Department of Mathematical Sciences, Ritsumeikan University Web Page

立命館大学数理データ科学セミナー (2026/11/2)

horie — Thu, 22 Oct 2026 05:02:42 +0000

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)

horie — Thu, 22 Oct 2026 04:51:20 +0000

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)

horie — Wed, 14 Oct 2026 06:11:09 +0000

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)

horie — Wed, 14 Oct 2026 06:07:11 +0000

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)

horie — Wed, 14 Oct 2026 06:03:32 +0000

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.

horie — Thu, 17 Sep 2026 01:21:43 +0000

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.

horie — Thu, 03 Sep 2026 05:15:14 +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:

Math-Fi seminar on 27 Aug.

horie — Thu, 27 Aug 2026 04:14:25 +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.

Math-Fi seminar on 20 Aug.

horie — Tue, 18 Aug 2026 07:14:18 +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 07:36:18 +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.