effect of tails/moments transformation by a dissipative drift for  solutions of SDEs driven by heavy-tailed noises.  In the first lecture we will discuss the history of the subject, illustrate how does this effect reveals itself in various settings, and provide a complete description of the effect in a general semi-martingale setting.
 
 
  • Speaker 3: Maria Elvira Mancino (University of Florence)
  • Time: 16:50-17:50
  • Title: Asymptotic Efficiency of the Fourier Spot Volatility Estimator with Noisy Data and an Application to the estimation of spot Beta and higher-order spot covariances.
  • Abstract:
We study the efficiency and robustness of the Fourier spot volatility estimator when high-frequency prices are contaminated by microstructure noise. Firstly, we show that the estimator is consistent and asymptotically efficient in  the presence of additive noise, establishing a Central Limit Theorem with the optimal rate of convergence 1/8. Feasible CLTs with the optimal convergence rate are also obtained, by proving the consistency of the Fourier estimators of the spot volatility of volatility and the quarticity in the presence of noise. The multivariate case is also studied.
Finally, we exploit this methodology to introduce a consistent estimator of the spot asset beta. We provide simulation results that suggest that our spot beta estimator has a robust finite-sample performance in the presence of realistic market features such as rough volatility, inhomogeneous asynchronous sampling, autocorrelated and price-dependent noise and price rounding. Additionally, we conduct an empirical study with tick-by-tick prices in which we reconstruct intraday spot beta paths.
 
 
  • Speaker 4: Shigeki Matsutani（Kanazawa University）
  • Time: 18:00-19:00
  • Title: 量子ウォークと光学
  • Abstract:
本講演では，一次元量子ウォークと光学におけるS行列理論との関連を示す．
光学における転送行列理論は，一次元のHermholz方程式を離散化することで得られる．
この転送行列の系を入射光と出射光で再定式化すると，S行列（散乱行列）が得られる．
さらに，入射光から出射光への静的な変換を，因果関係あるいは一種の離散的時間発展として動的な波動系を考えると，1次元量子ウォークと一致する．
産業界における光学現象には，波動系の根幹に関わる基本的な問題が非常に多い．
我々は，この量子ウォークを光学系として解釈することより，波動力学の本質と基礎が得られると考えている．
例えば，ファインマンの著書「光と物質のふしぎな理論」の描像に従い，量子ウォークはフェルマーの原理を満たし，波面は光速で弾道的に進むと見ることができる．
さらに，量子ウォークの振る舞いは，ド・ブロイ・ボーム理論のパイロット波を想起する結果を得る．

指数理論セミナー

2025.04.17 Thu up
日時: 4月10日から6月26日まで毎週木曜日 )
第1部10:45 – 11:30
第2部10:35 – 12:20 (全22部)
場所: ウェストウィング7階　数学第4研究室
講演者: Jesus Alvarez Lopez氏（サンティアゴ・デ・コンポステラ大学）
タイトル: Towards the Atiyah-Singer index theorem
アブストラクト: 指数理論を理解するために必要な知識である特性類や微分作用素の理論を基礎から解説する．


Math-Fi seminar on 17 Apr.

2025.04.15 Tue up
  • Date: 17 Apr. (Thu.) 
  • Place: West Wing, 6th floor, Colloquium Room and on the Web (zoom)
  • Time: 16:50–19:00 


