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Thursday, January 21, 2021 — 1:30 PM EST
Title: The growth of groups and algebras
| Speaker: | Jason Bell |
| Affiliation: | University of Waterloo |
| Zoom: | Contact Karen Yeats |
Abstract:
We give an overview of the theory of growth functions for associative algebras and explain their significance when trying to understand algebras from a combinatorial point of view. We then give a classification for which functions can occur as the growth function of a finitely generated associative algebra up to asymptotic equivalence. This is joint work with Efim Zelmanov.
Friday, January 22, 2021 — 3:30 PM EST
Title: Fast simulation of planar Clifford circuits
| Speaker: | David Gosset |
| Aflliation: | University of Waterloo |
| Zoom: | Please email Emma Watson |
Abstract:
Clifford circuits are a special family of quantum circuits that can be simulated on a classical computer in polynomial time using linear algebra. Recent work has shown that Clifford circuits composed of nearest-neighbor gates in planar geometries can solve certain linear algebra problems provably faster --as measured by circuit depth-- than classical computers.
Friday, January 29, 2021 — 3:30 PM EST
Title: Finding twin smooth integers for isogeny-based cryptography
| Speaker: | Michael Naehrig |
| Affliation: | Microsoft Research |
| Zoom: | Please email Emma Watson |
Abstract:
Efficient and secure instantiations of cryptographic protocols require careful parameter selection. For the isogeny-based cryptographic protocol B-SIDH, a variant of the Supersingular-Isogeny Diffie Hellman (SIDH) key exchange, one needs to find two consecutive B-smooth integers of cryptographic size such that their sum is prime. The smaller the smoothness bound B is, the more efficient the protocol becomes. This talk discusses a sieving algorithm to find such twin smooth integers that uses solutions to the Prouhet-Tarry-Escott problem.