Sadashige Ishida

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

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

About Me

Welcome to my page! I'm researching mathematics and physics of natural phenomena. I'm especially interested in studying 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

Publications

A symplectic structure on the space of implicitly represented codimension-2 mappings
with Albert Chern & Chris Wojtan
In preparation.
Symplectic structures on the space of space curves
with Martin Bauer & Peter Michor
In preparation.
Quantitative convergence of a discretization of dynamic optimal transport using the dual formulation
with Hugo Lavenant
Submitted. [Code]
Concept: With no regularity assumptions on input measures, we prove the quantitative convergence of a discrete dynamic optimal transport toward the continuous one.

Area formula for spherical polygons via prequantiation
with Albert Chern
Submitted.
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.

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.
Introduction to compressed sensing
with Raimundo Saona
Description: Teaching materials of lectures on compressed sensing at IST Austria in 2020 (as a part of the mathmatics track core course).
A goal of the lectures was to explain the result of Candes, Romberg, and Tao [2004].

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

Languages

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