Unsolved Problems
Showing 1-17 of 17 problems
The Dynamics of Networks
Develop high-dimensional mathematics to model and predict behavior in large-scale distributed networks....
21st Century Fluids
Extend classical fluid dynamics to handle complex substances like foams, suspensions, gels, and liquid crystals....
Biological Quantum Field Theory
Apply quantum and statistical field theory methods to model and potentially control pathogen evolution....
Beyond Convex Optimization
Determine whether algebraic geometry can systematically replace linear algebra in optimization....
Mathematics of Quantum Computing
Develop the mathematics required to control the quantum world for computation....
Game Theory at Scale
Create scalable mathematics for differential games, replacing traditional PDE approaches....
Computation at Scale
Develop asymptotics for systems with massive degrees of freedom....
Fundamental Laws of Biology
Identify governing principles for biological systems, analogous to physical laws....
Computational Duality
Use mathematical duality and geometry as foundations for developing novel computational algorithms....
Occam's Razor in Many Dimensions
Find lower bounds for sensing complexity as data collection grows, addressing entropy maximization....
Physical Consequences of Perelman's Proof
Apply Perelman's proof of the Poincaré conjecture to materials fabrication across scales....
Algorithmic Origami and Biology
Strengthen mathematical theory for isometric and rigid embedding relevant to protein folding....
Optimal Nanostructures
Develop mathematics for creating optimal symmetric structures through nanoscale self-assembly....
The Geometry of Genome Space
Establish appropriate distance metrics on genome space incorporating biological utility....
Symmetries and Action Principles for Biology
Extend understanding of symmetries and action principles in biology to include robustness, modularity, evolvability, and variability....
Geometric Langlands and Quantum Physics
Connect the Langlands program to fundamental physics symmetries....
Arithmetic Langlands, Topology, and Geometry
Explore homotopy theory's role in Langlands programs....