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UID:77d0971c056006d5995132ec65f0b2cc
CATEGORIES:Experimental Mathematics Seminar
CREATED:20250414T074944
SUMMARY: Modular arithmetic with trinomial moduli
LOCATION:https://rutgers.zoom.us/j/94346444480 [password: The 20th Catalan number\, 
 alias (40)!/(20!*21!)
DESCRIPTION:<p style="color: #000000; font-family: 'Times New Roman'; font-size: medium
 ; font-weight: 400; letter-spacing: normal; orphans: 2; text-align: start; 
 text-indent: 0px; text-transform: none; white-space: normal; widows: 2; wor
 d-spacing: 0px;">A popular approach to speed up computations is to reduce t
 he input modulo several relatively prime numbers, do arithmetic on the resi
 dues, then reconstruct the result at the end. This improves the running tim
 e if the moduli (and their pairwise inverses) have "nice" binary shapes, bu
 t only a limited number of such moduli are known. I will discuss a new syst
 em of moduli related to a family of trinomials. This system has shown promi
 sing real-world performance, can produce arbitrarily many moduli, and its e
 lements can be computed quickly. I will mention some theoretical limitation
 s of the system based on roots of unity and graph colorings, and point out 
 what remains to be discovered.</p><p style="color: #000000; font-family: 'T
 imes New Roman'; font-size: medium; font-weight: 400; letter-spacing: norma
 l; orphans: 2; text-align: start; text-indent: 0px; text-transform: none; w
 hite-space: normal; widows: 2; word-spacing: 0px;">Joint work with Mits Kob
 ayashi, Natalya Ter-Saakov, and Eugene Zima.</p>
CONTACT: Robert Dougherty-Bliss, Dartmouth College
DTSTAMP:20260826T201823
DTSTART;TZID=America/New_York:20250424T170000
DTEND;TZID=America/New_York:20250424T180000
SEQUENCE:0
TRANSP:OPAQUE
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