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Welcome! I am a postdoc at the Astronomy Department of the University of Maryland working on the Space Interferometry Mission Dynamics of Galaxies (SIMDOG) project. Because SIM will measure motion so accurately (4 microarcsecs/yr !), we can expect on the order of 30 transverse velocities. What can they be used for? Read below! 
Numerical Action Methods are designed to simulate the past orbits of known objects. In a sense, they act like Nbody simulations running backwards in time using actual galaxy positions and/or velocities today as "initial" conditions. One crucial difference is that they solve for all timesteps of the orbits simultaneously and exactly. While they cannot account for energy loss or gain to any specific halo, merger histories, etc., we have experimented with "mass growth" methods whereby halos gain the mass they have today in some parametric way from the background to great effect. Here is a plot showing the NAM recreated orbits for 1300+ objects within 3000 km/s (translation for cosmologists: sizeable halos within z=0.01 = 30/h ~ 41 Megaparsecs ); many galaxies have been grouped together to simplify tidal effects on our local group; the short, straight orbits signify a low choice of mass to light for this run.  
Using galaxy group catalogs from work by B. Tully and collaborators, we have shown the constraining power of NAM on the local MasstoLight values for Spirals and Ellipticals separately. On the left we show an example of a threeparameter chi^{2} analysis: one parameter, Ω_{S}, the density of smooth matter not in halos, is shown fixed; the other parameters are mass to light for elliptical and spiral galaxies. This example was on a small subset of the catalog shown above. Currently we are working on using NAM for a large catalog (~40 Mpc for cosmologists, 3,000 km/s for astronomers, z=0.01 for both) to "generate" initial conditions for use with an Nbody program such as Volker Springel's GADGET code. In this way, we can better simulate the local universe; the ultimate "Constrained Simulation". 
In a past life, well, a year or so ago, I was at the Department of Mathematics and Theoretical Physics (DAMTP for short) in the Relativity and Gravitation Group. There I worked on optimizing large scale weak lensing surveys by combining other large scale information; characterizing selection effects in SunyaevZel'dovich experiments on peculiar velocity statistics; and a careful critical analysis of unified dark energydark matter models. Other previous work (detailed below) has included (1) optimizing Cosmic Microwave Background (CMB) analysis methods, (2) Coding up a maximum likelihood estimator for CMB polarization modes, (3) estimating how much galaxy cluster peculiar velocities constrain cosmological parameters using linear theory, modified linear theory and simulations, (4) modeling point source contributions to the kinetic SZ effect, and (5) writing IDL code to make pretty pictures of hydrodynamic clusters. But everything in cosmology is fascinating, and I've been known to dabble in more esoteric stuff (well, esoteric to an Astronomer, anyway) such as quintessence, brane worlds and quantum cosmology. I'm guilty of other physics interests such as the "Arrow of Time" problem and (like all good theorists) grand unification. 
The kinetic SunyaevZel'dovich effect is the doppler shifting of Cosmic Microwave Background photons by the hot plasma in the center of very large mass haloes (~10^{14} M_{sol}) has to potential to provide a catalog of redshiftindependent galaxy cluster velocities. Using these velocities to constrain Ω_{m} seems natural since the velocities are responding to the amount of matter in the universe. Based on linear theory, the constraints on Ω_{m} from 1000 clusters are a few percent given a noise of about 100 km/s. However, because the kSZ only occurs for a specific mass cutoff, the selection bias greatly reduces this constraining power. Using Nbody simulations, I show in a recent paper that for a concordance universe, the dependency on Ω_{m} is close to nil for a constant value of sigma_{8} at very recent redshift. And at higher redshift, the dependency is reverse to what linear theory suggests.  
Peculiar velocities trace the density field in a great, nonbiased way (at
least in linear theory!). Recent excitement about using galaxy cluster
peculiar velocities is motivated by their possible uses to reconstruct
(large modes of) the realspace potential. Our paper details how many
cluster
velocities
we need from a given observational volume to determine modes based on
limitations from (1) confusion between dark matter and gas velocities and
(2) what we call the "undersampling noise" in that clustercluster
separation is larger than the precollapse radius of a typical cluster.
In principle, weak lensing provides complementary information about the
gravitational potential (the transverse modes as opposed to the radial
modes from velocities), but we show that such information is very weakly
constraining (no pun intended). The image to the right shows the
noise due to both limiations listed above (solid line) for particular
redshifts (note the redshift
dependence of the undersampling noise (dashed line)). The dotted line
represents (half) the typical distance between clusters since: 4/3 pi R^{3} n(z) = 1 The ranges at the top reflect three theoretical "reference" observational regimes. 

On the left, we show how well galaxy cluster peculiar velocities from linear theory might constrain Ω_{m} and the dark energy equation of state parameter, w. These 1 and 2sigma curves are based on a Fisher matrix analysis of 820 clusters. The dashed lines are for 820 sparsely sampled clusters from z=0.1 to 1.0 from an artificial grid; the solid lines for 820 neighboring clusters near z=1.0 based on the Virgo Consortium's Lightcone Simulation Cluster Catalog (link to our paper). These parameter forecasts are very optimistic and do not include selection effects. My current velocity paper shows that the mass selection bias effects in a SunyaevZel'dovich (SZ) experiment will alter the Ω_{m} dependency greatly. There are other issues with realistic data such as nonlinear evolution, temperature profiles, etc. Regardless of these complications, the constraints in parameter space are related to the time derivative of the growth factor, dD/dz, and therefore should be complementary to parameter constraints from dN/dz (per steradian) type cluster statistic measurements, CMB measurements, and supernovae type IA measurements. Upcoming SZ surveys and serendipitous SZ detections from Planck promise to create a useful SZ cluster survey catalog; followup multiwavelength (in submm) and Xray astrometry and redshift followup have the potential for attaining unprecendented accuracy in peculiar velocity data. I hope to develop the tools for using that data for cosmology.  
On the right, we show how well hierarchical decomposition can be expected to recover the angular power spectrum; the "exact" method shown for comparison refers to MADCAP. The solid line comes from CMBFAST using LambdaCDM model parameters and was in turn used by HEALPIX to generate a map of the whole sky. The hierarchical decomposition methods have incredible speed advantages (link to our paper) over more exact methods with minimal loss of information which will become a crucial issue for upcoming megapixel CMB missions such as the ongoing WMAP and upcoming Planck satellites when exact methods become unreasonably computer intensive.  
The background wallpaper is a Hubble image of galaxy cluster Abel 2218 (for full view click here) which is so massive that it acts as a magnifying and distorting strong lens on the galaxies behind it. The bright yellow galaxies are in the cluster itself, while the bluer elongated images are from galaxies far behind the cluster. This is an example of strong lensing. But even a less massive cluster will cause weak lensing, which can only be ferreted out by statistics. By combining weak lensing estimates of the shear caused by an overdensity with the line of sight estimated mass it may be possible to reconstruct the potential of such overdensities. 
So you might be wondering, "What's the otter doing up there at the top of your webpage? And why are you wearing a fez?" To which I reply, "The otter's eating abalone, of course. And I claim fezzes will be the next black after shawls depart (and none too soon!)." ***Update*** Shawls have departed. Rubber fezzes have arrived! 
You can email me at:
peel(at)astro.umd.edu
[the (at) is to be replaced by an @;
writing it this way helps deter spam] Snailmail me at: Alan Peel Department of Astronomy University of Maryland College Park, MD 207422421 USA tel: (301) 4056647 