Apr 2023-Mar 2024

Math-Fi seminar on 21 Dec.

2023.12.19 Tue up
  • Date: 21 Dec. (Thu.)
  • Place: W.W. 6th-floor, Colloquium Room and on the Web (Zoom)
  • Time: 16:30 – 18:00
  • Speaker: Noriyoshi Sakuma (Nagoya City University)
  • Title: The Outlier Problem from a View of non-commutative Probability Theory I
  • Abstract:
The outlier problem in random matrix theory is one of the important topics. In this talk, I will explain a non-commutative probabilistic method for considering the outlier problem. The notion of cyclic monotone independence plays a similar role to that of free independence. If time permits, I will also introduce nonrandom models.

Math-Fi seminar on 18 Dec.

2023.12.12 Tue up
  • Date: 18 Dec. (Mon.)
  • Place: W.W. 6th-floor, Colloquium Room and on the Web (Zoom)
  • Time: 16:30 – 18:00
  • Speaker: Hau-Tieng Wu (Courant Institute of Mathematical Sciences at New York University)
  • Title: Nonstationary biorhythm analysis through landmark diffusion with clinical application
  • Abstract:
Compared with the commonly collected health information, long-term and high-frequency physiological time series that exhibit nonstationary traits provide abundant information from an alternative perspective. However, it is challenging to extract clinically applicable data from these raw time series due to various impediments. Fueled by clinical necessities, physiological expertise, and clinical observations, we introduce a novel latent diffusion geometry-based signal processing method. The algorithm is explicitly designed to handle enormous datasets, including ultra-long and high-frequency time series, with ease, while remaining resilient to color and heterogeneous noise, underpinned by sound theoretical support. We will discuss an application of this method to assess the clinical outcome of liver transplants by uncovering the delicate details concealed in the arterial blood pressure signal recorded during surgery that remain indistinguishable to the naked eye.

Math-Fi seminar on 30 Nov.

2023.11.24 Fri up
  • Date: 30 Nov. (Thu.)
  • Place: W.W. 6th-floor, Colloquium Room and on the Web (Zoom)
  • Time: 16:30 – 18:00
  • Speaker: Andrea Macrina (University College London)
  • Title: Filtered Arcade Martingales: An Alternative Approach to Martingale Optimal Transport?
  • Abstract:
Arcade processes are a class of continuous stochastic processes that interpolate in a strong sense between zeros at fixed pre-specified times. Their additive randomization allows one to match any finite sequence of target random variables, indexed by the given fixed dates, on the whole probability space. The filtrations generated by such processes are utilized to construct a class of martingales which interpolate between the given target random variables. These so-called filtered arcade martingales (FAMs) are almost-sure solutions to the martingale interpolation problem and reveal an underlying stochastic filtering structure. In the special case of conditionally Markov randomized arcade processes, the dynamics of FAMs are informed through Bayesian updating. FAMs can be connected to martingale optimal transport (MOT) by considering optimally coupled target random variables. Moreover, FAMs allow to formulate an information-based martingale optimal transport problem, which enables the introduction of noise in MOT, in a similar fashion to how Schrödinger’s problem introduces noise in optimal transport. This information-based transport problem is concerned with selecting an optimal martingale coupling for the target random variables under the influence of the noise that is generated by an arcade process. 

Math-Fi seminar on 12 Oct.

2023.10.06 Fri up
  • Date: 12 Oct. (Thu.)
  • Place: W.W. 6th-floor, Colloquium Room and on the Web (Zoom)
  • Time: 16:30 – 18:00
  • Speaker: Syoiti Ninomiya (Tokyo Institute of Technology)
  • Title: 確率微分方程式の高次弱近似アルゴリズムの構造を模った深層学習機械
  • Abstract:
確率微分方程式の高次弱近似アルゴリズムの構造を模したネットワーク構造を持つ深層学習機械を提案する. この機械は学習によってある拡散過程を得ること—具体的には金融派生商品のヘッジ戦略をこの機械によって「陽に得る」こと—を目的とするものである. 実際にこれらを作成して数値実験を行なったところ, 高次弱近似に基づく機械はアメリカンオプションの価格計算とそのヘッジ過程を学習することに成功した. 

