セミナー

立命館大学幾何学セミナー（2025年8月29日（金））

2025.08.26 Tue up
<<立命館大学幾何学セミナー>>
日時: 2025年8月29日（金）16:30～17:30
場所：ウェストウィング6階談話会室
タイトル: Global lifting and fundamental solution of degenerate operators
講演者:  Wolfram Bauer 氏（Leibniz Universitaet Hannover）
アブストラクト:
PDFファイルをご覧ください．

集中講義及び立命館関数解析研究会 2025年9月1日(月)～9月5日(金)

2025.08.05 Tue up
日時：2025年9月1日(月)～9月5日(金)下記参照
場所：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 
講師：Lajos Molnar教授 (University of Szeged）
 
 
9月１日（月）
  • Lajos Molnar (University of Szeged)：9:00-12:20
  • Lajos Molnar (University of Szeged)：13:30-15:05
関数解析研究会（1日目）
  • 水口洋康（立命館大学)：15:30-16:10
  • Title: On the constants related to triangles inscribed to a half of the unit sphere of normed spaces
  • Abstract:
​To investigate the geometric structure of normed spaces, he geometric constants play important roles.
There exist a lot of geometric constants, and among them we treat constants related to arithmetic mean of the norms of x+y and x-y where x and y belong to the unit sphere of normed spaces.　　　
 
  • 安齋 真由（新潟大学)：16:20-17:00
  • Title: The linear preserver problem for C-symmetric operators
  • Abstract: TBA:
 
 
9月2日（火）
  • Lajos Molnar (University of Szeged）：9:00-12:20　　　　　　
  • Lajos Molnar (University of Szeged）：13:30-15:05
関数解析研究会（2日目）
  • 羽鳥理（新潟大学）：15:30-16:10
  • Title: POWER BOUNDED ELEMENTS IN BANACH ALGEBRAS
  • Abstract:
Let B be a unital Banach algebra. An element x ∈
B which satisfies supn∈N ∥x
n∥ < ∞ is called power bounded. If
moreover x is invertible in B, and if supn∈Z ∥x
n∥ < ∞, then x
is called doubly power bounded. Doubly power bounded elements
appeared in a classical and seminal theorem of Gelfand [2].
Theorem 1. Suppose that a is a doubly power bounded element in
a unital Banach algebra B. If σ(a) = {1}, then a is the unit of B.
A celebrated theorem of Sz.-Nagy [1] states that a Hilbert space
operator is doubly power bounded if and only if it is similar to
a unitary operator. The structures of power bounded elements
in Fourier or Fourier-Stieltjes algebras were studied by Kanius and
Ulger [3]. Schreiber [4] has studied the commutative case. Let ¨ U =
{u ∈ B−1
: ∥u∥ = ∥u
−1∥ = 1}, DP B = {u ∈ B : u is doubly power bounded in B},
S1 = {u ∈ B : σ(u) ⊂ T
 
  • Lajos Molnar (University of Szeged）：16:20-17:00
  • Title: Isomorphisms of positive cones in operator algebras with respect to geometric means
  • Abstract:
In this talk we are concerned with the descriptions of bijective maps between the positive definite cones in operator algebras that preserve different sorts of geometric means. We mainly focus on the Kubo-Ando geometric mean and the Fiedler-Pták geometric mean. As for the former one, we extend our existing result from the case of von Neumann
 
 
9月3日（水）
  • Lajos Molnar (University of Szeged）：9:00-12:20　　　　　　
  • Lajos Molnar (University of Szeged）：13:30-15:05

 
9月4日（木）
  • Lajos Molnar (University of Szeged）：9:00-12:20　　　　　　
  • Lajos Molnar (University of Szeged）：13:30-15:05
 
 
9月5日（金）
  • Lajos Molnar (University of Szeged）：9:00-12:20　　　

Math-Fi seminar on 24 July.

