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There has been extensive research on the connections between graph theory and hyperplane arrangements. Classical results include studies on freeness, which is an important class in the theory of hyperplane arrangements, for arrangements determined by graphs. More recently, research has diversified in multiple directions, such as modifying the definitions on the graph side or altering the properties required of the arrangements. In this talk, we provide a cross-sectional overview of these developments.

In the real world, we often encounter time series data, such as from finance, healthcare and industrial monitoring. In finance, one of the important problems is to forecast stock prices. In industrial monitoring, one of the important problems is to classify the data: to distinguish the source of the data or to determine whether a machine is broken.

There are many classical ways to do time series classification (TSC). For example, we often use dynamic time warping (DTW) to measure the difference between time series data. Then we use other algorithms, such as k-nearest neighbor (kNN) or support vector machines.

On the other hand, topological data analysis (TDA) is a new area in data analysis. It focuses on the topology of data, which is a robust feature. In time series data analysis, one of the famous theorems is Takens delay embedding theorem, which shows that generally we can see time series data as a sequence of observed values from a dynamical system. Through this theorem, it is possible to introduce TDA in time series data analysis.

In this talk, we will dive deeper into how these methods work.

As both a licensed attorney and a PhD student majoring in mathematics, the presenter examines a decision-making framework concerning causation in litigation. The index commonly employed in legal practice cannot be interpreted as the probability of causation without specific assumptions. In this presentation, the presenter emphasizes that the existing framework has been adopted without explicit consideration of such assumptions and clarifies the implicit premises underlying legal decisions. Furthermore, the presenter proposes a new decision-making framework that can be applied to more general cases in which those assumptions no longer hold.

When we arrange a finite set of lines in a two-dimensional real vector space, the complement of the lines can be regarded as a division of the plane. Let us call the maximal connected components chambers. It is well known that the number of chambers becomes maximal when all intersection points are double points. However, determining the arrangement that gives the minimal number is much more difficult. A very famous theorem in the theory of hyperplane arrangements, called Yoshinaga's criterion, provides a lower bound for the number of chambers in an algebraic way. We study the relationship between the chamber structures of line arrangements in $\mathbb{R}^2$ and algebraic structures called logarithmic derivation modules. 

We introduce the concept of "unbiasedness" for vertex labelings of graphs, which captures the absence of bias in label distributions. As a theoretical result, we show that for cubic graphs, the existence of an unbiased labeling is equivalent to the existence of a Tait coloring, the classical 3-edge-coloring. Beyond the theory, we explore its potential applications in conceptual art and design.

The calculus of variations has its roots in classical questions such as, finding paths of fastest descent, identifying geodesics or maximizing the area enclosed by a curve. At its core, it deals with the minimization or maximization of nonlinear functionals, namely, real-valued mappings defined on infinite-dimensional spaces of functions.

In this talk, I will present an overview of the main ideas and techniques of the field. We begin with the classical approach developed between the 17th and 19th centuries by Fermat, Bernoulli, Euler, and Lagrange. This “indirect method” led to the derivation of the Euler–Lagrange equation and to the solution of celebrated problems such as the isoperimetric problem and the brachistochrone.

We then move to the modern perspective that emerged in the late 19th and throughout the 20th century, through the work of Weierstrass, Hilbert, Tonelli, and many others. This development introduced fundamental tools such as Sobolev spaces, weak formulations, and the theory of distributions, which allow for a rigorous treatment of existence and regularity questions.

The talk concludes with a brief discussion of selected contemporary applications, including image processing, fracture mechanics, and elasticity theory.

During a February visit to POSTECH, we discussed applying Exact Multi-parameter Persistent Homology (EMPH) to tunnel void detection. We also explored analyzing African Swine Fever (ASF) microbiome evolution trajectories via NMF dimensionality reduction. This talk summarizes the key research topics from this collaborative visit. 

Invariance means that the output of a learning task does not change under certain transformations of the input. This idea is important in many machine learning problems. In this talk, we explain how using invariant feature representations can make supervised learning easier and more reliable. When representations respect the intrinsic invariances of the target, learning becomes simpler, more robust and more data-efficient, whereas ignoring or mismatching invariance can hinder learning performance. The talk emphasises invariance as a form of inductive bias and shows why careful choice of representations is essential in machine learning.
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