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Seminar information archive ～04/25｜Today's seminar 04/26 | Future seminars 04/27～

2025/03/17

Operator Algebra Seminars

16:45-18:15 Room #126 (Graduate School of Math. Sci. Bldg.)
The day of the week and the room are different from the usual ones.
Ingo Runkel (Univ. Hamburg)
Lattice models and topological symmetries from 2d conformal field theory
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm

Tokyo-Nagoya Algebra Seminar

14:30-16:00 Online
Junyang Liu (University of Science and Technology of China)
On Amiot's conjecture (English)

[ Abstract ]
In 2010, Claire Amiot conjectured that algebraic 2-Calabi-Yau categories with cluster-tilting object must come from quivers with potential. This would extend a structure theorem obtained by Keller-Reiten in the case where the endomorphism algebra of the cluster-tilting object is hereditary. Many other classes of examples are also known. We will report on the proof of the conjecture in the general case for categories with *algebraic* 2-Calabi-Yau structure. This result has been obtained in joint work with Bernhard Keller and is based on Van den Bergh's structure theorem for complete Calabi-Yau algebras. We also generalize his structure theorem to the relative case and use it to prove a relative variant of the conjecture.

ミーティング ID: 853 1951 5047
パスコード: 900788

[ Reference URL ]
https://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html

2025/02/21

Operator Algebra Seminars

13:30-15:00 Room #002 (Graduate School of Math. Sci. Bldg.)
The day of the week, the time slot and the room are different from the usual ones.
David O'Connell (OIST)
Colimits of $C^*$-algebras in Quantum Field Theory

[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm

2025/02/20

Operator Algebra Seminars

16:45-18:15 Room #122 (Graduate School of Math. Sci. Bldg.)
The day of the week is different from the usual one.
Christoph Schweigert (Univ. Hamburg)
Nakayama functors, relative Serre functors and some applications
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm

Discrete mathematical modelling seminar

16:00-17:30 Room #126 (Graduate School of Math. Sci. Bldg.)
Andy Hone (University of Kent)
Integrable maps associated with Stieltjes fractions and the Volterra lattice

[ Abstract ]
Quite recently, a classification of birational maps in 4D that have a Lagrangian structure and are Liouville integrable was derived by Gubbiotti, building on earlier results obtained with Joshi, Tran and Viallet. Here we show that the first member in this family naturally arises from the Stieltjes continued fraction expansion of a meromorphic function on a genus 2 curve, and is associated with special solutions of the Volterra lattice hierarchy. This construction extends to hyperelliptic curves of all genera, producing a family of Poisson maps on an affine space of Lax matrices, with explicit Hankel determinant expressions for the tau functions. In particular, in the genus 1 case one finds elliptic solutions of the Volterra lattice, obtained from a QRT map whose tau functions satisfy the Somos-5 relation. We also observe that the other 4D maps in Gubbiotti's classification correspond to genus 2 solutions of two distinct forms of the modified Voltera lattice. If time permits, we will also mention the connection with families of orthogonal polynomials. This is joint work with John Roberts, Pol Vanhaecke and Federico Zullo.

Seminar on Probability and Statistics

13:00-14:10 Room #056 (Graduate School of Math. Sci. Bldg.)
Evgeny Spodarev (Universität Ulm)
Non-ergodic statistics for stationary-increment harmonizable stable processes (English)

[ Abstract ]
We consider the class of stationary-increment harmonizable stable processes $𝑋=\{ 𝑋(𝑡): 𝑡\in \mathbb{R} \}$ defined by $$𝑋(𝑡)=𝑅𝑒\left( \int_{\mathbb{R}} (𝑒^{𝑖𝑡𝑥}−1) \Psi (𝑥) 𝑀_{\alpha}(𝑑𝑥) \right), \quad 𝑡\in\mathbb{R},$$ where $𝑀_{\alpha}$ is an isotropic complex symmetric $\alpha$-stable (𝑆$\alpha$𝑆) random measure with Lebesgue control measure. This class contains real harmonizable fractional stable motions, which are a generalization of the harmonizable representation of fractional Brownian motions to the stable regime, when $\Psi(𝑥)=|𝑥|−𝐻−1/\alpha, 𝑥\in\mathbb{R}$. We give conditions for the integrability of the path of $𝑋$ with respect to a finite, absolutely continuous measure, and show that the convolution with a suitable measure yields a real stationary harmonizable 𝑆$\alpha$𝑆 process with finite control measure. Such a process admits a LePage type series representation consisting of sine and cosine functions with random amplitudes and frequencies, which can be estimated consistently using the periodogram. Combined with kernel density estimation, this allows us to construct consistent estimators for the index of stability $\alpha$ as well as the kernel function $\Psi$ in the integral representation of $𝑋$ (up to a constant factor). For real harmonizable fractional stable motions consistent estimators for the index of stability $\alpha$ and its Hurst parameter $𝐻$ are given, which are computed directly from the periodogram frequency estimates.

