Christopher Hillar

**** NOTE: I am updating this website as this is a bit outdated. ***
Email: hillarmath at gmail
Address:
Redwood Center for Theoretical Neuroscience
University of California, Berkeley
575A Evans Hall, MC 3198
Berkeley, CA 94720-3198
Office: 573 Evans Hall
Phone: (510) 642-7252
FAX: (510) 642-7206

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 Hadamard-type lower bound for symmetric diagonally dominant positive matrices, Linear Algebra and Applications, 472 (2015) 135-141. 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 state-of-the-art 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 Lek-Heng Lim, we finished our paper about the computational intractibility of some problems involving tensors. Most tensor problems are NP-Hard, 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 Sohl-Dickstein 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.