Introduction
This is the SHA3 page of David A. Wilson.
For information about the NIST SHA3 competition, go here.
For an unofficial list of entries and analyses, go here.
DCH
I submitted a hash function called DCH. It is a blockcipherbased algorithm that alternates a nonlinear substitution, a Fourierlike linear transform, and a round key addition. You can find the submission package here. If you have any questions, comments, or analyses of DCH, please contact me at dwilson at alum dot mit dot edu. Note: There is an error in the reference implementation (see third bullet point below).
Analysis

Christian Rechberger has kindly pointed out that while the dithering scheme used renders DCH invulnerable to the secondpreimage attacks of Kelsey and Schneier, it does not protect against the variant of those attacks by Andreeva et al. published earlier this year. Since DCH uses a 512bit chaining value for all digest lengths, this appears to be a valid attack for DCH512 (requiring slightly more than 2^{450} computations), although for shorter digest lengths brute force is stil faster.
 There are several defenses against such an attack, some of which would involve changing the algorithm (e.g. to include a block number instead of just a small dither value, following the HAIFA approach). One option within the bounds of the submitted entry, however, is to increase the block size, which is explicitly listed as a tunable parameter. This will result in a larger chaining value; a block size of 576 bits should be large enough to make the attack of Andreeva et al. worse than brute force against 512bit DCH.
 Dmitry Khovratovich and Ivica Nikolic of the University of Luxembourg have pointed out that DCH contains an incorrect implementation of the MiyaguchiPreneel iteration method, and thus is susceptible to collision and preimage attack via Wagner's generalized birthday algorithm. Their writeup is available here.

This is correct; DCH as submitted is broken. This attack capitalizes on an error in implementation of the iteration method; it does not attack the compression function itself. Thus, correcting the error in the iteration method would defend against this attack, although for the purposes of the SHA3 competition it appears that DCH is out.
 Mario Lamberger and Florian Mendel of IAIK, Graz University of Technology, have pointed out that the above results in relatively trivial collision and preimage attacks, since once a dither input is repeated, if the same message block is used in both positions then the resulting contributions to the end hash value will cancel out.
Other Algorithms
My analyses of other SHA3 entries: