立命館大学数理科学科

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

horie — Wed, 14 Oct 2026 06:01:51 +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 — Thu, 01 Oct 2026 07:08:11 +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 17 Sep.

horie — Thu, 17 Sep 2026 01:20:59 +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 05:13:27 +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:

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