News&Events

Math-Fi seminar on 9 Apr.

2026.04.09 Thu up
  • Date: 9 Apr. (Thu.)
  • Place: West Wing, 6th floor, Colloquium Room and on the Web (zoom)
  • Time: 16:50-17:50
  • Speaker : Yohei Tanaka (Ritsumeikan University)
  • Title: On understanding chiral unitaries via real parts
  • Abstract: 
We study unitary operators with chiral symmetry, that is, unitary operators associated with a fixed involution. Such operators naturally arise in the study of quantum walks and related areas. A standard approach is to decompose the underlying Hilbert space according to this symmetry, which leads to a convenient block representation. In this framework, we focus on the real part of the unitary and use it as a useful tool to understand its spectral structure. Based on this viewpoint, we present several related topics and results, illustrating how the real-part perspective provides a simple and unified way to analyze chiral unitaries.

Ritsumeikan University Seminar

2026.04.07 Tue up
  • Date: 14 Sep-18 Sep
  • Place: West Wing, 6th floor, Colloquium Room or 7th floor seminar room and on the Web (zoom)
  • Time: 14 Sep-17 Sep 13:30-15:00 / 18 Sep 15:15-16:45
  • Speaker :  Fumio Hiai (Tohoku University)
  • Title: Matrix analysis and applications to quantum information
  • Abstract: 
In this intensive seminar, we begin by reviewing operator means and operator perspectives,
followed by explanations of operator inequalities, majorization, and trace inequalities for operators
and matrices. Next, we explain various quantum f-divergences that are important in
quantum information, including the recently developed hockey-stick f-divergence. Furthermore,
we discuss several topics related to the Fisher information (the monotonic metric) that
is important in quantum information geometry.

Math-Fi seminar on 2 Apr.

2026.04.07 Tue up
  • Date: 2 Apr. (Thu.) 
  • Place: West Wing, 6th floor, Colloquium Room and on the Web (zoom)
  • Time: 12:00-13:30
  • Speaker :  VU HUY HOANG (University of California, Santa Barbara)
  • Commentator :  Ju-Yi Yen (University of Cincinnati)
  • Title: Molchanov’s Formula and Quantum Walks: A Probabilistic Approach 
  • Abstract: 
This paper establishes a robust link between quantum dynamics and classical ones by deriving a probabilistic representation for both continuous-time and discrete-time quantum walks. We first adapt the Molchanov formula, originally employed in the study of Schrodinger operators on multidimensional integer lattices, to characterize the evolution of continuous time quantum walks. Extending this framework, we develop a probabilistic method to represent discrete time quantum walks on an infinite integer line, bypassing the locality constraints that typically inhibit direct application of the Molchanov formula. The validity of our representation is empirically confirmed through a benchmark analysis of the Hadamard walk, demonstrating high fidelity with traditional unitary evolution. Our results suggest that this probabilistic lens offers a powerful alternative for learning multidimensional quantum walks and provides new analytical pathways for investigating quantum systems via classical stochastic processes.

Math-Fi seminar on 31 Mar.

2026.04.07 Tue up
  • Date: 31 Mar. (Tue.) 
  • Place: West Wing, 6th floor, Colloquium Room and on the Web (zoom)
  • Time: 16:00–17:30 
  • Speaker : Joseph Najnudel (University of Bristol)  
  • Commentator :  Ju-Yi Yen (University of Cincinnati)
  • Title: The Riemann zeta function and its connection with random matrix theory.
  • Abstract: 
In this talk, we present some results and conjectures on the Riemann zeta function, its moments on the critical line, its extreme values, and its behaviour at the scale of the average spacing of the zeros.  We then connect these results to similar properties satisfied by the characteristic polynomial of random unitary matrices.

Ritsumeikan Geometry Seminar on 13 Mar.

2026.02.27 Fri up
Date: March 13, Friday, 2026 
Place: Colloquium room, West-Wing 6F, Biwako-Kusatsu Campus + Zoom meeting
Registration URL for Zoom:
https://ritsumei-ac-jp.zoom.us/meeting/register/A90nnMv0RNC7PFizhntG_w
 
 
-Program-
 
15:20-16:20 Olga Lukina (Leiden University)
      Cantor actions in dynamical systems
 
16:30-17:30 Steven Hurder (University of Illinois at Chicago)
      The dynamics of commensurators
 
 
-Abstract-
 
  • Speaker 1: Steve Hurder (University of Illinois at Chicago)
  • Title: The dynamics of commensurators
  • Abstract:
A commensurator of a countable group G is a virtual automorphism. That is, it is an isomorphism f : H -> K where H and K are subgroups of finite index of G.  We associate to a commensurator f of G, a homeomorphism F : C -> C of a Cantor set C. In the general case the space C is the profinite completion of G, but our interest is in more general case where C is a quotient of the profinite completion of G. We study the dynamical properties of the map F : C -> C. 
 