[ Reference URL ]
https://docs.google.com/forms/d/e/1FAIpQLSd5_4NM3xazVUAARMhyv_e55RsYZFyfpOHqC0oGYasM2NLOqQ/viewform

2025/02/13

Infinite Analysis Seminar Tokyo

13:30-17:00 Room #118, hybrid seminar (Graduate School of Math. Sci. Bldg.)
Genki Shibukawa (Kobe University) 13:30-15:00
Basics and developments of the $\mu$-function (First part) (日本語)

[ Abstract ]
First part (speaker: Genki Shibukawa) Starting from a short introduction to the original Zwegers' $\mu$ function, we explain some basic tools of $q$-special functions ( $q$-hypergeometric functions) and $q$-analysis ($q$-difference equations, $q$-Borel and $q$-Laplace transformations) which are necessary to give a special function theoretic interpretation of the $\mu $-function. In these settings, we introduce the generalized $\mu $-function which is a one-parameter deformation of the Zwegers' $\mu $-function, and derive its basic properties such as symmetry, explicit formulas, difference relations, and connection formulas. In particular, we explain the relationship between the generalized $\mu $-function and $q$-Hermite polynomial (function).

Satoshi Tsuchimi (Kobe University) 15:30-17:00
Basics and developments of the $\mu$-function (Second part) (日本語)

[ Abstract ]
Second part (speaker: Satoshi Tsuchimi)
In this part, we present some advanced topics of the $\mu$ function. First, we show that the $\mu$-functions naturally appear in special solutions of factorized higher-order $q$-difference equations. Next, by applying the above $q$-analytic methods, we introduce a multivariate analogue of the generalized $\mu$-function and give some formulas. Finally, by similar methods, we construct another generalization of the $\mu$-function from the Kontsevich function which is an important function in knot invariants. This generalization of the $\mu$-function is related to the big $q$-Hermite polynomial (function) which is a 1 parameter deform of the $q$-Hermite polynomial.

2025/02/07

Seminar on Probability and Statistics

14:00-15:10 Room #128 (Graduate School of Math. Sci. Bldg.)
ハイブリッド開催
Juho Leppänen (Tokai University)
A multivariate Berry–Esseen theorem for deterministic dynamical systems (English)

[ Abstract ]
Many chaotic deterministic dynamical systems with a random initial state satisfy limit theorems similar to those of independent random variables. A classical example is the Central Limit Theorem, which, for a broad class of ergodic measure-preserving systems, is known to follow from a sufficiently rapid decay of correlations. Much work has also been done on the rate of convergence in the CLT. Results in this area typically rely on additional structure, such as suitable martingale approximation schemes or a spectral gap for the Perron–Frobenius operator.
In this talk, we present an adaptation of Stein's method for multivariate normal approximation of deterministic dynamical systems. For vector-valued processes generated by a class of fibred systems with good distortion properties (Gibbs–Markov maps), we derive bounds on the convex distance between the distribution of scaled partial sums and a multivariate normal distribution. These bounds, which are deduced as a consequence of certain correlation decay criteria, involve a multiplicative constant whose dependence on the dimension and dynamical quantities is explicit.

[ Reference URL ]
https://u-tokyo-ac-jp.zoom.us/meeting/register/lmbyLgO6RNi1GnoovqW_Sg

2025/02/06

Tokyo Probability Seminar

16:00-17:30 Room #126 (Graduate School of Math. Sci. Bldg.)
We are having teatime from 15:15 in the common room on the second floor. Please join us.
Jacek Wesolowski (Warsaw University of Technology)
Asymptotics of random Motzkin paths

[ Abstract ]
We study Motzkin paths of length L with general weights on the edges and end points. We investigate the limit behavior of the initial and final segments of the random Motzkin path viewed as a pair of processes starting from each of the two end points as L becomes large. Macroscopic limits of the resulting processes (under two different asymptotic regimes) appear to be non-Brownian parts of stationary measures for the KPZ equation and hypothetical KPZ fixed point on the half-line. The talk is based on a joint paper with W. Bryc (Univ. of Cincinnati) and A. Kuztetsov (York Univ., Toronto) - to appear in IMRN, available also on arXiv: https://arxiv.org/abs/2402.00265