Topological Data Analysis and Dynamics I

Date: August 14
Time: 13:30--15:30
Room: 308

(Note: Click title to show the abstract.)

Hiraoka, Yasuaki (Tohoku Univ.)
Mischaikow, Konstantin (Rutgers Univ.)
Kokubu, Hiroshi (Kyoto Univ.)
Nishiura, Yasumasa (Tohoku Univ., WPI-AIMR)

Abstract: This is the first half of the multiple minisymposiums ˇ°Topological Data Analysis and Dynamics I & IIˇ±. The purpose of this multiple minisymposiums is to collect researchers studying theory, computations, and applications of topological data analysis (TDA). TDA is a rapidly growing research field, and offers powerful geometric and topological tools to understand complicated data sets, time series, dynamics, and so on. In this first half of the multiple minisymposiums, we aim to study some of the new specific mathematical and computational research topics such as inverse problems, Auslander-Reiten theory, and efficient computations.

ˇˇThis minisymposium is organized as follows. The first speaker Yasuaki Hiraoka (Kyushu University, minisymposiums organizer) will give a survey talk about TDA including persistence modules, quiver representations, stability, and several applications for the audience of this symposium.
The second speaker Marcio Gameiro (University of São Paulo) will give a talk about continuation methods of point cloud data by using persistence diagrams. This research is motivated by applications, especially materials science, in which we want to design atomic arrangements realizing some specific properties of persistence diagrams. To such an inverse problem, Gameiro develops a method combining pseudo-inverse Newton operators and continuations of bifurcation branches in dynamical systems.
The third speaker Emerson Escolar (Kyushu University) will give a talk about persistence modules on commutative ladders. This subject deals with a generalization of persistence modules on quivers which are not Gabriel types. One of the novel techniques used in his research is the Auslander-Reiten theory in representation theory. By this technique, he generalizes a concept of persistence diagrams of the generalized persistence modules as functions on Auslander-Reiten quivers. In addition, he develops a fast algorithm based on matrix reductions and discrete Morse theory, and applies them to the analysis of pressurizations of silica glasses. The fourth speaker Hubert Wagner (IST Austria) will talk about fast computations of persistence modules.

Topological Data Analysis and Dynamics: Theory, Computation, and Applications
Hiraoka, Yasuaki (Tohoku Univ.)

Point cloud deformations by continuation of persistence diagrams
Gameiro, Marcio (Univ. of Sao Paulo)

Matrix Method for Persistence Modules on Commutative Ladders of Finite Type
Escolar, Emerson (Kyushu Univ.)
Hiraoka, Yasuaki (Tohoku Univ.)

Efficient persistent homology computations
Wagner, Hubert (IST Austria)


Code: Type-Date-Time-Room No.
Type : IL=Invited Lecture, SL=Special Lectures, MS=Minisymposia, IM=Industrial Minisymposia, CP=Contributed Papers, PP=Posters
Date: Mo=Monday, Tu=Tuesday, We=Wednesday, Th=Thursday, Fr=Friday
Time : A=8:30-9:30, B=10:00-11:00, C=11:10-12:10, BC=10:00-12:10, D=13:30-15:30, E=16:00-18:00, F=19:00-20:00, G=12:10-13:30, H=15:30-16:00
Room No.: TBA