立命館大学数理科学科

Math-Fi seminar on 3 Sep.

horie — Thu, 03 Sep 2026 05:13:27 +0000

Date: 3 Sep. (Thu.)
Place: West Wing, 6th floor, Colloquium Room and on the Web (zoom)
Time: 16:50-18:20
Speaker: Jorge Gonzalez (IIMAS – UNAM)
Title: Convex minorants and the fluctuation theory of Lévy processes
Abstract:

We will introduce Lévy processes and establish the stick-breaking representation of its convex minorant using elementary symmetries and some convex geometry. Using this representation, we will derive many celebrated results in fluctuation theory and comment on its uses. In particular, we will not mention or use the Lévy-Khintchine formula, the Lévy-Itô decomposition, excursion theory, potential theory, or any of Skorokhod’s topologies.

Math-Fi seminar on 27 Aug.

horie — Thu, 27 Aug 2026 04:13:15 +0000

Date: 27 Aug. (Thu.)
Place: West Wing, 6th floor, Colloquium Room and on the Web (zoom)
Time: 16:50-18:20
Speaker: Nino Kordzakhia (Macquaire University, Australia)
Title: On calibration of diffusion processes: the multidimensional case.
Abstract:

We study general properties of maximum likelihood estimators (MLEs) for drift parameters in diffusion‑type models arising under the fixed time-horison and sequential sampling schemes within the framework of multi‑dimensional processes. In extending to multivariate drift parameter estimation, we use the Liptser-Shiryaev approach to generalise the results on MLEs obtained for one-dimensional diffusion-type processes.

For multivariate Ornstein-Uhlenbeck (O-U) processes, we discuss a general approach for obtaining the bias and mean‑square errors of the MLEs under a fixed time-horison.

We also illustrate the computational aspects of calibrating multivariate O-U processes in practical applications.

立命館大学幾何学セミナー（2026年8月24日（月））

mathstaff — Tue, 18 Aug 2026 11:43:59 +0000

<<立命館大学幾何学セミナー>>

日時：2026年8月24日（月）16:00-17:00

講演者：Elmar Schrohe (Leibniz Universität Hannover)

題目：
Elliptic boundary value problems and partial group actions

概要：
PDFファイルをご覧ください
会場：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

Math-Fi seminar on 20 Aug.

horie — Tue, 18 Aug 2026 07:06:46 +0000

Date: 20 Aug. (Thu.)
Place: West Wing, 6th floor, Colloquium Room and on the Web (zoom)
Time: 16:50-18:20
Speaker: Alex Novikov (University of Technology Sydney)
Title: On calibration of diffusion processes: introduction to the general theory, the one‑dimensional case.
Abstract:

We study the Maximum Likelihood Estimators (MLEs) of drift parameters in diffusion‑type models frequently deployed in quantitative finance.

The properties of these estimators are explored in the fixed‑horizon and sequential sampling schemes.

Extending the classical framework of Liptser–Shiryaev, we derive non‑asymptotic, semi‑analytic formulas for the moments of the MLEs

and establish their exponential boundedness.

We show that the bias and mean‑square error of the MLEs can be computed explicitly using integral‑transform techniques.

For ergodic diffusions, including Ornstein–Uhlenbeck and affine‑type processes, we demonstrate how to obtain exact numerical results

together with asymptotic expansions. We also discuss how these results may be adapted to high‑frequency discrete‑time observation schemes

relevant to financial data.

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

horie — Thu, 30 Jul 2026 07:33:56 +0000

Date: 4 Aug. (Thu.)
Place: West Wing, 6th floor, Colloquium Room and on the Web (zoom)
Time: 16:00-17:50

Speaker 1: Jyoti Rani (IISER Mohali)
Time:16:00-16:50
Title: A Study of the Joint q-Numerical Range and the A-q-Numerical Range of Operators
Abstract:

In this talk, we will discuss the concept of the numerical range and its extensions to different operator-theoretic frameworks. We begin with the notion of q-numerical range in multivariable operator theory, namely the joint q-numerical range. In this setting, we will discuss some equivalent conditions for the convexity of the joint q-numerical range, its relation to the joint C-numerical range, and its connections with the joint point spectrum and the joint approximate point spectrum. We will also go through a few key bounds for the joint q-numerical radius.
In the second part of the talk, we will consider the concept of the q-numerical range of a bounded linear operator in the framework of semi-Hilbertian spaces. Here, we will explore the convexity and compactness properties of the q-numerical range and present an equivalent condition for the equality case in an inequality for the q-numerical radius in semi-Hilbertian spaces. We will also examine several geometric properties of the A-q-numerical range, including spectral inclusion results and a circular disk union formula. Additionally, we will introduce the notion of an A-nilpotent operator. Furthermore, we will discuss several refined inequalities for the q-numerical radius via Orlicz functions.

Speaker 2: Anshu (University of Ulsan)
Time:17:00-17:50
Title: Quantum Wasserstein distance on quantum permutation group
Abstract:

In this talk, we will discuss the categorical definition of a quantum permutation group. Then we will describe the quantum Wasserstein distances on the trace space of the quantum permutation groups. We will also show how the Wasserstein distance recovers the Hamming distance in the classical case.

