Symposium Geometry Processing 2015

Saturday—Sunday July 4–5

[Graduate School]

Monday July 6

Tuesday July 7

Wednesday July 8

Keynote Talks: Abstracts

Robert J. Lang: From Flapping Birds to Space Telescopes: The Art and Science of Origami

The last decade of this past century has been witness to a revolution in the development and application of mathematical techniques to origami, the centuries-old Japanese art of paper-folding. The techniques used in mathematical origami design range from the abstruse to the highly approachable. In this talk, I will describe how geometric concepts led to the solution of a broad class of origami folding problems – specifically, the problem of efficiently folding a shape with an arbitrary number and arrangement of flaps, and along the way, enabled origami designs of mind-blowing complexity and realism, some of which you’ll see, too. As often happens in mathematics, theory originally developed for its own sake has led to some surprising practical applications. The algorithms and theorems of origami design have shed light on long-standing mathematical questions and have solved practical engineering problems. I will discuss examples of how origami has enabled safer airbags, Brobdingnagian space telescopes, and more. [July 6, 09:15]

Amit Singer: Solving the 3-D Puzzle of Rotation Assignment in Single Particle Cryo-Electron Microscopy

Single particle cryo-electron microscopy (EM) recently joined X-ray crystallography and nuclear magnetic resonance (NMR) spectroscopy as a high-resolution structural method for biological macromolecules. In single particle cryo-EM, the 3-D structure needs to be determined from many noisy 2-D projection images of individual, ideally identical frozen-hydrated macromolecules whose orientations and positions are random and unknown (i.e., random X-ray transform). This lecture will explore algorithms for estimating the unknown pose parameters. The main focus will be on semidefinite programming relaxations that are based on the Fourier transform over the group SO(3). Such semidefinite programs can be viewed as extensions to existing approximation algorithms to max-cut and unique games, two fundamental problems in theoretical computer science. The approach is quite general and can be used to handle other groups of transformations that arise in other applications in signal processing, image analysis, computer vision and computer graphics. [July 7, 09:15]

Mark Pauly: The Beauty of Geometry

In this talk, I want to convey what fascinates me about geometry. I will exemplify how nature and art can provide inspiration for research and how research in turn can inspire artists or lead to unexpected means for design. The core of the talk will be a personal and highly subjective speculation on the beauty of geometry. In the course of this discussion, I will reflect on several of our past and current projects to highlight how the same fundamental geometry processing problems re-occur in many guises. Connecting the dots between seemingly disparate research projects can hopefully provide insights into the general nature of these problems, but also reveal when specialized solutions are called for. The talk will conclude with a discussion of potential future challenges for geometry processing, both in terms of open problems, but also in the way we operate as a research community. [July 8, 09:00]