1. New results in the geometry of random fields, with applications to CMB and galaxy density Keith Worsley, Hugo Drouin, Pauline Klein Department of Mathematics and Statistics, McConnell Brain Imaging Centre, Montreal Neurological Institute, McGill University

2. Milky way

4. The 2dF Galaxy Redshift Survey: spectra and redshifts Mon. Not. R. Astron. Soc. 328, 1039–1063 (2001) Milky way

6. fMRI data: 120 scans, 3 scans each of hot, rest, warm, rest, hot, rest, … T = (hot – warm effect) / S.d. ~ t 110 if no effect

7. Gaussianized χ 2 field? Gaussian threshold EC

8. Gaussianized T field? Gaussian threshold EC

9. EC for WMAP, unsmoothed, FWHM = 1.6 o -5-4-3-2012345 -2500 -2000 -1500 -1000 -500 0 500 1000 1500 2000 2500 Gaussian threshold EC Observed Expected -8-7-6-5-4 -10 0 10 45678 0 20

10. Observed – Expected EC, with Poisson sd in tails EC Gaussian threshold

11. EC for WMAP smoothed to FWHM o (expected) no smoothing scale space

12. Simulation (expected) no smoothing scale space

13. Scale space WMAP data -5-4-3-2012345 -1000 -500 0 500 1000 1500 2000 1.6 o  20.5 o Gaussian threshold EC Observed Expected -4.5-4-3.5 -10 0 10 3.544.55 0 10 20