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

horie — Thu, 09 Jul 2026 07:23:55 +0000

Date: 9 Jul. (Thu.)
Place: West Wing, 6th floor, Colloquium Room and on the Web (zoom)
Time: 15:40-19:00

Speaker 1: Jyoti Rani (IISER, Mohali)
Time:15:40-16:40
Title: A Study of the Joint q-Numerical Range and the A-q Numerical Range of Operators
Abstract:

In this talk, we will discuss the concept of the numerical range and its exten

sions to different operator-theoretic frameworks. We begin with the notion of

q-numerical range in multivariable operator theory, namely the joint q-numerical

range. In this setting, we will discuss some equivalent conditions for the convexity

of the joint q-numerical range, its relation to the joint C-numerical range, and its

connections with the joint point spectrum and the joint approximate point spec

trum. We will also go through a few key bounds for the joint q-numerical radius.

In the second part of the talk, we will consider the concept of the q-numerical

range of a bounded linear operator in the framework of semi-Hilbertian spaces.

Here, we will explore the convexity and compactness properties of the q-numerical

range and present an equivalent condition for the equality case in an inequality

for the q-numerical radius in semi-Hilbertian spaces. We will also examine sev

eral geometric properties of the A-q-numerical range, including spectral inclusion

results and a circular disk union formula. Additionally, we will introduce the

notion of an A-nilpotent operator. Furthermore, we will discuss several refined

inequalities for the q-numerical radius via Orlicz functions

Speaker 2: Takashi Komatsu（University of Yamanashi）
Time:16:50-17:50
Title:行列ゼータ関数の行列式表示
Abstract:

量子ウォークはランダムウォークの量子版として導入され、量子探索アルゴリズムへの応用やスペクトル構造の解析において注目を集めている。一方、伊原康隆氏によって導入された伊原ゼータ関数(Selberg型のゼータ関数)は数論の分野で登場し、Serre氏の指摘により、グラフ理論と密接に関わっていることが分かった。本講演では、これら異なる分野から登場した「量子ウォーク」と「伊原ゼータ関数」の接点である『Grover/Zeta 対応』を行列ゼータ関数の観点から紹介し、その行列式表示の構造を紐解く。この対応関係において中心的な役割を担うのが「今野・佐藤の定理」であり、その証明においては第2種重み付きゼータ関数(佐藤ゼータ)が鍵を握っている。また、時間が許せば、有限グラフが基本有限グラフの被覆となっている状況において、この今野・佐藤の定理がどのように被覆構造を反映した形式として現れるかについて焦点を当てたい。本研究は、今野紀雄氏(立命館大/横浜国立大)、佐藤巖氏(小山高専)、三橋秀生氏(法政大)との共同研究に基づく。

Speaker 3: Yuki Fujii (Hiroshima University, Mitsubishi Electric）
Time:18:00-19:00
Title:Szegedy walkの一般化と無限二面体群のユニタリ表現
Abstract:

Szegedy walkは2部グラフ上のランダムウォークの量子版であり、量子計算における探索アルゴリズムへの応用から盛んに研究されている。

Szegedy walkを一つ固定すると、その生成に用いられる二つの部分空間の組が定まり、これらから無限二面体群のユニタリ表現が自然に得られる。

本講演では、Szegedy walkの定義を拡張した「一般化Szegedy walk」を考察する。この一般化のもとでは、任意の無限二面体群のユニタリ表現を一般化Szegedy walkとして実現できる（特定の一次元表現の違いを除いて）ことを示す。さらに、対応する2部グラフは高々次数2の重み付き有向2部グラフとして構成できることを説明する。以上の結果は、著者らによる無限二面体群のユニタリ表現に関する分解定理（Y. Fujii, T. Tsurumaru, “Estimating the spectral radius of Bell-type operators via finite dimensional approximation of orthogonal projections”, Linear Algebra and its Applications, 2026）の応用として得られる。

立命館大学幾何学セミナー（2026年7月24日（金））

mathstaff — Sun, 05 Jul 2026 13:54:33 +0000

<<立命館大学幾何学セミナー>>

日時：2026年7月24日（金）17:00-18:00

講演者：Jérémie Pierard de Maujouy

題目：

Gibbs distributions on nilpotent coadjoint orbits

概要：
PDFファイルをご覧ください
会場：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

立命館大学幾何学・数理工学勉強会（2026年7月10日（金））

mathstaff — Fri, 03 Jul 2026 09:06:27 +0000

<<立命館大学幾何学・数理工学勉強会>>

日時：2026年7月10日（金）17:00-18:00

講演者：Jérémie Pierard de Maujouy

題目：

Introduction to Souriau’s geometric thermodynamics

概要：

Jean-Marie Souriau developed a geometric approach to equilibrium statistical mechanics based on symmetry and Lie group actions. In this introductory talk, I will present the main ideas of the theory, starting from their physical motivation and building the formalism step by step. We will see how temperature is connected to the symmetries of a system and how the space of thermodynamic states carry a natural geometric structure. The discussion will be illustrated by two simple examples: a centrifuge and the family of Gaussian distributions.

会場：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

Math-Fi seminar on 2 Jul. (Co-organized as a Quantum Walk Seminar)

horie — Thu, 02 Jul 2026 01:24:37 +0000

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。

Math-Fi seminar on 25 Jun.

horie — Thu, 25 Jun 2026 03:44:08 +0000

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 −

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 −

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.