News&Events

Ritsumeikan Mathematics Data Science Seminar (2026/12/7)

2026.11.05 Thu up
  • Date: 7 Dec. (Mon.)
  • Place: West Wing, 6th floor, Colloquium Room and on the Web (zoom) 
  • Time: 18:00-19:00
  • Speaker : Tomoyuki Higuchi (Faculty of Science and Engineering, Chuo University)
  • Title: Data Assimilation Being Transformed by Generative AI
  • Abstract:
In general, numerical simulation is a procedure that discretizes the governing equations of a phenomenon in time and space and performs numerical integration. Numerical simulations inevitably involve a wide variety of errors, including computational errors, as well as uncertainties arising from unknown conditions, which hinder improvement in the accuracy of predictions. Data assimilation was proposed to partially solve this problem. Data assimilation in a form close to the current one emerged in meteorology and oceanography in the 1990s, and its usefulness has since spread to a wide range of fields. The essence of data assimilation lies in integrating the information from numerical simulations with big observational and measurement data by means of Bayes’ theorem. Over the past two to three years, the trend in research and development of data assimilation has been changing significantly due to generative AI. Research on using generative AI to accelerate numerical simulations itself began about five or six years ago, using what are now regarded as legacy generative AI models such as variational autoencoders and GANs. What is currently having a major impact is prediction by Transformer-based foundation models and super-resolution based on diffusion models. The former has greatly benefited the accuracy and speed of prediction; indeed, in forecasting the track of Typhoon No. 30 this year, AI clearly outperformed conventional methods. The latter contributes to simplifying computation and to discovering unknown phenomena. In this talk, I will review the history of data assimilation research and explain the current state of the major advances brought about by generative AI.

立命館大学数理データ科学セミナー (2026/11/2)

2026.10.22 Thu up
  • Date: 2 Nov. (Mon.)
  • Place: West Wing, 6th floor, Colloquium Room and on the Web (zoom) 
  • Time: 17:00-18:00
  • Speaker : Tatsuya Kawahara（Kyoto University Graduate School of Informatics）
  • Title: 自動音声認識の進展と数理・データサイエンス的考察
  • Abstract:
人間の話す音声を自動で認識（テキスト化）する研究は、約70年前に京都大学 で開始された。その後、様々な方法論と技術の革新を経て、会議録の作成や会 話ロボットなどに実用化されている。数理的なモデル化から深層学習モデルへ の進展への経緯をふりかえり、データサイエンス的な観点から考察を行う。

Math-Fi seminar on 29 Oct. (Co-organized as a Quantum Walk Seminar)

2026.10.22 Thu up
  • Date: 29 Oct. (Thu.)
  • Place: West Wing, 6th floor, Colloquium Room and on the Web (zoom)
  • Time: 16:50-19:00

  • Speaker 1: Naoki Kubota（Nihon University）
  • Time:16:50-17:50
  • Title: フロッグモデルにおける拡散度合の変化について
  • Abstract:
本講演では，拡散現象を記述する数理モデルの1つである“フロッグモデル”を扱う．このフロッグモデルは，次のように「目覚めたカエル」と「眠ったカエル」の2種類によって構成される．まずは，正方格子の原点にのみ目覚めたカエルがいて，その他の頂点には眠ったカエルが確率正で配置されているとする．原点にいる目覚めたカエルはランダムウォークしながら正方格子上をぴょんぴょんと移動していき，眠ったカエルに遭遇する度にそれを目覚めさせていく（例えば，背中に乗っかって衝撃を与える様子を想像してほしい）．このようにして目覚めたカエル達は，正方格子上をそれぞれ独立にランダムウォークしていき，やはり眠ったカエル達を次々と目覚めさせていく．この覚醒の連鎖によって，時間の経過とともに目覚めたカエル達は増殖し正方格子上に拡散していく．
　例えば，カエルを情報，病原菌，火の粉の運搬者に置き換えれば，フロッグモデルはうわさ・伝染病の拡大，火災の延焼といった拡散現象を表すと考えられる．このような拡散現象において，「どの程度の時間でどこまで拡散するのか？」という“拡散度合”の解析は主要な課題の1つである．拡散度合の性質として，眠ったカエルの配置密度が高いほど目覚めたカエル達の拡散が加速することは容易に想像できる．本講演ではこの単調性の問題に着目し，眠ったカエル達の配置密度の変化が拡散度合に与える影響について，近年得られた結果を紹介する．
　なお，本講演の内容はVan Hao Can氏（Vietnam Academy of Science and Technology），中島秀太氏（慶應義塾大学），福島竜輝氏（筑波大学）との共同研究に基づく．

 

  • Speaker 2: Tomoyuki Shirai（Kyushu University）
  • Time:18:00-19:00
  • Title: 層状点過程の相関構造
  • Abstract:
実直線上の点配置が互いに交互に並ぶ interlacing (編み込み、絡み合い)構造はさまざまな場面に自然に現れる。典型的な例として、実零点のみをもつ $n$ 次多項式 $p_n$ を考えると、その導関数 $p’_n$ の零点は、もとの $n$ 個の実零点の間に一つずつ入り、互いに interlace する。さらに微分を繰り返すと、零点たちは階層的な interlacing 構造をなす。また，ランダム行列の主小行列の固有値などでも自然に現れる．本講演では，この構造をもつ層状点過程と，直列待ち行列から生じる層状点過程を取り上げ，それらの定常分布と相関構造を考察する．

Math-Fi seminar on 15 Oct. (Co-organized as a Quantum Walk Seminar)

2026.10.14 Wed up
  • Date: 15 Oct. (Thu.)
  • Place: West Wing, 6th floor, Colloquium Room and on the Web (zoom)
  • Time: 16:50-19:00

