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SUMMARY:Dense and smooth lattices in any genus [MPIM]
DTSTART:20241205T140000Z
DTEND:20241205T150000Z
DTSTAMP:20260420T151600Z
UID:indico-event-132@math-events.uni-bonn.de
DESCRIPTION:https://www.mpim-bonn.mpg.de/node/13685MPI-Oberseminar and Con
 ference on "The Mathematics of Post-Quantum Cryptography"\nThe Lattice Iso
 morphism Problem (LIP) was recently introduced as a new hardness assumptio
 n for post-quantum cryptography. The strongest known efficiently computabl
 e invariant for LIP is the genus of a lattice. To instantiate LIP-based sc
 hemes one often requires the existence of a lattice that (1) lies in some 
 fixed genus\, and (2) has some good geometric properties such as a high pa
 cking density or a small smoothness parameter.\nIn this talk I will show t
 hat such lattices exist. In particular\, building upon classical results b
 y Siegel (1935)\, we will see that essentially any genus contains a lattic
 e with a close to optimal packing density\, smoothing parameter and coveri
 ng radius.\n\nhttps://math-events.uni-bonn.de/event/132/
LOCATION:MPIM\, Vivatsgasse\,  7 - Lecture Hall (Max Planck Institute for 
 Mathematics)
URL:https://math-events.uni-bonn.de/event/132/
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