立命館大学数理科学科 » 数理ファイナンスセミナー http://www.math.ritsumei.ac.jp/home2 立命館大学理工学部数理科学科です。幅広い領域での数学の研究・活用を通して人類の福祉と発展に貢献できる人材を育成することを目標としています。 Sun, 05 Jul 2026 13:54:33 +0000 ja hourly 1 https://wordpress.org/?v=3.9.40 Math-Fi seminar on 2 Jul. (Co-organized as a Quantum Walk Seminar) http://www.math.ritsumei.ac.jp/home2/?p=2321 http://www.math.ritsumei.ac.jp/home2/?p=2321#comments Thu, 02 Jul 2026 01:24:37 +0000 http://www.math.ritsumei.ac.jp/home2/?p=2321
  • Date: 2 Jul. (Thu.)
  • Place: West Wing, 6th floor, Colloquium Room and on the Web (zoom)
  • Time: 16:50-19:00
     
  • Speaker 1: Trung Dung Vuong  (VNU-HCMHigh School for the Gifted）
  • Time:16:50-17:50
  • Title: Polar paths for generalized quantum fidelities
  • Abstract:
    • This talk is based on the generalized-fidelity framework introduced by Afham and Ferrie, together with recent developments from my preprint on polar fidelities, Holevo bases, and unitary factors of generalized fidelity. In this framework, a base point \[
    F_R(P,Q)
    =
    \Tr\!\left[
    (R^{1/2}PR^{1/2})^{1/2}R^{-1}
    (R^{1/2}QR^{1/2})^{1/2}
    \right].
    \]
    The framework recovers the Uhlmann, Holevo, and Matsumoto fidelities through special choices of the base.
     
    \hspace{1cm}
    I will discuss recent progress on the \(x\)-polar paths \(R=P^x\) and \(R=Q^x\). In particular, the associated polar fidelities form a monotone bridge from the Matsumoto fidelity to the Uhlmann fidelity, passing through the Holevo fidelity. I will also explain how this approach solves several fixed-pair realization and base-selection problems, including pointwise recovery of \(z\)-fidelities and the Log-Euclidean fidelity, the classification of Holevo bases, and the unitary factors arising from generalized fidelity. Along the way, I will mention several related open questions motivated by these results.
     
    \hspace{1cm}\textbf{Keywords:} \textit{Generalized quantum fidelity,
    polar fidelity,
    Uhlmann fidelity,
    Holevo fidelity,
    Matsumoto fidelity,
    Log-Euclidean fidelity,
    positive definite matrices,
    open problems}.
     
    • Speaker 2: Toru Fuda (Kokushikan University)
    • Time:18:00-19:00
    • Title:量子ウォークはいつ検出されるか：測定・初検出時刻・残余検出時間
    • Abstract:
    古典的なランダムウォークでは、ある集合に初めて到達する時刻は自然な確率変数として定義される。一方、量子ウォークでは、測定を指定しなければ「いつ到達したか」は確率変数として定義されない。また、「検出されなかった」という観測結果は、単なる情報更新ではなく、状態そのものを変化させる。
    本講演では、古典ランダムウォークや簡単な二点量子ウォークの例から出発し、量子ウォークにおける測定、初検出時刻、生存確率、残余検出時間について説明する。特に、ユニタリ発展 U、検出射影 P、非検出射影 Q=I-P に対して、非検出発展 T=QU を考え、時刻 n まで未検出だったという条件の下で、さらにどれくらい検出されずに残るかを調べる。
    有限次元の例では残余時間は幾何型になり、現在時刻と同じスケールの残余時間は残らない。一方、無限系や臨界的な状況では、生存確率のべき乗型減衰に由来して、スケール不変な残余時間分布が現れ得る。最後に、一次元 coined quantum walk や split-step quantum walk の局所検出との関係にも触れる。