  • Speaker 1: Riki Kitano（Ritsumeikan University）
  • Time:16:50-17:50
  • Title: パスグラフ上の反射ウォークとゼータ関数
  • Abstract:
有限パスグラフ上の反射壁ランダムウォークと、それに対応する Szegedy ウォークに付随するゼータ関数を考える。推移確率が対称でない場合も含めた一般化反射原理を考え、ランダムウォークのゼータ関数を、境界部分と、二つの境界反射が生成する無限二面体群の各元に対応する局所対応部分との積として表す。さらに、古典系と量子系のゼータ関数を結ぶ Konno-Sato 対応を局所対応部分ごとに定め、この分解を量子ウォークへ移す。本講演では、これらの構成やトレース公式を紹介し、得られる分解と極限における構造との関係にも触れる。
 
  • Speaker 2: Akinari Hoshi（Nigata University）
  • Time:18:00-19:00
  • Title: Rationality problem for fields of invariants, norm one tori and Hasse norm principle
  • Abstract:
The aim of this talk is to give a survey of recent developments in the rationality problem
for fields of invariants, e.g. Noether’s problem, rationality problem for algebraic tori,
norm one tori and quasi-monomial actions.
I will give some explicit examples of (non-)stably (resp. retract) rational fields
which are weaker concepts than the rationality.
Negative results may be obtained by using (stable) birational invariants, e.g. flabby class,
unramified Brauer (cohomology) group which is an avatar of the Artin-Mumford invariant.
By Colliot-Thelene and Voisin’s result (2012, Duke Math. J.), an explicit example of
non-vanishing of the unramified cohomology group of degree three provides an explicit
counter-example of the integral Hodge conjecture.
A counter-example of Noether’s problem for N\rtimes A_6 over C is also given
where A_6 is the alternating group of degree 6 and N=(Z/10Z)^9.
As an application, we present recent results about Hasse norm principle for K/k
where K/k is a finite separable field extension of a global field k.
 

Math-Fi seminar on 1 Oct. (Co-organized as a Quantum Walk Seminar)

2026.10.14 Wed up
  • Date: 1 Oct. (Thu.)
  • Place: West Wing, 6th floor, Colloquium Room and on the Web (zoom)
  • Time: 16:50-18:20
  • Speaker: Shingo Sugiyama (Kanazawa University) 
  • Title: L関数の零点分布とランダム行列の固有値分布について
  • Abstract:
L関数とはRiemannゼータ関数の一般化にあたる関数であり，素数分布の観点で整数論の重要な対象として研究されてきた．20世紀末にKatz と Sarnak は，「L関数の族の低い位置にある零点の分布は，コンパクト行列群内のランダム行列の固有値の分布と一致するはずである」という密度予想を提唱した．
講演者は近年，L関数の特殊値で重み付けられたL関数の族の零点密度に関する，重み付き密度予想を提唱した．
本講演では，重み付き密度予想に関してDirichlet L関数の族や保型L関数の族の場合に得られた結果を紹介する．
講演内容の一部はAde Irma Suriajaya（九州大学）との共同研究および源嶋孝太（大谷大学）との共同研究に基づく．
 

Math-Fi seminar on 15 Oct. (Co-organized as a Quantum Walk Seminar)

2026.10.14 Wed up
有限パスグラフ上の反射壁ランダムウォークと、それに対応する Szegedy ウォークに付随するゼータ関数を考える。推移確率が対称でない場合も含めた一般化反射原理を考え、ランダムウォークのゼータ関数を、境界部分と、二つの境界反射が生成する無限二面体群の各元に対応する局所対応部分との積として表す。さらに、古典系と量子系のゼータ関数を結ぶ Konno-Sato 対応を局所対応部分ごとに定め、この分解を量子ウォークへ移す。本講演では、これらの構成やトレース公式を紹介し、得られる分解と極限における構造との関係にも触れる。
 
The aim of this talk is to give a survey of recent developments in the rationality problem
for fields of invariants, e.g. Noether’s problem, rationality problem for algebraic tori,
norm one tori and quasi-monomial actions.
I will give some explicit examples of (non-)stably (resp. retract) rational fields
which are weaker concepts than the rationality.
Negative results may be obtained by using (stable) birational invariants, e.g. flabby class,
unramified Brauer (cohomology) group which is an avatar of the Artin-Mumford invariant.
By Colliot-Thelene and Voisin’s result (2012, Duke Math. J.), an explicit example of
non-vanishing of the unramified cohomology group of degree three provides an explicit
counter-example of the integral Hodge conjecture.
A counter-example of Noether’s problem for N\rtimes A_6 over C is also given
where A_6 is the alternating group of degree 6 and N=(Z/10Z)^9.
As an application, we present recent results about Hasse norm principle for K/k
where K/k is a finite separable field extension of a global field k.
 
  • Date: 15 Oct. (Thu.)
  • Place: West Wing, 6th floor, Colloquium Room and on the Web (zoom)
  • Time: 16:50-19:00
    • Speaker 1: Riki Kitano（Ritsumeikan University）
    • Time:16:50-17:50
    • Title: パスグラフ上の反射ウォークとゼータ関数
    • Abstract:
    • Speaker 2: Akinari Hoshi（Nigata University）
    • Time:18:00-19:00
    • Title: Rationality problem for fields of invariants, norm one tori and Hasse norm principle
    • Abstract:

Math-Fi seminar on 17 Sep.

2026.09.17 Thu up
  • Date: 17 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 3 Sep.

2026.09.03 Thu up
  • 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.

2026.08.27 Thu up
  • 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.

Math-Fi seminar on 20 Aug.

2026.08.18 Tue up
  • 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)

2026.07.30 Thu up
  • 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.

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