Math-Fi seminar on 18 May

2023.05.15 Mon up
  • Date: 18 May (Thu.)
  • Place: W.W. 6th-floor, Colloquium Room and on the Web (Zoom)
  • Time: 16:30 – 18:00
  • Speaker: Toru Igarashi (Chuo University)
  • Title: Dually Flat Structure on Asset Pricing Models
  • Abstract: 
In this talk, we consider asset pricing models as dually flat manifolds and give financial interpretations to its geometric properties. We find that (1) the coefficients of dual connection correspond to the prudence of utility function; (2) a unique equilibrium is the intersection of two submanifolds (that represent investment strategies and prices); (3) the Hansen–Jagannathan distance of risk-neutral measures can be interpreted as a special case of a Bregman divergence that is a natural divergence on dually flat manifolds. We also provide a computational method for finding equilibrium numerically.

Math-Fi seminar on 27 Apr.

2023.04.24 Mon up
  • Date: 27 Apr. (Thu.)
  • Place: W.W. 6th-floor, Colloquium Room and on the Web (Zoom)
  • Time: 16:30 – 18:00
  • Speaker: Katsunori Fujie (Hokkaido University)
  • Title: Combinatorial approach to finite free probability
  • Abstract: 
Abstract: Since the 2010s, when Marcus, Spielman, and Srivastava solved the Kadison–Singer conjecture and found a connection between its solution and free probability theory, this research area has been called finite free probability.
Much progress has been made recently, and of particular interest are finite free cumulants by Octavio and Perales, where free cumulants are the basic tool used as a discretization for the characteristic function in the context of free probability.
Just recently, the speaker, Octavio Arizmendi (CIMAT) and Yuki Ueda (Hokkaido Education University) have proved a few limit theorems in finite free probability by a unified approach using finite free cumulants in arXiv:2303.01790.
The purpose of this talk is to introduce our approach.
After a brief description of the field, we will explain the combinatorial formulas that are key to the solution.
Then, as an application, we will present the limit theorems in finite free probability and their correspondence with free probability theory.

Math-Fi seminar on 20 Apr.

2023.04.17 Mon up
  • Date: 20 Apr. (Thu.)
  • Place: W.W. 6th-floor, Colloquium Room and on the Web (Zoom)
  • Time: 16:30 – 18:00
  • Speaker: Thomas Cavalazzi (Université de Rennes 1)
  • Title: Quantitative weak propagation of chaos for McKean-Vlasov SDEs driven by $\alpha$-stable  processes
  • Abstract: 
In this talk, we will deal with McKean-Vlasov Stochastic Differential Equations (SDEs) driven by $\alpha$-stable processes, with $\alpha \in (1,2)$. We make Hölder-type assumptions on the coefficients, with respect to both space and measure variables. 
We will study the associated semi-group, acting on functions defined on the space of probability measures, through the related backward Kolmogorov Partial Differential Equation (PDE), which describes its dynamics. 
We will focus in particular on its regularizing properties. 
The study relies on differential calculus for functions defined on the space of measures, and on Itô’s formula along flows of marginal distributions of jump processes defined with Poisson random integrals. 
We will finally use the preceding tools to prove quantitative weak propagation of chaos for the mean-field interacting particle system associated with the McKean-Vlasov SDE.

Math-Fi seminar on 6 Apr.

2023.04.04 Tue up
  • Date: 6 Apr. (Thu.)
  • Place: W.W. 6th-floor, Colloquium Room and on the Web (Zoom)
  • Time: 16:30 – 18:00
  • Speaker: Tommaso Mariotti (Scuola Normale Superiore di Pisa)
  • Title: Coding examples with Python