    ]]>     http://www.math.ritsumei.ac.jp/home2/?feed=rss2&p=2321 0     Math-Fi seminar on 25 Jun. http://www.math.ritsumei.ac.jp/home2/?p=2318 http://www.math.ritsumei.ac.jp/home2/?p=2318#comments Thu, 25 Jun 2026 03:44:08 +0000 http://www.math.ritsumei.ac.jp/home2/?p=2318
  • Date: 25 Jun. (Thu.)
  • Place: West Wing, 6th floor, Colloquium Room and on the Web (zoom)
  • Time: 16:50-19:00
     
  • Speaker 1: Junichiro Matsuda (Ritsumeikan University)
  • Time:16:50-17:50
  • Title: Recent approaches to expander quantum graphs
  • Abstract:
    • The notion of quantum graph was introduced in the early 2010s motivated by quantum information theory. Quantum graphs are a non-commutative analogue of classical graphs, replacing the function algebra over the vertices with a non-commutative algebra and considering the quantum adjacency matrix acting on it. As in the classical case, we can characterize several properties of quantum graphs in terms of the spectrum of the related operators, e.g., connectedness, bipartiteness, and expanders. Expanders are families of $d$-regular graphs with a common lower bound of the spectral gap, on which the random walk expands rapidly.
    In this talk, I will overview recent approaches to expander quantum graphs, and discuss possible definitions of quantum walks on quantum graphs.
     
    • Speaker 2: Vu Thi Huong (University of Transport and Communications)
    • Time:18:00-19:00
    • Title: Some results on Caputo stochastic fractional delay differential equations
    • Abstract:
    This talk consists of two parts.
    Part I. A brief overview of recent developments on Caputo stochastic fractional delay differential equations. The main topics include
    • Well-posedness and regularity for solutions of Caputo stochastic fractional
    delay differential equations.
    • Variation-of-constants formulas
    • Stability analysis.
    • Several estimates for integrals involving singular kernels of the form (t −
    s)
    1−α, as well as matrix Mittag–Leffler functions Eα,α
    (t − s)
    αB
    
    and
    Eα,α
    (t − s)
    αB
    
    . A key ingredient in these analyses is the exploitation of
    the structural properties of the matrix Mittag–Leffler function Eα,α
    (t −
    s)
    αB
    
    in combination with the Jordan canonical form and a Djrbashiantype summation formula.
    • Several numerical approximation schemes for this class of equations that
    have been developed in the existing literature.
    Part II. I will present some recent results from a joint work with my coauthors, which has been submitted to the Journal of Computational and Applied
    Mathematics under the title Stability and Infinite-Time Convergence of the θMittag–Leffler Euler–Maruyama Approximation for Stochastic Fractional Delay
    Differential Equations. This work is joint work with Prof. Ngo Hoang Long,
    Hanoi National University of Education and Dr. Phan Thi Huong, Le Quy Don
    Technical University.
    This paper establishes, for the first time, the strong convergence of numerical
    approximations over infinite time intervals for stochastic fractional delay differential equations. In contrast to existing results on finite horizons, where error
    bounds typically depend on Mittag–Leffler functions that grow with the terminal
    time, we establish a time-uniform error estimate. The analysis is based on a suitable weighted norm combined with stability properties of the linear part, which
    allows us to control the singular kernels and the memory terms. Under suitable assumptions, we establish the uniform moment boundedness, stability, and
    global-in-time strong convergence rate of the θ-Mittag–Leffler Euler–Maruyama
    scheme. Numerical experiments illustrate the theoretical results and confirmthe
    effectiveness of the method over long time intervals.

