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]



About Me

Welcome to my page! I'm researching mathematics, physics, and CS 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

Publications

Symplectic structures on a class of infinite-dimensional manifolds
In preparation.
Symplectic and Liouville structures on the space of codimension-2 zeros
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
Role: main instructor. Coinstructors: Daniel Holmes & Chris Wojtan. Autumn 2024-25 semester at ISTA.
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.
[Browser 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)