2025.07.15 Tue up
  • Date: 24 July. (Thu.)
  • Place: West Wing, 6th floor, Colloquium Room and on the Web (zoom)
  • Time: 16:50-17:50
  • Speaker: Dai Taguchi (Kansai University)
  • Title: Approximation of irregular functionals of SDEs
  • Abstract:
Avikainen (2009) provided a sharp upper bound for the expectation of |1_{D}(X)-1_{D}(Y)|^{p} by the expectation of |X-Y|^{q}, for any one-dimensional random variables X with a bounded density function and Y, and intervales D. Then Giles and Xie (2017) give a simple proof. For multidimensional case, if both random variables X and Y have bounded densities, then this estimate is generalized by Taguchi, Tanaka and Yuasa (2022) for D with smooth boundary. In this talk, we generalize these results to the case where only one of X and Y has bounded density function and more general domain D (e.g. Lipschitz domains, convex sets). We apply our main result to numerical approximation for irregular functional of a solution to stochastic differential equations (SDEs) based on the Euler–Maruyama scheme and the multilevel Monte Carlo method. This is based on an ongoing research work with Hoang-Long Ngo (Hanoi National University of Education).

Math-Fi seminar on 10 July. (Co-organized as a Quantum Walk Seminar)

2025.07.08 Tue up
  • Date: 10 July. (Thu.)
  • Place: West Wing, 6th floor, Colloquium Room and on the Web (zoom)
  • Time: 17:50-19:00

  • Speaker 1: Shuhei Mano（The Institute of Statistical Mathematics）
  • Time: 16:50-17:50
  • Title: Symmetric quantum walks on Hamming graphs and their limit distributions
  • Abstract: 
We studied a class of symmetric quantum walks on Hamming graphs, where the distance between vertices specifies the transition probability. The simple quantum walk on the hypercube, which has been discussed in literature, is a special case. The zeros of certain self-reciprocal polynomials determine the dynamics of the quantum walks. We obtained a spectral representation of the wave function, where working with the coin space isomorphic to the state space and the commutative association scheme enables our systematic treatment. The limit distributions of several quantum walks are obtained. They are represented as the mixtures of a distribution that appears in random walks and another unknown distribution.
 
  • Speaker 2: Hideo Mitsuhashi（Hosei University）
  • Time: 18:00-19:00
  • Title: 四元数重み付きグラフのゼータ関数とその一般化
  • Abstract:
有向辺上に四元数重みをもつグラフのゼータ関数の、行列式表示やオイラー積表示に
ついて概観し、四元数環の元に重みをもつグラフへの一般化について、説明する。
四元数は非可換であるため、四元数行列の行列式は、通常の行列式の定義では
うまくいかないので、四元数行列の行列式についての概説も行って、初学者にも
わかるように解説したい。

Math-Fi seminar on 3 July. (Co-organized as a Quantum Walk Seminar)

2025.07.01 Tue up
  • Date: 3 July. (Thu.)
  • Place: West Wing, 6th floor, Colloquium Room and on the Web (zoom)
  • Time: 17:30-18:30
  • Speaker: Yuki Ueda (HOKKAIDO UNIVERSITY OF EDUCATION)
  • Title: 一般化Meixner型自由ガンマ分布とそのポテンシャル対応
  • Abstract:
自由確率論はVoiculescuによって提唱され、ランダム行列理論を介して古典確率論と深い関係を持つことが知られている。両者の対応関係を記述する方法は複数存在するが、それらは一般に一致しない。代表的なものとして、Bercovici–Pata対応や直交多項式系に基づく対応が挙げられるが、近年ではポテンシャル対応と呼ばれる新たな対応関係が注目されている。この対応は、Voiculescuによる自由エントロピーの理解において本質的な役割を果たす概念である。本講演では、Anshelevichによって導入された自由ガンマ分布を一般化する形で、「一般化Meixner型自由ガンマ分布」を定義し、その分布的性質、たたみこみ公式、Beta–Gamma代数に関する構造的特徴について報告する。さらに、この分布クラスに対するポテンシャル対応の枠組みを構築し、対応する古典確率側の分布クラスの性質についての考察も行う。本研究は佐久間紀佳氏 (大阪大学) との共同研究である。
 