  • Speaker 2: Olga Lukina (Leiden University)
  • Title: Cantor actions in dynamical systems
  • Abstract:
In this talk, we consider dynamical systems on Cantor sets, given by group actions. Such systems arise as transverse dynamical systems in strange attractors and exceptional minimal sets of foliations. We present a few classification results.
 
 
Organizers:
Fukumoto Yoshihiro, Tarama Daisuke, Nozawa Hiraku
 
Contact:
hnozawa@fc.ritsumei.ac.jp

Math-Fi seminar on 12 Feb.

2026.02.10 Tue up
  • Date: 12 Feb. (Thu.) 
  • Place: West Wing, 6th floor, Colloquium Room and on the Web (zoom)
  • Time: 16:00–17:30 
  • Speaker : George Yin (University of Connecticut)
  • Title: Stochastic Approximation and Applications
  • Abstract: 
We will give an introduction to stochastic approximation
methods.  It will begin with a discussion on what stochastic approximation is and
what problems can be solved by using stochastic approximation methods. The RM and KW algorithms will be introduced.  An overview of the analysis (including convergence, rates of convergence, weak convergence, efficiency, as well as time-varying parameter problems, and tracking  algorithms etc.) is provided.  Several application examples will be mentioned.
A reference for the talk is the book by H.J. Kushner and G. Yin,
Stochastic Approximation and Recursive Algorithms and Applications, 2nd Edition,
Springer-Verlag, New York, 2003, [Applications of Mathematics, Volume 35].

Math-Fi seminar on 15 January. (Co-organized as a Quantum Walk Seminar)

2026.01.13 Tue up
Date: 15 Jan. (Thu.)
Place: West Wing, 6th floor, Colloquium Room and on the Web (zoom)
Time: 17:00-19:15
 
  • Speaker 1: Yuma Tamura（Ritsumeikan University）
  • Time:17:00-18:00
  • Title: Affine過程の表現公式と部分積分公式
  • Abstract:
本講演では，次の確率微分方程式で定義される拡散型のAffine processを扱う：
\[
    dX^x_t = \sqrt{ \alpha X^x_t } \,dW_t + ( \beta X^x_t + b )dt,\quad X^x_0=x.
\]
ここで，\(W\)は\(1\)次元Brown運動であり，\( \alpha > 0 \), \( \beta \in \mathbf{R} \), \( b \ge 0 \)は定数のパラメータである．Affine processのクラスは，代表的な金利モデルであるCox–Ingersoll–Ross (CIR)モデルを含むため，数理ファイナンスにおいて重要である．
 
本研究では，テスト関数\(f\)に対し，期待値の初期値\(x\)による微分
\[
    \partial_x E[ f(X^x_T) ]
\]
の表現公式および部分積分公式を導出する．特に前者は，数理ファイナンスにおける「オプションのデルタ」に対応し，実務的な応用可能性を持つ．
 
また，本講演ではこれらの公式の発見の端緒となったsquared Bessel processに関する考察についても述べる．
さらに，学生に向けて，最初にsquared Bessel processの基本事項の解説も行う予定である．
 
なお，本講演の内容はArturo Kohatsu-Higa氏（立命館大学）との共同研究に基づく．
 
  • Speaker 2: Takuya Nakagawa (Ritsumeikan University)
  • Time:18:15-19:15
  • Title: $L^{\alpha-1}$ distance between two one-dimensional stochastic differential equations with drift terms driven by a symmetric $\alpha$-stable process
  • Abstract:
This paper develops a quantitative stability theory for one-dimensional SDEs with non-zero drift and time-dependent coefficients, driven by a symmetric $\alpha$-stable process for $\alpha\in(1,2)$. We establish the first explicit convergence rates for this broad class. Our main result is a H\”older-type estimate for the $L^{\alpha-1}(\Omega)$ distance between two solution paths, which quantifies stability with respect to the initial values and coefficients. In this estimate, the distance between coefficients is measured by a weighted integral norm constructed from the transition probability density of one of the solutions. The proof is based on a refined analysis of a mollified auxiliary function, for which we establish a new, sharper derivative estimate to control the drift terms.

