I am a co-PI for the Math+ project "Smooth discrete surfaces" and an active member of the DFG Collaborative Research Center "Discretization in Geometry and Dynamics" project "Discrete Geometric Structures Motivated by Applications and Architecture". I received my PhD (supervised by Max Wardetzky) in October 2017 from the Discrete Differential Geometry Lab at the University of Göttingen.

My research uses the language of differential geometry and topology to provide insight into the behavior of objects that are inherently discrete. Beyond providing an essential link between smooth formulations and computation, discrete geometric objects arise in applications ranging from large architectural structures down to molecular polymer networks and across to nonlinear superposition principles.

Here are some example questions that motivate my work in discrete differential geometry:

What are discrete analogues of the theories of curves and surfaces that preserve an underlying geometric structure? What new insights or perspectives do they offer their corresponding smooth theories? At the same time, can we build a geometrically aware computational framework?

Many materials are built from interlocking fibers or rods at the mesoscale. Examples include woven fabric, tent-like structures, and polymer networks. How does the geometry of a 2D material’s discrete mesostructure lead to a given macroscopic behavior? Can we use this knowledge to better understand or design application specific materials?

discrete differential geometry/topology, discrete integrable systems, mechanics of textiles/polymer networks, computer graphics, computational fabrication

	Chebyshev Nets from Commuting PolyVector Fields Andrew O. Sageman-Furnas, Albert Chern, Mirela Ben-Chen, and Amir Vaxman. ACM Transactions on Graphics (SIGGRAPH Asia) 38:6, pp. 172:1–172:16, 2019. [pdf] [doi]
	Topology determines force distributions in one-dimensional random spring networks Knut M. Heidemann, Andrew O. Sageman-Furnas, Abhinav Sharma, Florian Rehfeldt, Christoph F. Schmidt, and Max Wardetzky. Physical Review E 97, 022306, 2018. [pdf] [doi]
	Topology counts: force distributions in circular spring networks Knut M. Heidemann, Andrew O. Sageman-Furnas, Abhinav Sharma, Florian Rehfeldt, Christoph F. Schmidt, and Max Wardetzky. Physical Review Letters 120, 068001, 2018. [pdf] [doi]
	Form finding in elastic gridshells Changyeob Baek, Andrew O. Sageman-Furnas, Mohammad K. Jawed, and Pedro M. Reis. Proceedings of the National Academy of Sciences (USA) 2018 January, 115 (1) 75-80. [pdf] [doi]
	A discrete parametrized surface theory in R^3 Tim Hoffmann, Andrew O. Sageman-Furnas, and Max Wardetzky. International Math Research Notices, Volume 2017, Issue 14, July 2017, Pages 4217–4258. [pdf] [doi]
	A 2x2 Lax representation, associated family, and Baecklund transformation for circular K-nets Tim Hoffmann and Andrew O. Sageman-Furnas. Discrete and Computational Geometry (2016) 56:472. [pdf] [doi]
	Meltables: Fabrication of Complex 3D Curves by Melting [video] Andrew O. Sageman-Furnas, Nobuyuki Umetani, and Ryan Schmidt. 2015 Conference Proceedings: ACM SIGGRAPH Asia. 4 pages, 2015. [pdf] [doi]
	Wire Mesh Design [overview video] [fabrication video] Akash Garg, Andrew O. Sageman-Furnas, Bailin Deng, Yonghao Yue, Eitan Grinspun, Mark Pauly, and Max Wardetzky. ACM Transactions on Graphics (SIGGRAPH) 33:4, pp. 66:1–66:12, 2014. [pdf] [doi]
	The Sphereprint: An approach to quantifying the conformability of flexible materials Andrew O. Sageman-Furnas, Parikshit Goswami, Govind Menon, and Stephen J Russell. Textile Research Journal vol. 84:8, pp. 793–807, 2014. [pdf] [doi]

	Towards a curvature theory for general quad meshes Andrew O. Sageman-Furnas (joint work with Tim Hoffmann and Max Wardetzky), Oberwolfach Reports No. 13/2015. [pdf]
	SGP 2015 Course Slides on Variational Time Integrators Andrew O. Sageman-Furnas Please contact me with corrections or comments. [keynote] [pdf] [pptx]