    ]]>     http://www.math.ritsumei.ac.jp/home2/?feed=rss2&p=2318 0     Math-Fi seminar on 18 Jun. (Co-organized as a Quantum Walk Seminar) http://www.math.ritsumei.ac.jp/home2/?p=2313 http://www.math.ritsumei.ac.jp/home2/?p=2313#comments Tue, 16 Jun 2026 07:58:12 +0000 http://www.math.ritsumei.ac.jp/home2/?p=2313
  • Date: 18 Jun. (Thu.)
  • Place: West Wing, 6th floor, Colloquium Room and on the Web (zoom)
  • Time: 16:50-19:00
     
  • Speaker 1: Hirotaka Akatsuka （Otaru University of Commerce）
  • Time:16:50-17:50
  • Title: リーマンゼータ関数に対する深リーマン予想について
  • Abstract:
    • リーマンゼータ関数は素数を走る積表示であるオイラー積表示と, sと1-sの間の
    関係式である関数等式を持つ. オイラー積の絶対収束域と関数等式を用いること
    で, 実部が1より大の領域と実部が0より小の領域におけるゼータ関数の零点の位
    置を容易に特定することができる.  一方で, 上記領域とその境界を除いた部分(
    実部が0より大かつ1未満)は臨界帯領域と呼ばれ, オイラー積を直接的に用いる
    ことができない. そのため, 臨界帯領域における零点を調べるには様々な工夫が
    必要である.
     
    本講演では, 臨界帯領域にある各点においてx以下の素数を走る部分オイラー積を考え,
    xを無限大に飛ばしたときの漸近挙動を考察する. 特に, オイラー積の漸近挙動
    を素数定理の誤差評価やリーマンゼータ関数の零点分布のしかるべき予想と結び付ける.
    そして, 関数等式の中心点s=1/2におけるオイラー積の漸近挙動で定式化される,
    深リーマン予想を解説する.
     
    本講演では, 講演者の古い結果を複雑になりすぎない範囲で概説する予定である.
    時間に余裕があれば, オイラー積の漸近挙動の応用（約数関数の評価など）につ
    いても言及したい.
     
    • Speaker 2: VU HUY HOANG (UC Santabarbara)
    • Time:18:00-19:00
    • Title:Quantum Walks: A Stochastic Analysis and Potential Application to Optimization Problems
    • Abstract:
    We introduce quantum walks and its potential application to combinatorial optimization problems. Quantum walk, a counterpart of random walk in the quantum realm, is traditionally studied via combinatorial approach or Fourier analysis, and is rarely seen under stochastic analysis. We propose a new probabilistic representation of the quantum walk, starting with the Mochalnov formula, originally employed in the study of Schrodinger operators on multidimensional integer lattices. This representation can be used to study the solution of Dirac’s PDEs. 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 tool and new analytical pathways for investigating quantum dynamical systems, associated with optimization problems, via classical stochastic processes.
    ]]>     http://www.math.ritsumei.ac.jp/home2/?feed=rss2&p=2313 0     Math-Fi seminar on 4 Jun. (Co-organized as a Quantum Walk Seminar) http://www.math.ritsumei.ac.jp/home2/?p=2306 http://www.math.ritsumei.ac.jp/home2/?p=2306#comments Thu, 04 Jun 2026 03:08:51 +0000 http://www.math.ritsumei.ac.jp/home2/?p=2306
  • Date: 4 Jun. (Thu.)
  • Place: West Wing, 6th floor, Colloquium Room and on the Web (zoom)
  • Time: 17:00-19:10
     
  • Speaker 1: Santhosh K. Pamula (IISER, Mohali)
  • Time:17:00-18:00
  • Title: Structure of local completely contractive maps
  • Abstract:
    • Local completely contractive maps are a particular class of continuous linear maps on
    locally C∗-algebras, which are inverse limit of inverse system of C∗-algebras in the category of
    topological ∗-algebras. In this talk, we present a structure theorem for unbounded operator valued
    local completely contractive map ψ on a locally C∗-algebra A. There is a unique commutant
    operator T in the structure of ψ with norm at most 2. We show that the operator T is a contraction
    if and only if the block map
    Φ= φ ψ
          ψ∗ φ
    defined on M2(A) is local completely positive, for some local completely positive and local
    completely contractive map φ on A. In general, such a map φ may not exist for a given ψ, we
    illustrate this situation with an example. However, we prove a block representation of ψ in the sense
    that there always exist a local completely positive and local completely bounded map φ such that Φ
    is a local completely positive map. This is a joint work with R. Siddique
     
