数理ファイナンスセミナー

Math-Fi seminar on 4 Jun. (Co-organized as a Quantum Walk Seminar)

2026.06.04 Thu up
  • 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).
     

Math-Fi seminar on 21 May.

2026.05.21 Thu up
  • 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。
 

Math-Fi seminar on 14 May.

2026.05.14 Thu up
  • 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.

Math-Fi seminar on 23 Apr. (Co-organized as a Quantum Walk Seminar)

2026.04.23 Thu up
  • 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．

Math-Fi seminar on 17 Apr.

2026.04.16 Thu up
  • 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.

Math-Fi seminar on 9 Apr. (Co-organized as a Quantum Walk Seminar)

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.

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.

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.

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