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

About Me
Welcome to my page! I'm researching mathematics and physics of natural phenomena. I'm especially interested in studying dynamics as infinitedimensional geometry (e.g. hydrodynamics, optimal transport, and timeevolving 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 codimension2 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)] 

Kikanbo (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)