  • Speaker 1: Dima Ivanenko (Taras Shevchenko National University of Kyiv)
  • Time: 16:50–17:50 
  • Title: ON APPROXIMATION OF SOME LÉVY PROCESSES 3
  • Abstract:
A Levy process X(t) has the structure X(t) = at + σW(t) + J(t) where W(t) is standard
Brownian motion (BM) and J(t) an independent pure jump process. This class of processes
has been used in numerous application areas, of which we in particular mention nance
and queueing. Calculations for a Levy process are, however, in general more dicult than
for BM, and an abundance of expressions that are explicit for BM are not so even in the
most popular parametric Levy models. Simulation of X(t) is therefore one of the main
computational tools.
A Levy process has countably many jumps on any interval [0, T] and nitely many jumps
of size bigger than some xed ε > 0. In order to simulate Z, we need to take nitely many
jumps of Z, which gives an adequate description of Z. Apart from some particular cases,
e.g. Brownian motion, Gamma process, α-stable process, simulation of the Levy process
with a given triplet is not an easy task.
Usually, the distribution function of a Levy process is unknown or has a rather compli-
cated form, which makes the simulation rather perplex. For the methods of generating
innitely divisible random variables (r.v.’s) and Levy processes (e.g. methods of Khinchin,
Fergusson-Klass, Bondesson, LePage, Rosinski) we refer to Rosinski (2001) and propose
our own method. We also would like to mention that the Damien-Laud-Smith algorithm
from Damien, Laud, and Smith (1995) gives a way to simulate an (approximation of)
an arbitrary onedimensional innitely divisible r.v., which allows us to simulate a Levy
process. On the other hand, it was observed by Bondesson (1982) and later by Asmussen
and Rosinski (2001), that under some conditions small jumps can be substituted by an
(arithmetic) Brownian motion.
The series of seminars includes a general theory of Levy processes, an overview of known
methods for modeling such processes, and a comparison of these methods with our own.
 
  • Speaker 2: Oleksii Kulik　 (Wroclaw University of Science and Technology)
  • Time: 18:00–19:00 
  • Title: A moments respecting explicit simulation scheme for L\’evy driven SDEs, I: Transformation of a heavy-tailed L\’evy noise by a dissipative drift
  • Abstract:
This is the first of two lectures devoted to the effect of tails/moments transformation by a dissipative drift for  solutions of SDEs driven by heavy-tailed noises.  In the first lecture we will discuss the history of the subject, illustrate how does this effect reveals itself in various settings, and provide a complete description of the effect in a general semi-martingale setting.

Math-Fi seminar on 10 Apr. (Co-organized as a Quantum Walk Seminar)

2025.04.08 Tue up
  • Date: 10 Apr. (Thu.) 
  • Place: West Wing, 6th floor, Colloquium Room and on the Web (zoom)
  • Time: 16:50–17:50 
  • Speaker 1: Dima Ivanenko (Taras Shevchenko National University of Kyiv)
  • Title: ON APPROXIMATION OF SOME LÉVY PROCESSES 2
  • Abstract:
A Levy process X(t) has the structure X(t) = at + σW(t) + J(t) where W(t) is standard
Brownian motion (BM) and J(t) an independent pure jump process. This class of processes
has been used in numerous application areas, of which we in particular mention nance
and queueing. Calculations for a Levy process are, however, in general more dicult than
for BM, and an abundance of expressions that are explicit for BM are not so even in the
most popular parametric Levy models. Simulation of X(t) is therefore one of the main
computational tools.
A Levy process has countably many jumps on any interval [0, T] and nitely many jumps
of size bigger than some xed ε > 0. In order to simulate Z, we need to take nitely many
jumps of Z, which gives an adequate description of Z. Apart from some particular cases,
e.g. Brownian motion, Gamma process, α-stable process, simulation of the Levy process
with a given triplet is not an easy task.
Usually, the distribution function of a Levy process is unknown or has a rather compli-
cated form, which makes the simulation rather perplex. For the methods of generating
innitely divisible random variables (r.v.’s) and Levy processes (e.g. methods of Khinchin,
Fergusson-Klass, Bondesson, LePage, Rosinski) we refer to Rosinski (2001) and propose
our own method. We also would like to mention that the Damien-Laud-Smith algorithm
from Damien, Laud, and Smith (1995) gives a way to simulate an (approximation of)
an arbitrary onedimensional innitely divisible r.v., which allows us to simulate a Levy
process. On the other hand, it was observed by Bondesson (1982) and later by Asmussen
and Rosinski (2001), that under some conditions small jumps can be substituted by an
(arithmetic) Brownian motion.
The series of seminars includes a general theory of Levy processes, an overview of known
methods for modeling such processes, and a comparison of these methods with our own.
 
  • Speaker 2: Sohei Tateno (Nagoya University)
  • Time: 18:00–19:00 
  • Title: Iwasawa theory for discrete-time quantum walks in graphs
  • Abstract:
Transition matrices of discrete-time quantum walks in graphs are closely related to Ihara zeta functions of weighted graphs. For example, the celebrated Konno—Sato theorem has an application to calculate the eigenvalues of transition matrices. In this talk, by applying the methods of Iwasawa theory for graphs, we establish an asymptotic formula for the values of the characteristic polynomials of the transition matrices in a $\mathbb{Z}_p^d$-tower of graphs when an element of $\overline{\mathbb{Q}}_p$ is substituted to the polynomials. This is a joint work with Taiga Adachi and Kosuke Mizuno. 

