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Thursday, January 28, 2021 — 1:00 PM EST
Title: The multispecies TAZRP and modified Macdonald polynomials
| Speaker: | Olya Mandelshtam |
| Affiliation: | University of Waterloo |
| Zoom: | Contact Karen Yeats |
Abstract:
Recently, a formula for the symmetric Macdonald polynomials $P_{\lambda}(X;q,t)$ was given in terms of objects called multiline queues, which also compute probabilities of a statistical mechanics model called the multispecies asymmetric simple exclusion process (ASEP) on a ring. It is natural to ask whether the modified Macdonald polynomials $\widetilde{H}_{\lambda}(X;q,t)$ can be obtained using a combinatorial gadget for some other statistical mechanics model.
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.