Math-Fi seminar on 19 June. (Co-organized as a Quantum Walk Seminar)

2025.06.17 Tue up
  • Date: 19 Jun. (Thu.)
  • Place: West Wing, 6th floor, Colloquium Room and on the Web (zoom)
  • Time: 17:10-19:00

  • Speaker 1: Hoang Vu (UC santa barbara)
  • Time: 17:10-17:50
  • Title: Combinatorial Optimization Via Quantum Walks
  • Abstract:
Combinatorial optimization is a crucial area of research focused on finding optimal solutions from a finite set of discrete options. The landscape of this field has evolved significantly in recent years, driven by the increasing complexity of problems and the demand for efficient algorithmic solutions with applications spanning logistics, transportation, finance, and beyond. A transformative shift in combinatorial optimization has arisen with the introduction of quantum computing methodologies. We will review recent quantum algorithms and introduce some new ideas on using quantum walks to solving the combinatorial optimization problem.
 
  • Speaker 2: 佐竹 翔平 (熊本大学)
  • Time: 18:00-19:00
  • Title: On the embeddability of the Markoff mod $p$ graph
  • Abstract:
 “素数$p>3$に対し, Markoff mod $p$ graph $G_p$は位数$p$の有限体上のMarkoff方程式の非自明な解の集合上で定義される有限3-正則グラフである.
Bourgain-Gamburd-Sarnak (2016) によって$G_p$はエクスパンダー族をなすことが予想されており (BGS予想), 現在も未解決である.
一方で, BGS予想の傍証に関してはいくつかの結果が知られており, Courcy Ireland (2023) は $p=7$の場合を除いて, $G_p$が平面グラフではないことを証明した.
実際, 平面グラフはLipton-Tarjan (1971) のセパレーター定理よりエクスパンダー族をなしえないことから, 非平面性はエクスパンダー性の一つの必要条件でもある.
本発表では, $G_p$内の完全2部グラフ$K_{3,3}$の細分を具体的に複数構成することで, $p=7$の場合を除いて, $G_p$が射影平面にもトーラスにも埋め込み不可能であることを示す.
この結果はCourcy Ireland (2023) の結果の拡張となっており, 有界種数をもつグラフに関するセパレーター定理から, やはりBGS予想の傍証を与えている.
時間が許せば, 一般化したMarkoff mod $p$ graphに関する結果も紹介する.
本発表は山﨑 義徳 氏 (愛媛大学) との共同研究に基づく.”

Math-Fi seminar on 5 June. (Co-organized as a Quantum Walk Seminar)

2025.06.03 Tue up
  • Date: 5 June. (Thu.) 
  • Place: West Wing, 6th floor, Colloquium Room and on the Web (zoom)
  • Time: 15:40-19:00
 
  • Speaker 1: 鈴木良一 (東京理科大学)
  • Time: 15:40–16:40
  • Title: Malliavin-Mancino-Taylor type formulas and their applications to finance
  • Abstract: 
This presentation briefly introduces the Clark-Ocone-Haussmann (COH) formula, providing a martingale representation of random variables, and its Taylor-type extension, the Malliavin-Mancino-Taylor (MMT) formula. We then focus on developing MMT type formulas formulas for jump processes, specifically for $L^1$and $L^2$-pure jump additive processes, including versions under a change of measure. A key application is the derivation of explicit risk-minimizing hedging strategies in financial market models driven by pure jump additive processes. 
These results, from joint work by M. Handa, M.E. Mancino, advance Malliavin calculus tools for finance.
 
