DARPA Math Challenges

These are good times for Artificial Intelligence research; DARPA (the Defense Advanced Research Projects Agency) has put out a request for proposals on 23 contemporary mathematical challenges that has the potential for changing the state of AI as we know it.

The challenges are:

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1

The Mathematics of the Brain.

2

The Dynamics of Networks.

3

Capture and Harness Stochasticity in Nature.

4

21st Century Fluids.

5

Biological Quantum Field Theory.

6

Computational Duality.

7

Occam’s Razor in Many Dimensions.

8

Beyond Convex Optimization.

9

What are the Physical Consequences of Perelman’s Proof of Thurston’s. Geometrization Theorem?

10

Algorithmic Origami and Biology.

11

Optimal Nanostructures.

12

The Mathematics of Quantum Computing, Algorithms, and Entanglement.

13

Creating a Game Theory that Scales.

14

An Information Theory for Virus Evolution.

15

The Geometry of Genome Space.

16

What are the Symmetries and Action Principles for Biology?

17

Geometric Langlands and Quantum Physics.

18

Arithmetic Langlands, Topology, and Geometry.

19

Settle the Riemann Hypothesis.

20

Computation at Scale.

21

Settle the Hodge Conjecture.

22

Settle the Smooth Poincare Conjecture in Dimension 4.

23

What are the Fundamental Laws of Biology?

I am partial to challenges 15 and 16 as they fall within areas of my doctoral research work. One result of this work is my paper detailing new perspectives on genotype-phenotype map geometries.

Challenges 3, 14, 20 and 23 also look very appealing. Please email me (dom_wilson at yahoo dot com) if you are looking for collaboration on any of the challenges.

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