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ニュース＆イベント

立命館大学数理工学セミナー（2022年12月15日（木））

2022.12.02 Fri up

<立命館大学数理工学セミナー>>

日時：2022年12月15日（木） 16:30～18:00

講演者：

永原正章（北九州市立大学）

題目：リーマン多様体上の最適化数理と非線形共役勾配法の一般的な枠組みについて

概要：
PDFファイルをご覧ください．

開催方法：

ウェストウィング6階談話会室での講演の模様をZoomミーティングで配信する予定です．

上記ファイル内に記載されたURLの申込フォームより12月14日（水）までにお申し込みください．

登録された方にセミナー当日の昼頃までにZoomミーティングの情報をお送りいたします．

対面参加を希望される方は、12月11日（日）までに多羅間へご連絡ください．

COVID-19の感染防止のため，対面参加者数が多い場合は適宜人数制限を行いますので，ご了承ください．

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 1 Dec.

2022.12.01 Thu up

Date: 1 Dec. (Thu.)
Place: W.W. 6th-floor, Colloquium Room and on the Web (Zoom)
Time: 16:30-18:00
Speaker: Ju Yi Yen (University of Cincinnatti)
Title: Mathematical analysis of automated market makers
Abstract:

Automated market makers (AMMs) are examples of Decentralized Finance systems. Nowa- days, AMMs are dominated by the Constant Function Market Makers (CFMMs). CFMMs pool liquidity from its takers and providers, and set the relative prices of the two assets within the pool by a mathemat- ical formula. The relative price is determined by the reserves of the two assets in the pool. Notice that the assets in the liquidity pool are risky assets, their performances are impacted by the market risk. In this talk, we describe the stochastic process used for modeling the relation between the pool price and the corresponding market price for assets traded via CFMMs, and present limit theorems of this stochastic process. Our results are deduced from properties of the Brownian motion and its local time process.

数理科学科談話会（2022/12/7）

2022.11.24 Thu up

12月7日（水）に談話会を開催します．

学外からご参加いただける場合は原則，zoom（オンライン）上での参加をお願いいたします．ご参加の場合は平良（ktaira@fc.ritsumei.ac.jp ）までご連絡ください．

日程：12月7日（水） 16:30-17:30

場所：立命館大学BKCキャンパスウエストウイング談話会室（対面とzoomのハイブリッド開催）

講演者：本永翔也（立命館大学）

タイトル：Aubry-Mather理論における作用最小化集合とMather関数の関係

アブストラクト：

古典力学におけるEuler-Lagrange方程式および対応するHamilton力学系の解軌道は，作用汎関数を極小化するものとして特徴づけられることが知られている（変分原理）．では，作用汎関数を（極小化ではなく）最小化する解軌道は，どのような挙動を示すだろうか？Aubry-Mather理論では，作用を最小化するという観点から，Mather集合・Aubry集合・Mañé集合という不変集合が導入される．本講演では，これらの定義や性質を紹介するとともに，パラメータ付き作用汎関数の最小値として定義されるMatherのβ関数・α関数との関係について講演者が得た結果を述べる．また，Matherのβ関数の微分可能性が，対応する力学系のある種の可積分性(Lagrangeグラフによる葉層構造の存在)を特徴付けるかという問題に対して，主結果から分かることについても説明する．

International workshop “Foliated spaces, Tilings, Group actions 2022″（2022年12月17日（土），18日（日））

2022.11.23 Wed up

Date: 17th and 18th December, 2022
Place: Zoom meeting and Room R101 in Rarcadia (17th Dec.), Room F205 in Forest House (18th Dec.) Biwako-Kusatsu Campus, Ritsumeikan University Campus map.
Registration for on-site participation: Please fill this form. The deadiline is 12th December.
Registration for online participation: Please fill this form. The deadline is 15th December.
The website of the workshop is here

Please contact hnozawa(at)fc.ritsumei.ac.jp (replace (at) with @) if you have any problem.

立命館大学幾何学セミナー（2022年12月19日（月））

2022.11.23 Wed up

日時：2022年12月19日（月） 16:30–17:30

タイトル： 3価ファットグラフスパインの数値的不変量について

講演者：久野雄介氏（津田塾大学）

アブストラクト：
ファットグラフスパインとは、向きづけられた穴あき(あるいは境界付き)曲面に変位レトラクトとして埋め込まれたグラフである。この様なグラフは、曲面のタイヒミュラー空間の自然なセル分割に現れる。3価ファットグラフスパインの数値的不変量を、背景(写像類群のねじれ係数コホモロジー、森田-Penner構成、曲面のスピン構造)と共にいくつか紹介する。本講演の一部は竹澤花恵氏との共同研究(Topology Appl. 312 (2022))に基づく。
開催方法：
ウェストウィング6階談話会室での講演の模様をZoomミーティングで配信する予定です．
以下の申込フォームより12月18日までにお申し込みください。
https://ritsumei-ac-jp.zoom.us/meeting/register/tJcvde6vrT0vGtxERSTdeaotwTKZkDcVwkbU
登録後、ミーティング参加に関する情報の確認メールが届きます。

Math-Fi seminar on 24 Nov.