  • Speaker 2: Johannes Ruf (London School of Economics)
  • Time: 16:50-17:50
  • Title: Predictable variations in stochastic calculus
  • Abstract: 
The focus of this talk is the transformation of increments of a stochastic process by a predictable function. Many operations in stochastic analysis can be considered under this point of view. Stochastic integrals, for example, are linear functionals of process increments.  Although mathematically equivalent, focusing on transformation of increments often leads to simpler proofs of more general statements in stochastic calculus. In this talk specifically, we illustrate how considering predictable variations lead to various Ito-type formulas.
Joint work with Ales Cerny
 
  • Speaker 3: 寺田 知幸（金沢工業大学）
  • Time: 18:00-19:00
  • Title: Szegedy walkの確率測度と再帰性に関する最近の研究
  • Abstract: 
量子ウォークの挙動を明らかにする上で、ウォーカーの確率測度を明示的に求めることは、基本的かつ重要な問題である。本講演では、パスグラフ上のSzegedy walkに対するスペクトル解析を通じて、この確率測度を導出する手法を紹介する（今野・井手・寺田, 2023,YMJ）。具体的には、パスグラフ上のランダムウォークから誘導されるヤコビ行列の固有値および固有ベクトルを用いて、確率測度の公式を得る。パスグラフ上のランダムウォークでは、直交多項式の性質を活用し、Karlin–McGregorの公式によって確率測度が具体的に記述されることが知られているが、本研究はこれに対応する量子ウォークの結果とも言える。また、ランダムウォークおよび量子ウォークにおける再帰確率に関する最近の話題についても紹介する。
 

Math-Fi seminar on 29 May.

2025.05.29 Thu up
Date: 29 May. (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: Quantifying Uncertainty in Time-Frequency Analysis under Nonstationary Noise

Abstract: 
Time-frequency (TF) analysis provides a flexible framework for studying nonstationary time series, with wide applications across the sciences and engineering. Yet in real-world data, noise is ubiquitous and often nonstationary, and our ability to quantify uncertainty in TF representations remains limited. In this talk, we present recent progress on understanding and addressing this challenge. We show that the short-time Fourier transform (STFT) of a broad class of nonstationary noise processes that is defined via filtrations satisfying mild moment and dependence conditions can be approximated in L2 by a Gaussian process. This result arises from a sequential Gaussian approximation theorem, which may be of independent interest. In the presence of signal (the nonnull setup), we prove that the reconstruction formula underlying the synchrosqueezing transform (SST) remains stable under such noise, with uniform error bounds. When the noise satisfies a stronger local stationarity property, we develop a bootstrap procedure with theoretical guarantee to quantify uncertainty in both the STFT and SST, which relies on a time-varying autoregressive approximation of the noise. We conclude by demonstrating the practical value of this framework through an application to airflow signals recorded during sleep.

Math-Fi seminar on 22 May. (Co-organized as a Quantum Walk Seminar)

2025.05.20 Tue up
  • Date: 22 May. (Thu.) 
  • Place: West Wing, 6th floor, Colloquium Room and on the Web (zoom)
  • Time: 16:50–19:00
 
  • Speaker 1: 難波 隆弥（京都産業大学）
  • Time: 16:50-17:50
  • Title: 多重ゼータ関数と高次元ランダムウォーク
  • Abstract: 
一般にある多変数関数が特性関数となるか否かを判別することは, 対応する測度が高次元離散型確率分布となることが自明でない場合には難しいことが知られている. 本講演ではd次元整数格子上に有限個の点, または可算無限個の点に重みをもつ高次元離散型分布及びその畳込により得られるランダムウォークを多重ゼータ関数及び多変数Eule 積を用いて表記する. 特に後者の場合に, 対応する特性関数が無限分解可能となるための簡易な十分条件を与える.
 
