What sort of computations are used for localising sound with the ears, and how does the brain compute the time difference between sounds reaching each ear? I am interested in the specific mechanisms rather than a general account.
The location of a sound is defined on three dimensions: distance, elevation, and azimuth. When the distance between a listener and a sound source is changed there is a change in the overall level as well as the relative levels of direct and reverberant sound energy. When the elevation is changed the overall level and the direct to reverberant ratio say roughly constant. The pinna, and to some extent the head and body, shape the spectrum of the sound in an elevation dependent way. This so called pinna filtering is typically talked about as introducing a notch in the spectrum, at around 8 kHz, and that the frequency of this notch varies with elevation. Changing the azimuth of a sound changes the relative levels at the two ears and the relative timing between the ears. The interaural level difference (ILD) arises from the head shadow effect, basically the head blocks some of the sound from reaching the "far" ear. The interaural time difference (ITD) is a result of differences in the distance the sound needs to travel; a sound coming from the side needs to travel about 0.5 ft further, which takes about 0.6 ms, to get to the "far" ear.
All the information the brain has about a sound comes from the auditory nerve. The firing rate of auditory neurons depend on the spectrum of the sound and the sound level. In addition to firing rate, auditory neurons have the remarkable ability to "phase lock" to a stimulus up to 1-2 kHz. How the brain decodes the pattern of firing rate and timing information across the neuron is not fully understood.
The lateral superior olive (LSO) has neurons that are responsible for extracting ILD cues. The neurons receive excitatory inputs from the ipsilateral ear and inhibatory inputs from the contralateral ear. This excitatory-inhibitory (EI) layout means the firing rate is essentially invariant to overall level, but changes with the ILD.
The medial superior olive (MSO) has neurons that are responsible for extracting ITD cues. The neruons receive excitatory inputs from both the ipsilateral and contralateral ears. The is specialized anatomy that preserves the timing of the neural firings such that these excitatory-excitatory (EE) neurons can act as a coincidence detector and only fire if they receive both ipsilateral and contralateral input at the same time. In some species there are intricate axonal "delay lines" that change the relative time of arrivals of the contralateral and ipsilateral inputs such that each MSO neuron is tuned to a particular ITD. Brand et al. (2002) argue that fast inhibitory inputs are required for ITD tuning.
The dorsal cochlear nucleus (DCN) has neurons that are thought to be responsible for detecting spectral notches due to the convergence of both narrow band and wide band inhibitory inputs.
Sensitivity to changes in overall level is generally well predicted by the rate level (and to some extent timing) behaviour of the auditory nerve.
Not much work has looked at the neural processing of the direct to reverberant ratio.
From the physics(acoustics) perspective, the sensory input changes depending upon pitch. When you hear a sound that is high-pitched, your head blocks the sound wave, creating a sound shadow for the ear on the opposite side of your head from the sound source. This sound shadow means that your ears hear the sound at two different volumes, which the brain then uses to calculate direction.
For low-pitched sound, the distance between your ears creates a phase difference between the sound perceived in each ear. And that phase difference indicates sound direction. If I understand your question, it centered upon the brain's processing of this phase difference information.
For mixed-pitch sounds, you utilize both, which makes complex sounds even easier to locate.
Some neuroscience papers on sound localization: