- Date: 25 Apr. (Thu.)
- Place: W.W. 6th-floor, Colloquium Room and on the Web (Zoom)
- Time: 16:30 – 18:00
- Speaker: 楯 辰哉 (東北大学）
- Title: 1 次元 2 状態量子ウォークの一般固有関数展開
セミナー
Math-Fi seminar on 25 Apr. (Co-organized as a Quantum Walk Seminar)
2024.04.24 Wed up
Math-Fi seminar on 18 Apr.
2024.04.16 Tue up
Date: 18 Apr. (Thu.)
Place: W.W. 6th-floor, Colloquium Room and on the Web (Zoom)
Time: 16:30 – 18:30
Speaker 1: Jie Yen Fan (Monash University)
Title: Mimicking: Martingales with Matching Marginals (Lecture 2)
Abstract: Click here
Speaker 2: Ju-YI Yen (University of Cincinnati)
Title : A brief discussion on Brownian motion and related processes with applications (Lecture 2)
Abstract: Click here
Math-Fi seminar on 11 Apr.
2024.04.10 Wed up
Date: 11 Apr. (Thu.)
Place: W.W. 6th-floor, Colloquium Room and on the Web (Zoom)
Time: 16:30 – 18:30
Speaker 1: Gabriel Berzunza Ojeda (University of Liverpool)
Title: Fragmentation Process derived from $\alpha$-stable Galton-Watson trees (Lecture 2)
Abstract: Click here
Speaker 2: Ronnie Loeffen (University of Liverpool)
Title : Optimal control of risk processes in insurance (Lecture 2)
Abstract: Click here
Abstract: Click here
Math-Fi seminar on 18 Jan. (Co-organized as a Quantum Walk Seminar)
2024.01.17 Wed up
- Date: 18 Jan. (Thu.)
- Place: W.W. 6th-floor, Colloquium Room and on the Web (Zoom)
- Time: 16:30 – 18:00
- Speaker: 成松明廣 (福知山公立大学)
- Title: 量子ウォークの局所的挙動から考える固有値問題と局在化
- Abstract:
量子ウォークは、ランダムウォークを量子化したモデルとして注目を集めており、特徴的な性質として線形的拡散と局在化が知られている。
このうち局在化現象について、その状態は、数式的には量子ウォークの時間発展作用素の特定（一つとは限らない）の固有関数で記述されるが、ウォーカーが出発点付近にとどまり続ける現象として説明されることも多い。
本講演では、空間的に一様な一般の次元の正方格子上の量子ウォークに対し、局在化の起こる状態の「とどまり続ける」と説明される特徴について、拡散する範囲が有限である固有関数が存在することとして解釈できることを示し、局所的な挙動に注目することでその必要条件を考察する。
Math-Fi seminar on 21 Dec.
2023.12.19 Tue up
- Date: 21 Dec. (Thu.)
- Place: W.W. 6th-floor, Colloquium Room and on the Web (Zoom)
- Time: 16:30 – 18:00
- Speaker: Noriyoshi Sakuma (Nagoya City University)
- Title: The Outlier Problem from a View of non-commutative Probability Theory I
- Abstract:
The outlier problem in random matrix theory is one of the important topics. In this talk, I will explain a non-commutative probabilistic method for considering the outlier problem. The notion of cyclic monotone independence plays a similar role to that of free independence. If time permits, I will also introduce nonrandom models.
Math-Fi seminar on 18 Dec.
2023.12.12 Tue up
- Date: 18 Dec. (Mon.)
- Place: W.W. 6th-floor, Colloquium Room and on the Web (Zoom)
- Time: 16:30 – 18:00
- Speaker: Hau-Tieng Wu (Courant Institute of Mathematical Sciences at New York University)
- Title: Nonstationary biorhythm analysis through landmark diffusion with clinical application
- Abstract:
Compared with the commonly collected health information, long-term and high-frequency physiological time series that exhibit nonstationary traits provide abundant information from an alternative perspective. However, it is challenging to extract clinically applicable data from these raw time series due to various impediments. Fueled by clinical necessities, physiological expertise, and clinical observations, we introduce a novel latent diffusion geometry-based signal processing method. The algorithm is explicitly designed to handle enormous datasets, including ultra-long and high-frequency time series, with ease, while remaining resilient to color and heterogeneous noise, underpinned by sound theoretical support. We will discuss an application of this method to assess the clinical outcome of liver transplants by uncovering the delicate details concealed in the arterial blood pressure signal recorded during surgery that remain indistinguishable to the naked eye.