2022.11.22 Tue up

Date: 24 Nov. (Thu.)
Place: W.W. 6th-floor, Colloquium Room and on the Web (Zoom)
Time: 16:30-18:00
Speaker: Michael Zierhut (KIER, Kyoto University)
Title: The Arbitrage Pricing Theory in Incomplete Markets
Abstract:

The arbitrage pricing theory (APT) is traditionally viewed as a descriptive theory: If asset prices are decomposed into systematic and idiosyncratic components, the latter are negligible for almost all assets in large markets. This paper analyzes its role as a predictive theory: When prices of systematic risk factors are estimated by means of linear regression, these estimates are a lower-dimensional representation of a pricing kernel. Such estimates can be used to predict arbitrage-free prices for new assets. Market structure matters: When markets are complete, there is a unique pricing kernel and factor pricing is always arbitrage-free. When markets are incomplete, this method may select a nonpositive pricing kernel. This leads to a problem that is robust in a topological sense: For an open set of arbitrage-free markets, estimated factor models do not assign arbitrage-free prices out of sample. The critical assumption is therefore not that markets grow large, but that markets grow complete.

Math-Fi seminar on 17 Nov.

2022.11.11 Fri up

Date: 17 Nov. (Thu.)
Place: W.W. 6th-floor, Colloquium Room and on the Web (Zoom)
Time: 16:30-18:00
Speaker: Etsuo Segawa (Yokohama National University)
Title: 量子ウォークの快適度とグラフの組合わせ構造

Abstract:

外部との流出入のある量子ウォークモデルは、ある条件のもと、時刻無限大で定常状態に達する。この定常状態によって、特徴づけられるグラフの幾何構造や、組合わせ構造について考察する。特に、このモデルのグラフの流入と流出の関係を与える散乱行列の特徴づけと、内部に滞在している量子ウォークの量(=快適度)が、ある全域部分グラフの族の個数の数え上げによって、与えられることを紹介する。

Math-Fi seminar on 20 Oct.

2022.10.18 Tue up

Date: 20 Oct. (Thu.)
Place: W.W. 6th-floor, Colloquium Room and on the Web (Zoom)
Time: 16:30-18:00
Speaker: Luis Iván Hernández Ruíz (Kyoto University)
Title: Results on Limit Theorems for the Renewal Hawkes Process
Abstract:

Point processes are often used to model occurrences of events in time. One of such models that has seen applications in Finance is the self-exciting process proposed by Hawkes in 1971, in which previous occurrences of events increase the chance for new events to occur. In this process, immigrants arrive to the system following a Poisson process, then, each immigrant has the possibility to have offspring. At the same time, each new offspring individual has the possibility to give birth to further offspring. In this work, we present an extension to the original Hawkes process, but we consider that the arrival of immigrants is given by a Renewal process; the interarrival times are still independent, but they follow an arbitrary distribution. Existence is proved by exploiting the cluster structure of the process and we use martingale theory to prove a Law of Large Numbers. We give a conjecture for a functional Central Limit Theorem.

Math-Fi seminar on 6 Sep.

2022.09.05 Mon up

Date: 6 Sep. (Tue.)
Place: W.W. 6th-floor, Colloquium Room and on the Web (Zoom)
Time: 16:30-18:00
Speaker: Dan Crisan (Imperial College London)
Title: Classical and modern results in the theory and applications of stochastic filtering

Abstract:

Onwards from the mid-twentieth century, the stochastic filtering problem has caught the attention of thousands of mathematicians, engineers, statisticians, and computer scientists. Its applications span the whole spectrum of human endeavour, including satellite tracking, credit risk estimation, human genome analysis, and speech recognition. Stochastic filtering has engendered a surprising number of mathematical techniques for its treatment and has played an important role in the development of new research areas, including stochastic partial differential equations, stochastic geometry, rough paths theory, and Malliavin calculus. It also spearheaded research in areas of classical mathematics, such as Lie algebras, control theory, and information theory. The aim of this talk is to give a historical account of the subject concentrating on the continuous-time framework. I will also present a recent application of filtering to the estimation of partially observed high dimensional fluid dynamics models. In particular, I will introduce a so-called particle filter that incorporates a nudging mechanism. The nudging procedure is used in the prediction step. In the absence of nudging, the particles have trajectories that are independent solutions of the model equations. The nudging presented here consists in adding a drift to the trajectories of the particles with the aim of maximising the likelihood of their positions given the observation data. This introduces a bias in the system that is corrected during the resampling step. The methodology is tested on a two-layer quasi-geostrophic model for a beta-plane channel flow with O(10^6) degrees of freedom out of which only a minute fraction are noisily observed.

The talk is based on the papers:

[1] D Crisan, The stochastic filtering problem: a brief historical account, Journal of Applied Probability 51 (A), 13-22

[2] C Cotter, D Crisan, D Holm, W Pan, I Shevchenko, Data assimilation for a quasi-geostrophic model with circulation-preserving stochastic transport noise, Journal of Statistical Physics, 1-36, 2020.

[3] D Crisan, I Shevchenko, Particle filters with nudging, work in progress.