Math-Fi seminar on 4 Apr.

2025.04.04 Fri up
  • Date: 4 Apr. (Fri.) 
     
  • Place: West Wing, 6th floor, Colloquium Room and on the Web (zoom)
     
  • Time: 16:30–18:00
     
  • Speaker:  Dima Ivanenko (Taras Shevchenko National University of Kyiv)
     
  • Title: ON APPROXIMATION OF SOME LÉVY PROCESSES
     
  • Abstract:
A Levy process X(t) has the structure X(t) = at + σW(t) + J(t) where W(t) is standard
Brownian motion (BM) and J(t) an independent pure jump process. This class of processes
has been used in numerous application areas, of which we in particular mention nance
and queueing. Calculations for a Levy process are, however, in general more dicult than
for BM, and an abundance of expressions that are explicit for BM are not so even in the
most popular parametric Levy models. Simulation of X(t) is therefore one of the main
computational tools.
A Levy process has countably many jumps on any interval [0, T] and nitely many jumps
of size bigger than some xed ε > 0. In order to simulate Z, we need to take nitely many
jumps of Z, which gives an adequate description of Z. Apart from some particular cases,
e.g. Brownian motion, Gamma process, α-stable process, simulation of the Levy process
with a given triplet is not an easy task.
Usually, the distribution function of a Levy process is unknown or has a rather compli-
cated form, which makes the simulation rather perplex. For the methods of generating
innitely divisible random variables (r.v.’s) and Levy processes (e.g. methods of Khinchin,
Fergusson-Klass, Bondesson, LePage, Rosinski) we refer to Rosinski (2001) and propose
our own method. We also would like to mention that the Damien-Laud-Smith algorithm
from Damien, Laud, and Smith (1995) gives a way to simulate an (approximation of)
an arbitrary onedimensional innitely divisible r.v., which allows us to simulate a Levy
process. On the other hand, it was observed by Bondesson (1982) and later by Asmussen
and Rosinski (2001), that under some conditions small jumps can be substituted by an
(arithmetic) Brownian motion.
The series of seminars includes a general theory of Levy processes, an overview of known
methods for modeling such processes, and a comparison of these methods with our own.

立命館大学幾何学セミナー（2025年3月28日（金））

2025.03.23 Sun up
日時：2025年3月28日（金）16:30 — 17:30
会場：立命館大学びわこ・くさつキャンパス ウェストウィング6階談話会室 および Zoomミーティング
講演者：Gael Meigniez氏 （エクス・マルセイユ大学）
タイトル：Vanishing cycles in foliations and laminations
アブストラクト：The classical Novikov theorem admits several generalizations to codimension-one foliations and laminations on manifolds of arbitrary dimensions. I will also give applications to transversely real-analytic foliations.

開催方法：
立命館大学びわこ・くさつキャンパス ウェストウィング6階談話会室での講演をZoomミーティングで配信する予定です．オンライン参加のためには以下のフォームよりご登録ください．
https://ritsumei-ac-jp.zoom.us/meeting/register/J5t9P-hTQLW5rzsPeJm0rg

Meigniez氏による葉層構造入門セミナー

2025.03.01 Sat up
Meigniez氏は葉層構造という幾何構造のトポロジーの研究において大きな成果をあげられている研究者です．
以下の通り，学生向けの入門セミナーを行いますので，よろしければぜひご参加ください．

講演者：Gael Meigniez氏（エクス・マルセイユ大学）
タイトル：Introduction to the h-principle for foliations
会場：立命館大学BKCウェストウィング6階談話会室　および　Zoomミーティング
日時：
3月4日　16:00-17:00
3月11日　15:00-16:00
3月12日　15:00-16:00

ZoomミーティングURL（3日間共通，登録不要）：
https://ritsumei-ac-jp.zoom.us/j/97046113160?pwd=VVnb2NnLE5pxUbHL2Gjbx35dcvp6pW.1

Math-Fi seminar on 30 Jan.

