Sadashige Ishida

Email: sdsgisd(at)gmail.com
Github: here

Ref: [Ishida et al. 2017] [Ginder, Katayama, Svadlenka 2016]
More bubbles and geometric flows here. [Source code]

News

I will be teaching a course "Geometric Mechanics" in the upcoming 2024 Autumn semester! For details, see Syllabus on Athena or Detailed syllabus. Credits from ISTA, Uni Wien, and TU Wien are transferable between each other.

About Me

Welcome to my page! I'm researching mathematics and physics of natural phenomena. I especially like to study dynamics as infinite-dimensional geometry (e.g. hydrodynamics, optimal transport, and time-evolving shapes). Currently, I'm doing a PhD in mathematics at IST Austria. Prior to that, I worked in optics industry and game industry after a master's study in mathematics.

Research interests

Geometric mechanics i.e. study of dynamics from viewpoints of symplectic/contact/Poisson geometry
Hydrodynamics, optimal transport, evolution of shapes as infinite-dimensional geometry
Low-dimensional & differential topology
Numerical discretization and discrete-to-continuous limit
Geometric quantization in mathematics and physics
Mathematical modeling of natural phenomena

Publications

Symplectic structures on a class of infinite-dimensional manifolds In preparation.
Symplectic and Liouville structures on the spaces of implicitly represented codimension-2 shapes with Albert Chern & Chris Wojtan In preparation.
Symplectic structures on the space of space curves with Martin Bauer & Peter Michor [Slides] Submitted. Concept: New symplectic structures on the space of space curves different from the only known canonical symplectic structure.
Quantitative convergence of a discretization of dynamic optimal transport using the dual formulation with Hugo Lavenant Accepted at Foundations of Computational Mathematics (FoCM), 2024 Concept: With no regularity assumptions on input measures, we prove the quantitative convergence of a discrete dynamic optimal transport toward the continuous one. [Code]
Area formula for spherical polygons via prequantization with Albert Chern Accepted at SIAM Journal on Applied Algebra and Geometry (SIAGA), 2024 Concept: A new area formula for spherical polygons derived via a prequantum circle bundle over \(\mathbb{S}^2\).
Hidden Degrees of Freedom in Implicit Vortex Filaments Sadashige Ishida, Chris Wojtan, Albert Chern ACM Transactions on Graphics (SIGGRAPH Asia 2022) Concept: An implicit representation of curve dynamics and its hidden degrees of freedom.
A Model for Soap Film Dynamics with Evolving Thickness Sadashige Ishida, Peter Synack, Fumiya Narita, Toshiya Hachisuka, Chris Wojtan joint first authors (alphabetical order) ACM Transactions on Graphics (SIGGRAPH 2020)* Concept: A mathematical model for surface deformation and thickness evolution of soap films.
A Hyperbolic Geometric Flow for Evolving Films and Foams Sadashige Ishida, Masafumi Yamamoto, Ryoichi Ando, Toshiya Hachisuka ACM Transactions on Graphics (SIGGRAPH ASIA 2017) Concept: A reformulation of soap film dynamics as a hyperbolic geometric flow.

Teaching

Geometric Mechanics

I will be teaching a course as the main instructor at IST Austria in Autumn 2024-25 semester (Coinstructors: Daniel Holmes & Chris Wojtan).
Description: Introduction to geometric mechanics, which is a study of dynamics through the lens of geometry.
See Syllabus on Athena or Detailed syllabus.

Introduction to compressed sensing

with Raimundo Saona, at IST Austria, 2022.
Description: Lectures on compressed sensing (as a part of the mathmatics track core course), with focus on understanding the proof of the seminal work by Candes, Romberg, and Tao [2004.

[Day 1] [Day 2] [Day 3] [Day 4] [Exercise Sheet 1] [Exercise Sheet 2]

Notes

Weak solutions of the semigeostrophic equations from a viewpoint of optimal transport
Description: A survey of the works of Figalli [2018] and of Benamou and Brenier [1998] on an application of optimal transport to the semigeostrophic equations.

[Note (PDF)]

Softwares and Demos

Evolving curves under different curvature flows. [Brouser demo] [Video (Youtube)] [Source code (JavaScript)]
Kikan-bo (Stickers for LINE app) In Japanese. It costs 120 yen (1 US dollar approximately). [Line app store]
Okome and Friends (Stickers for LINE app) In Japanese. It costs 120 yen (1 US dollar approximately). [Line app store]

Education/Working experience

October 2019 - Present, PhD Candidate in Mathematics, IST Austria
Pipeline Programmer, Northlight Game Engine Team, Remedy Entertainment
Algorithm Researcher & Designer, Mathematical Sciences Laboratory & Optical Research Laboratory, Nikon Corporation
Master of Mathematics, Hokkaido University / ETH Zürich

Languages

Japanese (native), English (advanced), French (intermediate), German (trying to become intermediate), Finnish (elementary)