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Nguyen Thac Dung

2012-12-07
10:30:00 - 12:00:00

308 , Mathematics Research Center Building (ori. New Math. Bldg.)

In this talk, I will show uniform upper and lower bounds for the L^2 norm of the restriction of eigenfunctions of the Laplacian on the three-dimensional standard flat torus to surfaces with non-vanishing curvature. The main ingredients of the proof are the estimation of lattice points in spherical caps and the estimation of oscillatory sums. The contain of my talk covers the section 8 and section 9 in [BR]. References. [BR] Bourgain and Rudnick, Restriction of toral eigenfunctions to hypersurfaces and nodal sets, to appear in GAFA. http://link.springer.com/article/10.1007%2Fs00039-012-0186- 3?LI=true# (See sections 2, 8, 9. and formula: (3.10), (7.7)).