    • Speaker 2: Takuya Machida (Nihon University) 
    • Time:18:10-19:10
    • Title:非局在化状態を初期状態とする量子ウォークの極限分布
    • Abstract:
      2002年に局在化状態を初期状態とする量子ウォークの長時間極限分布が導出されてから（Konno [1]），ある1点（局在化状態）から出発する量子ウォークに対する多くの極
      限分布・極限定理が明らかにされてきた。その一方で，非局在化状態を初期状態とする量子ウォークに対する極限定理の数理研究は，これまでに多くは行われていない。量子の特徴として，量子は異なる状態を重ね合わせの状態でとることができる。量子ウォーカーも重ね合わせの状態として異なる場所に同時に存在することができ，量子ウォークの初期状態として非局在化状態を考えることは不自然なことではない。本講演では，非局在化状態を初期状態とする量子ウォークに対して得られる長時間極限分布を紹介する。具体的な例とともに，局在化初期状態で出発する量子ウォークの極限分布との違いを見ていく。講演内容は、Machida [2,3]に基づく。
       
      [1] Norio Konno, Quantum random walks in one dimension, Quantum Information
      Processing, 1(5), 345-354 (2002).
       
      [2] Takuya Machida, Realization of the probability laws in the quantum
      central limit theorems by a quantum walk, Quantum Information and
      Computation, Vol.13 No.5&6, pp.430-438 (2013).
       
      [3] Takuya Machida, A quantum walk with a delocalized initial state:
      contribution from a coin-flip operator, International Journal of Quantum
      Information, Vol.11, No.5, 1350053 (2013).
       
    ]]>     http://www.math.ritsumei.ac.jp/home2/?feed=rss2&p=2306 0     Math-Fi seminar on 21 May. http://www.math.ritsumei.ac.jp/home2/?p=2302 http://www.math.ritsumei.ac.jp/home2/?p=2302#comments Thu, 21 May 2026 04:05:29 +0000 http://www.math.ritsumei.ac.jp/home2/?p=2302
  • Date: 21 May. (Thu.) 
  • Place: West Wing, 6th floor, Colloquium Room and on the Web (zoom)
  • Time: 16:50-18:20
  • Speaker :  Naoki Masuda (University of Michigan)
  • Title: 高次ネットワーク上の意見形成確率モデル
  • Abstract: 
    • 本講演では、まず、ネットワーク科学という研究分野の簡単な紹介を行う。次に、いくつかの種類の高次ネットワーク上の進化ダイナミクスの研究について紹介する。進化ダイナミクスは、本研究の範囲で言えば、平たく言うと、集団意見形成ダイナミクスを表す確率過程である。高次ネットワークとしては、近年のネットワーク科学で盛んに研究されている構造でもあるハイパーグラフ、多層ネットワーク、テンポラル（＝ネットワーク自体が時間変化する）・ネットワークを考える。（逆に、高次でないネットワークは、典型的なネットワーク、すなわち数学で言う「グラフ」のことを表す。）これらの高次ネットワーク上での上記確率過程の振る舞いは、典型的なネットワークの上での同じ確率過程と比べてかなり異なる。具体的には、ネットワークが進化の「増幅器」でありやすいか、「抑制器」でありやすいか、が異なる。このことを、マルチンゲール解析、数値計算などによって示す。
     

