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

Currently I'm exploring postdoctorate/research fellow opportunities related to geometry and dynamics in mathematics and physics, starting in late 2025 (mainly in Europe but all over the world). Please reach out to me if you have any leads.
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 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
Symplectic structures on a class of infinitedimensional manifolds
In preparation. 

Symplectic and Liouville structures on the spaces of implicitly represented codimension2 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
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. 
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)