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数理科学科談話会（2026/06/08）

2026.06.08 Mon up
日時：2026年6月8日（月）
場所：立命館大学BKCキャンパスウェストウィング6階　談話会室
 
プログラム：
17:00~17:50 Frederic Herau (Univ. Nantes)
>From hypocoercivity with small parameters to immiscibility considerations

18:00~18:50 木上淳（京都大学）
Toward  ”Analysis on Metric spaces”; Constructions of Sobolev spaces and Brwonian motions
（距離空間上の解析学に向けて：ソボレフ空間とブラウン運動の構成）
 
19:00~ レセプションパーティー
 
 
アブストラクト：
From hypocoercivity with small parameters to immiscibility considerations 
Abstract : The theory of hypocoercivity is rather new, going back
to the early 20′ and dealing with the large time behavior of kinetic equations and out of equilibrium systems.
In this talk, I will recall some historical points about hypocoercivity and present some recent preliminary asymptotic
results related to immiscibility of fluids.
 
 
Toward  ”Analysis on Metric spaces”; Constructions of Sobolev spaces and Brwonian motions
Abstract: A wide variety of “Analysis” has been developed  and applied to every area of science since the introduction of differentiation by Newton and Leibniz. However, the emergence of “fractals” as models of natural objects and phenomena has raised the question of how we can tackle analysis on spaces that are nowhere smooth. For example, typical self-similar sets, such as the Sierpinski gasket and carpet, do not possess a differential structure; hence, it is difficult to apply analyses based on differentiation. Based on this question, studies on analysis on fractals began in the late 1980s with the pioneering works of Goldstein, Kusuoka, and Barlow-Perkins who constructed the Brownian motion on the Sierpinski gasket. In this talk, I will review some of the progress made toward analyzing (non-smooth) metric spaces, specifically the construction of Sobolev spaces and Brownian motions.
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タイトル：距離空間上の解析学に向けて：ソボレフ空間とブラウン運動の構成
アブストラクト：ニュートンとライプニッツによって微分の概念が導入されて以来、様々な解析学が発展し、応用されてきた。一方、１９７０年代にマンデルブローは自然界の物の形のモデルとしてフラクタルという概念を導入した。自己相似集合に代表されるフラクタルは、至る所滑らかでない構造をもっており、従来の微分を基礎とした解析学を適用することは難しい。それでは、フラクタルのような複雑な空間の上での現象を記述する解析学はどのように構築すればよいのであろうか？この疑問に答えるべく、１９８０年代後半から「フラクタル上の解析学」の研究が、Goldstein, Kusuoka, Barlow-Bass による Sierpinski gasket 上へブラウン運動の構成を嚆矢として発展してきた。この講演では、フラクタルのような（滑らかでない）距離空間上での解析学の研究の発展を、とくにソボレフ空間とブラウン運動の構成という視点から概観する。
 

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

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.

立命館大学 集中セミナー

2026.04.07 Tue up
  • Date: 9月14日－18日
  • Place: ウエストウィング6階談話会室あるいは７階のセミナー室　対面およびオンライン
  • Time: 
9月14日(月)～17日 (木)
2コマ:  
(1) 13:30～15:00
(2) 15:15～16:45
9月18日 (金)
1コマ13:30～15:00
  • Speaker :  日合文雄（東北大学名誉教授）
  • Title: 行列解析と量子情報への応用 
  • Abstract: 
この集中セミナーでは，最初に作用素平均と作用素パースペクティブを復習してから，作用素・
行列の作用素不等式，マジョリゼーション，トレース不等式などを解説する．次に，量子情報
で重要な種々の量子f-ダイバージェンスを説明する．特に最近発展しているホッケースチック
f-ダイバージェンスを取り上げる．さらに，量子情報幾何で重要なFisher 情報量（単調計量）
と関連するいくつかの話題を解説する．
 
 
 

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.

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