Math-Fi seminar on 7 Dec. (Co-organized as a Quantum Walk Seminar)
2023.12.04 Mon up
- Date: 7 Dec. (Thu.)
- Place: W.W. 6th-floor, Colloquium Room and on the Web (Zoom)
- Time: 16:30 – 18:00
- Speaker: 井手勇介（日大文理）
- Title: 固有解析から眺める連続時間量子ウォーク
- Abstract:
連続時間量子ウォークは、グラフに付随するエルミート行列から定まるユニタリ行列によって駆動される連続時間の量子系である。
連続時間量子ウォークの挙動を調べるためには、その時間発展を定義するエルミート行列の固有値・固有ベクトルを調べることが本質的であり、舞台となるグラフの性質が固有値・固有ベクトルを通じて連続時間量子ウォークの挙動に反映される。本講演では、連続時間量子ウォークの定義と良く知られた結果について述べたのちに、隣接行列・グラフラプラシアンなどから定まる典型的な連続時間量子ウォークの挙動について、固有値・固有ベクトルの解析から見えてくる諸性質をご紹介したい。
Math-Fi seminar on 30 Nov.
2023.11.24 Fri up
- Date: 30 Nov. (Thu.)
- Place: W.W. 6th-floor, Colloquium Room and on the Web (Zoom)
- Time: 16:30 – 18:00
- Speaker: Andrea Macrina (University College London)
- Title: Filtered Arcade Martingales: An Alternative Approach to Martingale Optimal Transport?
- Abstract:
Arcade processes are a class of continuous stochastic processes that interpolate in a strong sense between zeros at fixed pre-specified times. Their additive randomization allows one to match any finite sequence of target random variables, indexed by the given fixed dates, on the whole probability space. The filtrations generated by such processes are utilized to construct a class of martingales which interpolate between the given target random variables. These so-called filtered arcade martingales (FAMs) are almost-sure solutions to the martingale interpolation problem and reveal an underlying stochastic filtering structure. In the special case of conditionally Markov randomized arcade processes, the dynamics of FAMs are informed through Bayesian updating. FAMs can be connected to martingale optimal transport (MOT) by considering optimally coupled target random variables. Moreover, FAMs allow to formulate an information-based martingale optimal transport problem, which enables the introduction of noise in MOT, in a similar fashion to how Schrödinger’s problem introduces noise in optimal transport. This information-based transport problem is concerned with selecting an optimal martingale coupling for the target random variables under the influence of the noise that is generated by an arcade process.
立命館大学幾何学セミナー（2023年9月8日（金））
2023.10.11 Wed up
<<立命館大学幾何学セミナー>>
日時：2023年9月8日（木）15:00-16:00
日時：2023年9月8日（木）15:00-16:00
講演者：Wolfram Bauer (Leibniz Universität Hannover)
題目：Subriemannian geometry and spectral analysis
概要：
A regular subriemannian manifold $M$ carries a geometric hypoelliptic operator which often is referred to as sublaplacian. Due to the specific degeneracy of its symbol, interesting geometric and analytic effects can be observed in the study of this operator, which have no counterpart in the area of Riemannian geometry. In particular, during the last decades an inverse spectral problem which aims to extract geometric information from the operator spectrum has been considered by various authors. Typical approaches are based on the analysis of the induced subriemannian heat or wave equation.
In this talk we survey some results on the spectral theory of the sublaplacian in the case of certain compact nilmanifolds or so-called $H$-type foliations and we address some seemingly open problems. This presentation is based on joint work with K. Furutani, C. Iwasaki and A. Laaroussi, I. Markina and G. Vega-Molino.
開催方法：ハイブリッド開催（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 階談話会室での対面開催及びZoom ミーティングによる配信）を予定．
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Math-Fi seminar on 12 Oct.
2023.10.06 Fri up
- Date: 12 Oct. (Thu.)
- Place: W.W. 6th-floor, Colloquium Room and on the Web (Zoom)
- Time: 16:30 – 18:00
- Speaker: Syoiti Ninomiya (Tokyo Institute of Technology)
- Title: 確率微分方程式の高次弱近似アルゴリズムの構造を模った深層学習機械
- Abstract:
確率微分方程式の高次弱近似アルゴリズムの構造を模したネットワーク構造を持つ深層学習機械を提案する. この機械は学習によってある拡散過程を得ること—具体的には金融派生商品のヘッジ戦略をこの機械によって「陽に得る」こと—を目的とするものである. 実際にこれらを作成して数値実験を行なったところ, 高次弱近似に基づく機械はアメリカンオプションの価格計算とそのヘッジ過程を学習することに成功した.
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