formating modified; posted 10 Sep 07
Broad Agency Announcement (BAA 07-68)
Defense Sciences Office (DSO)
DARPA/DSO SOL, DARPA Mathematical Challenges, BAA 07-68;
BAA CLOSING DATE: 9/8/08;
TECHNICAL POC: Dr. Benjamin Mann, DARPA/DSO, Ph: (571) 218-4246,
Funding Opportunity Description
DARPA is soliciting
innovative research proposals in the area of DARPA Mathematical
Challenges, with the goal of dramatically revolutionizing mathematics
and thereby strengthening the scientific and technological
capabilities of DoD. To do so, the agency has identified twenty-three
mathematical challenges, listed below, which were announced at DARPA
DARPA seeks innovative
proposals addressing these Mathematical Challenges. Proposals should
offer high potential for major mathematical breakthroughs associated
to one or more of these challenges. Responses to multiple challenges
should be addressed individually in separate proposals. Submissions
that merely promise incremental improvements over the existing state
of the art will be deemed unresponsive.
Mathematical Challenge One: The Mathematics of the Brain
Develop a mathematical theory to build a functional model of the brain
that is mathematically consistent and
predictive rather than merely biologically inspired.
Mathematical Challenge Two: The Dynamics of Networks
Develop the high-dimensional mathematics needed to accurately model and
predict behavior in large-scale
distributed networks that evolve over time occurring in communication,
biology, and the social sciences.
Mathematical Challenge Three:
Capture and Harness Stochasticity in Nature
Address Mumford's call for new mathematics for the 21st
century. Develop methods that capture persistence
in stochastic environments.
Mathematical Challenge Four: 21st Century Fluids
Classical fluid dynamics and the Navier-Stokes Equation were
extraordinarily successful in obtaining quantitative
understanding of shock waves, turbulence, and solitons, but new methods
are needed to tackle complex fluids
such as foams, suspensions, gels, and liquid crystals.
Mathematical Challenge Five:
Biological Quantum Field Theory
Quantum and statistical methods have had great success modeling virus
evolution. Can such techniques be
used to model more complex systems such as bacteria? Can these techniques be
used to control pathogen
Mathematical Challenge Six: Computational Duality
Duality in mathematics has been a profound tool for theoretical
understanding. Can it be extended to develop
principled computational techniques where duality and geometry are the
basis for novel algorithms?
Mathematical Challenge Seven:
Occam's Razor in Many Dimensions
As data collection increases can we do more with less by finding lower
bounds for sensing complexity in
systems? This is related to questions about entropy maximization algorithms.
Mathematical Challenge Eight: Beyond Convex Optimization
Can linear algebra be replaced by algebraic geometry in a systematic way?
Mathematical Challenge Nine:
What are the Physical Consequences of Perelman's Proof of
Thurston's Geometrization Theorem?
Can profound theoretical advances in understanding three dimensions be
applied to construct and manipulate
structures across scales to fabricate novel materials?
Mathematical Challenge Ten:
Algorithmic Origami and Biology
Build a stronger mathematical theory for isometric and rigid embedding that
can give insight into protein folding.
Mathematical Challenge Eleven: Optimal Nanostructures
Develop new mathematics for constructing optimal globally symmetric
structures by following simple local
rules via the process of nanoscale self-assembly.
Mathematical Challenge Twelve:
The Mathematics of Quantum Computing, Algorithms, and
In the last century we learned how quantum phenomena shape our world. In
the coming century we need to
develop the mathematics required to control the quantum world.
Mathematical Challenge Thirteen:
Creating a Game Theory that Scales
What new scalable mathematics is needed to replace the traditional Partial
Differential Equations (PDE)
approach to differential games?
Mathematical Challenge Fourteen:
An Information Theory for Virus Evolution
Can Shannon's theory shed light on this fundamental area of biology?
Mathematical Challenge Fifteen: The Geometry of Genome Space
What notion of distance is needed to incorporate biological utility?
Mathematical Challenge Sixteen:
What are the Symmetries and Action Principles for Biology?
Extend our understanding of symmetries and action principles in biology
along the lines of classical
thermodynamics, to include important biological concepts such as
robustness, modularity, evolvability,
Mathematical Challenge Seventeen:
Geometric Langlands and Quantum Physics
How does the Langlands program, which originated in number theory and
representation theory, explain the
fundamental symmetries of physics? And vice versa?
Mathematical Challenge Eighteen:
Arithmetic Langlands, Topology, and Geometry
What is the role of homotopy theory in the classical, geometric,
and quantum Langlands programs?
Mathematical Challenge Nineteen:
Settle the Riemann Hypothesis
The Holy Grail of number theory.
Mathematical Challenge Twenty: Computation at Scale
How can we develop asymptotics for a world with massively many degrees
Mathematical Challenge Twenty-one:
Settle the Hodge Conjecture
This conjecture in algebraic geometry is a metaphor for transforming
into algebraic ones.
Mathematical Challenge Twenty-two:
Settle the Smooth Poincare Conjecture in Dimension 4
What are the implications for space-time and cosmology? And might
the answer unlock the secret of
Mathematical Challenge Twenty-three:
What are the Fundamental Laws of Biology?
Dr. Tether's question will remain front and center in the next 100
years. I place this challenge last as finding
these laws will undoubtedly require the mathematics developed in
answering several of the questions listed
Please Note: White Papers and Full Proposals may be submitted and
received at any time until the final BAA deadline of 4:00PM ET,
September 8, 2008.
VII. Agency Contacts
The Technical POC for
this effort is Dr. Benjamin Mann, Phone: (571) 218-4246, E-mail:
ATTN: BAA 07-68, Dr. Benjamin Mann
3701 North Fairfax Drive
Arlington, VA 22203-1714