    ]]>     http://www.math.ritsumei.ac.jp/home2/?feed=rss2&p=2302 0     Math-Fi seminar on 14 May. http://www.math.ritsumei.ac.jp/home2/?p=2300 http://www.math.ritsumei.ac.jp/home2/?p=2300#comments Thu, 14 May 2026 02:51:49 +0000 http://www.math.ritsumei.ac.jp/home2/?p=2300
  • Date: 14 May. (Thu.) 
  • Place: West Wing, 6th floor, Colloquium Room and on the Web (zoom)
  • Time: 16:50-18:20
  • Speaker :  Alessio Rondelli (University of Bologna)
  • Title: McKean-Vlasov SDEs and particle systems: What, Why and How.
  • Abstract: 
    • McKean-Vlasov SDEs are a class of Stochastic Differential Equations
    where the coefficients depend upon the marginals of the solution. Their
    study is justified by their usefulness in modeling the evolution of
    multi-agent systems using the mean-field approximation. Both classical
    and modern techniques are presented for strong and weak well-posedness
    and the concept of propagation of chaos gets explored.
    ]]>     http://www.math.ritsumei.ac.jp/home2/?feed=rss2&p=2300 0     Math-Fi seminar on 23 Apr. (Co-organized as a Quantum Walk Seminar) http://www.math.ritsumei.ac.jp/home2/?p=2297 http://www.math.ritsumei.ac.jp/home2/?p=2297#comments Thu, 23 Apr 2026 07:15:53 +0000 http://www.math.ritsumei.ac.jp/home2/?p=2297
  • Date: 23 Apr. (Thu.)
  • Place: West Wing, 6th floor, Colloquium Room and on the Web (zoom)
  • Time: 16:50-17:50
  • Speaker : Hiromichi OHNO (Shinshu University)
  • Title: Maze solving by quantum walk
  • Abstract: 
    • 本講演では，グラフを迷路に見立て，スタートとゴールを設定し，グローバーウォークを用いてスタートからゴールまでの経路を発見するアルゴリズムについて解説する．このアルゴリズムでは，量子ウォークの収束することは示せているが，収束先の確率分布から経路を発見できるかどうかは部分的な解答しか得られていない．これらの内容について数学的な証明を与えながら，具体的ないくつかの例を紹介する．
    ]]>     http://www.math.ritsumei.ac.jp/home2/?feed=rss2&p=2297 0     Math-Fi seminar on 17 Apr. http://www.math.ritsumei.ac.jp/home2/?p=2295 http://www.math.ritsumei.ac.jp/home2/?p=2295#comments Thu, 16 Apr 2026 07:41:03 +0000 http://www.math.ritsumei.ac.jp/home2/?p=2295
  • Date: 17 Apr. (Thu.) 
  • Place: West Wing, 6th floor, Colloquium Room and on the Web (zoom)
  • Time: 16:20-17:50
  • Speaker :  Antoine Jacquier (Imperial College)
  • Title: Quantum Computing, a new toolbox for Stochastic Analysis & Machine Learning?
  • Abstract: 
    • We are interested here in recent developments in Quantum Computing from an algorithmic standpoint and with a view towards applications (with an emphasis on Mathematical Finance and Stochastic Analysis). We shall in particular focus on Universal Approximations theorems for Parameterised Quantum Circuits as well as on the links between (partial) measurements of Quantum systems and Stochastic diffusions.
    ]]>     http://www.math.ritsumei.ac.jp/home2/?feed=rss2&p=2295 0     Math-Fi seminar on 9 Apr. (Co-organized as a Quantum Walk Seminar) http://www.math.ritsumei.ac.jp/home2/?p=2291 http://www.math.ritsumei.ac.jp/home2/?p=2291#comments Thu, 09 Apr 2026 06:15:09 +0000 http://www.math.ritsumei.ac.jp/home2/?p=2291
  • 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.
    ]]>     http://www.math.ritsumei.ac.jp/home2/?feed=rss2&p=2291 0     Math-Fi seminar on 2 Apr. http://www.math.ritsumei.ac.jp/home2/?p=2287 http://www.math.ritsumei.ac.jp/home2/?p=2287#comments Tue, 07 Apr 2026 01:51:01 +0000 http://www.math.ritsumei.ac.jp/home2/?p=2287
  • 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.
    ]]>     http://www.math.ritsumei.ac.jp/home2/?feed=rss2&p=2287 0