 
  • Speaker 2: 渡邉 聡（株式会社KDDI総合研究所）
  • Time: 18:00–19:00
  • Title: Lackadaisical quantum walkによる頂点探索
  • Abstract: 
quantum walkは頂点グラフの目標点(marked points)を探索する際に用いられる。このquantum walkでself loopを加えたものをlackadaisical quantum walkと呼び、探索の成功確率の向上や探索の高速化に用いられてきた。
　ここで頂点グラフに置いて、従来のコイン作用素では探索できないような例外的な配置が存在する。例えば2次元の周期境界条件を課した格子において、隣接した2点がmarked pointsの場合、対角線上にmarked pointsが並んだ場合などは例外的な配置に相当し、従来のGrover walkやlackadaisical quantum walkでは探索できないような配置になっている。
　本発表ではlackadaisical quantum walkのコイン演算子を変形した新たなコインを導入することによって頂点グラフにおける様々な例外的配置を探索できることを紹介する。また他のコインでは例外的な配置を探索できないことをquantum walkの定常状態を構成することによって理論的に示せるということを紹介する。発表に置いては今回新たに研究した2次元の周期境界条件を課した格子にHanoi型のlong edgeを付け加えたグラフについての結果を紹介する。本研究はGiri Ranjan Pulak氏(株式会社KDDI総合研究所)との共同研究に基づいている。

Math-Fi seminar on 15 May.

2025.05.13 Tue up
  • Date: 15 May. (Thu.) 
  • Place: West Wing, 6th floor, Colloquium Room and on the Web (zoom)
  • Time:  16:50–19:00
     
  • Speaker 1: Ju-Yi Yen (University of Cincinnatti)
  • Time: 16:50–17:50
  • Title: Excursion-Theoretic Approaches to Limit Theorems for Additive Functionals of Markov Processe
  • Abstract:
This talk explores a uni ed excursion-theoretic framework for proving limit theorems of additive functionals associated with various classes of Markov processes, including Brownian motion, null recurrent di usions, and symmetric strong Markov processes. Motivated by classical results such as the Darling Kac theorem and the Ray Knight theorems, we investigate how local time provides a natural time scale for analyzing functionals of processes that do not admit nite invariant measures. We begin with Brownian motion, where the inverse local time at zero enables a strong law of large numbers and central limit theorem for time integrals of functions along sample paths. These results are revisited using Itos excursion theory, highlighting its utility in both deriving moments and capturing uctuation behavior. We then extend these ideas to null recurrent linear di usions by transforming them into time-changed Brownian motions via Zvonkins method. Excursion-based representations again yield central limit theorems, even in the absence of stationary distributions. Finally, we examine a broader setting of symmetric strong Markov processes, where local times are used to de ne regenerative structures. By leveraging generalized RayKnight theorems and Gaussian process techniques, we establish limit theorems under minimal assumptions, unifying previous results under a single probabilistic strategy. This excursion-centric viewpoint not only clari es asymptotic behaviors but also opens paths toward analyzing more complex dynamics such as complex-valued processes and higher-dimensional extensions.

 
  • Speaker 2: Loïc Chaumont (Université d’Angers)
  • Time: 18:00–19:00
  • Title: Levy processes resurrected in the positive half-line
  • Abstract:
Levy processes resurrected in the positive half-line is a Markov process obtained by removing successively all jumps that make it negative. A natural question, given this construction, is whether the resulting process is absorbed at 0 or not. In this work, we give conditions for absorption and conditions for non absorption bearing on the characteristics of the initial Levy process. First, we shall give a detailed definition of the resurrected process whose law is described in terms of that of the process killed when it reaches the negative half line. In particular, we will specify the explicit form of the resurrection kernel. Then we will see that when the initial Levy process X creeps downward and satisfies certain additional condition, the resurrected process is absorbed at 0 with probability one, independently of its starting
point. Some criteria for absorption and some criteria for non absorption will be given. The most delicate case is when X enters immediately in the negative half line and drifts to -infinity. It is then possible to give a sufficient condition for absorption but up to now, even when X is the negative of a subordinator, we do not know whether this condition can be dropped or not. We shall take a closer look at the case of stable processes. This is a joint work with Victor Rivero (CIMAT, Guanajuato) and Marria Emilia Caballero (Instituto de Matematicas, UNAM, Mexico).
 

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