Math-Fi seminar on 8 January. (Co-organized as a Quantum Walk Seminar)

2026.01.08 Thu up
Date: 8 Jan. (Thu.)
Place: West Wing, 6th floor, Colloquium Room and on the Web (zoom)
Time: 16:50-19:00
 
  • Speaker 1: Takahiro Aoyama（Okayama University of Science）
  • Time:16:50-17:50
  • Title: 多重ゼータ関数と高次元測度論
  • Abstract:
一般にある多変数関数が与えられたとき，それがある確率分布の特性関数となるか否かについて判定することは困難である. その方法としては測度の半正値性を確認するための Bochner の定理等いくつか存在するが，実際には対応する測度が確率分布となることがほぼ自明な関数しか取り扱われていない.特に多次元の無限個の点に重みをもつ離散分布に対応する関数については，ただ単に分布を定義する，もしくはその非無限分解可能性までを示した結果はいくつか存在するが，それ以外の有用な情報は殆ど得られていない.
本講演では多重ゼータ関数を用いて東京理科大学中村隆氏とともに導入した無限個の点に重みをもつ多次元離散型確率分布のクラスを紹介し，高次元格子上を運動する様々なランダムウォークやレヴィ過程と確率分布との関係について述べる.
 
  • Speaker 2: Takashi Nakamura (Tokyo University of Science)
  • Time:18:00-19:00
  • Title: 多重ゼータ関数とレヴィ-ヒンチンの標準形
  • Abstract:
本講演において、各点の確率質量が多重ゼータ関数で与えられ、
かつレヴィ-ヒンチンの標準形におけるレヴィ測度がリーマン
ゼータ関数である特性関数を構成する。
この研究は東京理科大学大学院創域理工学研究科数理科学専攻
修士課程一年生の大森皓平氏との共同研究である。
 

Math-Fi seminar on 12 December. (Co-organized as a Quantum Walk Seminar)

2025.12.19 Fri up
Date: 25 Dec. (Thu.)
Place: West Wing, 6th floor, Colloquium Room and on the Web (zoom)
Time: 16:50-19:00
 
  • Speaker 1: Kiyoto Yoshino (Hiroshima Institute of Technology）
  • Time:16:50-17:50
  • Title: グラフ上のグローバーウォークにおける完全状態遷移について
  • Abstract:
量子ウォークにおいて，ある頂点に確率１で局在した初期状態が有限時間後に別の頂点に確率１で局在する現象を完全状態遷移という．
本講演ではグラフ上の標準的な離散時間量子ウォークの一つであるグローバーウォークにおける完全状態遷移に関する結果を紹介する．
主結果として，グラフの正規化隣接行列を用いた完全状態遷移の特徴づけを与える．
これにより例えばグラフのスペクトルによる完全状態遷移が起きる必要条件を得ることができる．
本研究の内容は，主に久保田匠氏（愛知教育大学）との共同研究の成果であるCirculant graphs with valency up to 4 that admit perfect state transfer in Grover walks, JCTA, 216 (2025)に基づく．
 
  • Speaker 2: Hiroshi Isozaki (Ritsumeikan University)
  • Time:18:00-19:00
  • Title: 量子ウオークと速度作用素
  • Abstract:
量子ウオークの典型例に対してその速度作用素を古典力学の Lagrange形式によって導出し, 速度分布の密度関数, 速度作用素を記述するLagrangean の楕円積分表示を導く. 1次元  , 高次元の離散・連続時間量子ウオーク, さらに連続極限等の問題を考察する.
 

Math-Fi seminar on 16 Dec.

2025.12.16 Tue up
  • Date: 16 Dec. (Thu.) 
  • Place: West Wing, 6th floor, Colloquium Room and on the Web (zoom)
  • Time: 16:50–18:20 
  • Speaker : Hau-Tieng Wu (New York University, Courant)
  • Title: Manifold denoising for Nonstationary Biomedical Time Series with Neuromodulation Applications
  • Abstract: 
Recent advances in technologies enable continuous acquisition of high frequency and multimodal physiological waveforms, moving well beyond traditional pointwise or sparse clinical measurements. These data streams are usually represented as nonstationary time series, often exhibiting complicated time-varying periodic structure and nonlinear dynamics, which pose fundamental challenges for statistical modeling and machine learning. To handle such time series, we introduce a manifold-denoising based data sharpening technique that processes raw nonstationary time series by converting it into manifold-valued point cloud for learning. The proposed technique leverages random matrix theory and spectral geometry to achieve manifold denoising, and hence time series analysis, and has rigorous theoretical guarantees. In addition to open problems, a clinical application in real-time neuromodulation will be presented to illustrate how this framework improves artifact suppression and signal interpretation, highlighting its potential to enhance physiological data analysis and support medical decision-making.

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