Christopher Hillar


Address:
Redwood
Center for Theoretical Neuroscience
University of California, Berkeley
575A Evans Hall, MC 3198
Berkeley, CA 947203198
Office: 573 Evans Hall
Phone: (510) 6427252
FAX: (510) 6427206
Ph.D. U.C. Berkeley (Mathematics,
2001  2005)
B.S. Yale University (Mathematics,
Computer Science, 2000)
Currently: Assistant Project Scientist, Redwood Center (through the Helen Wills Neuroscience Institute) and UCSF (Tecott Lab). Partially supported by the Simons Foundation and an NSF grant.
NSF Joint Institutes
Postdoctoral Fellowship: I was awarded
this
at the Mathematical Sciences Research Institute
with the following proposal.
MSRI is awesome.
NSA Grant: I was awarded an NSA
Young Investigators Grant. My proposal can
be found here.
Careers in Math: If you've ever wondered what you could do with a math degree (undergrad or otherwise), I highly recommend you check out SIAM's careers in math brochure
"The Misfortunes of a Trio of Mathematicians Using Computer Algebra Systems. Can We Trust in Them?"
Yikes!
And
NIPS proves NIPS review process is broken: most papers at NIPS would be rejected if one reran the conference review process


Theoretical Neuroscience: I am a mathematician working at University of California, San Francisco (Tecott Mouse Behavioral Lab) and the Redwood Center for Theoretical Neuroscience
at the University of California, Berkeley.
New: (with Ngoc Tran) Robust exponential memory in Hopfield networks. pdf  code  arxiv
Recent Research
(with A. Wibisono) A Hadamardtype lower bound for symmetric diagonally dominant positive matrices, Linear Algebra and Applications, 472 (2015) 135141. pdf
With Friedrich Sommer,
we finished a paper (accepted to IEEE Transactions on Information Theory): When can dictionary learning uniquely recover sparse data from subsamples? pdf. (also see NIPS
2010 accepted spotlight submission pdf)
New: (with Ram Mehta and Kilian Koepsell) A Hopfield recurrent neural network trained on natural images performs stateoftheart image compression, IEEE International Conference on Image Processing (ICIP), 2014.
(with Andre Wibisono) We have a manuscript up: Maximum entropy distributions on graphs. pdf  arxiv
With LekHeng Lim, we finished our paper about the computational intractibility of some
problems involving tensors. Most tensor problems
are NPHard, Journal of the ACM.  pdf  arxiv  Ex 1.5 SINGULAR code  Appendix SINGULAR code, Macaulay 2 code
With Shaowei Lin and Andre Wibisono, we finished a paper on inverses of symmetric diagonally dominant matrices, with applications to numerical linear algebra and random graph distributions. Tight bounds on the infinity norm of inverses of symmetric diagonally dominant positive matrices, submitted. pdf
(with Jascha SohlDickstein
and Kilian Koepsell) Efficient and optimal binary Hopfield associative memory storage using minimum probability flow, 2011, NIPS (DISCML), 2012. pdf  arxiv.


Research Interests: Structured polynomial
systems, computational algebraic geometry, combinatorics,
matrix analysis, applications of mathematics to
neuroscience 

Recent Talk on Nonliner Algebra: "A potpourri of nonlinear algebra" at the Institute for Computational and Experimental Research in Mathematics (ICERM)  Computational Nonlinear Algebra (June 2  6, 2014)
Talk: A potpourri of nonlinear algebra, slides  video
Abstract:
I will present several examples demonstrating that solving structured polynomial systems has great potential for producing new and interesting mathematics. Along the way, I will present several open conjectures and problems in nonlinear algebra. 
Chris
Hillar 