2025.01.29 Wed up
  • Date: 30 Jan. (Thu.) 
  • Place: West Wing, 6th floor, Colloquium Room and on the Web (zoom)
  • Time: 16:30–18:30
  • Speaker: 大坪 立サミュエル (滋賀県工業技術総合センター)
  • Title: 動的システムに対する仮説検定の為の制御則に関する検討
  • Abstract: 
現在,工業製品の検査業務では、人材不足や精神的・肉体的な負担の大きさが課題となっ
ており,その解決策として自動化が急務である.モーターや油圧ピストンなどの検査では,
製品に入力を与え,その出力を基に正常か異常かを判断する手法がとられている.このよう
な検査では,外乱やノイズに対するロバスト性を確保しつつ,検査対象や装置への負荷を最
小限に抑え,効率的に必要な情報を取得できる制御則の構築が求められる.
本発表では,1 次元動的線形システムを特徴づけるパラメータに関する仮説検定問題を検
討する。不規則挙動をパワースペクトル密度によって特徴づけられる連続関数空間上の確
率変数としてモデル化する.また,不規則挙動を与えられた場合の線形システムの挙動を議
論する.不規則挙動をオルンシュタイン=ウーレンベック過程として扱った場合との比較
も行う.これらの議論を基に,本問題に対する制御則の設計について検討する.
 

Math-Fi seminar on 23 Jan.

2025.01.22 Wed up
  • Date : 23 Jan. (Thu.) 
  • Place: West Wing, 6th floor, Colloquium Room and on the Web (zoom)
  • Time : 16:30 – 18:45 
  • Speaker 1: Ryoji Takano (Osaka University) 16:30 –17:30
  • Title:On Some new integration by parts formula for finance and their Monte Carlo simulation
  • Abstract:
A rough volatility model is a stochastic volatility model for an asset price process with volatility being rough, meaning that the H\”{o}lder regularity of the volatility path is less than half. In this talk, we will focus on the asymptotic behavior of the implied volatility for the short maturity and show that the short-time large deviation principle for rough volatility models characterize the asymptotic behavior of the implied volatility.
 
 
  • Speaker 2:Yushi Hamaguchi (Kyoto University) 17:45 –18:45
  • Title: A generalized coupling approach for the weak approximation of stochastic functional differential equations
  • Abstract:
In this talk, we study functional type weak approximation of weak solutions of stochastic functional differential equations by means of the Euler–Maruyama scheme. Under mild assumptions on the coefficients, we provide a quantitative error estimate for the weak approximation in terms of the Lévy–Prokhorov metric of probability laws on the path space. The weak error estimate obtained in this paper is sharp in the topological and quantitative senses in some special cases. We apply our main result to ten concrete examples appearing in a wide range of science and obtain a weak error estimate for each model. The proof of the main result is based on the so-called generalized coupling of probability measures. This talk is based on a joint work with Dai Taguchi (Kansai University). The preprint is available at arXiv:2412.18523.

立命館大学幾何学セミナー(2025年1月27日（月）)

2025.01.15 Wed up
日時：2025年1月27日（月）16:30 — 17:30
会場：立命館大学びわこ・くさつキャンパス ウェストウィング6階談話会室 および Zoomミーティング
講演者：兒玉 悠弥氏 （鹿児島大学）
タイトル：Finiteness property of the n-adic Lodha–Moore group and its applications
アブストラクト：群が左不変な有限加法的測度をもつとき、その群は従順であるといいます。従順群の典型的な例は有限群や可換群で、非従順群の典型的な例は階数２以上の自由群です。群の従順性はその部分群に遺伝するので、自由群を部分群にもつ群は全て非従順群です。ところが、その逆は一般に成り立ちません。本講演では、「自由群を部分群にもたない非従順群で、さらにある主の有限性ももつ群がたくさんある」ということと、この事実から得られた応用についてお話したいと思います。


開催方法：
立命館大学びわこ・くさつキャンパス ウェストウィング6階談話会室での講演をZoomミーティングで配信する予定です．オンライン参加のためには以下のフォームよりご登録ください．
<a href=”https://ritsumei-ac-jp.zoom.us/meeting/register/pvX5pMkaRiOBXn6btJpC6Q”>https://ritsumei-ac-jp.zoom.us/meeting/register/pvX5pMkaRiOBXn6btJpC6Q<a/>

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