Colloquium, Michael Björklund
Plats: MH:H, Hörmandersalen
Kontakt: mikael [dot] persson_sundqvist [at] math [dot] lth [dot] se
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Speaker: Michael Björklund, Chalmers University of Technology
Title: Counting points in random lattices
Abstract: The problem of counting lattice points inside various shapes (like balls) goes back a long time. Under mild assumptions, the counting is roughly proportional to the volume of the confining set, and the real problem is really to understand the error term. For a fixed lattice, like the standard integer lattice, confined to a growing sequence of centered Euclidean balls, the true nature of the error term has puzzled mathematicians since the era of Gauss (and probably before that as well).
For other sequences of confining sets, however, like truncated fattened hyperboloids, the counting problem is more tractable, at least for generic lattices, as techniques from dynamical systems become available. During the talk, I will survey some of the recent developments in this direction.