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CATEGORIES:Academics,Lectures/Seminars
DESCRIPTION:Biography: Andrew Sills earned a B.A. from Rutgers\, M.A. from
Penn State\, and Ph.D. from University of Kentucky\, all in mathematics. Hi
s thesis advisor was George Andrews of Penn State. After a postdoctoral pos
ition at Rutgers under the mentorship of Doron Zeilberger\, he began a tenu
re-track position at Georgia Southern University\, attaining full professor
ship in 2015. He is the past recipient of an NSA research grant. His resear
ch interests include the theory of integers partitions\, q-series\, and rel
ated topics. Most recently\, his research activities have expanded to inclu
de work in mathematical statistics and applications of mathematics to music
.\n\n \n\nAbstract: In 1894\, L. J. Rogers published a paper on the expansi
on of certain infinite products that\nincluded a pair of q-series identitie
s that were later rediscovered independently by S. Ramanujan (at\nfirst wit
hout proof). These analytic identities\, traditionally written in the varia
ble “q”\, each asserted\nthe equality of an infinite product with an infini
te series where the general term involved a power of\nq and rising q-factor
ials. Ramanujan’s mentor G. H. Hardy was unaware of Rogers’ work\, and\ncir
culated the identities among various European mathematicians as unproven co
njectures. Later\nRamanujan discovered a proof\, and then came across Roger
s’ earlier work in an old issue of the\nProceedings of the London Mathemati
cal Society. These identities came to be known as the Rogers--\nRamanujan i
dentities. In hindsight\, some earlier identities due to Euler\, Jacobi\, a
nd Heine could be\nclassified as identities “of Rogers--Ramanujan type.” Ro
gers and Ramanujan each discovered quite a\nfew identities of similar type
in the 1910s\, but then the subject remained relatively dormant until W.\nN
. Bailey (who knew Ramanujan while undergraduate at Cambridge) and his then
-Ph.D. student L.\nJ. Slater revived the study of Rogers--Ramanujan type id
entities in the 1940s. These identities of\nanalytic functions can also be
viewed as generating functions for classes of combinatorial objects\n(often
integer partitions). This combinatorial view became particularly popular i
n the 1960s under\nthe leadership of Basil Gordon and George Andrews\, when
a torrent of infinite families of\ncombinatorial identities of Rogers--Ram
anujan type were discovered. Since the 1980s\, many\nadditional application
s of Rogers--Ramanujan type identities have been found in a variety of area
s of\nmathematics and physics. As time allows\, I will discuss some recent
advances and open problems\,\nincluding some of my own work in the area.
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DTSTAMP:20231128T171409Z
DTSTART:20230314T170000Z
GEO:47.119655;-88.548223
LOCATION:Grover C Dillman\, 204
SEQUENCE:0
SUMMARY:Rogers-Ramanujan Type Identities
UID:tag:localist.com\,2008:EventInstance_42640594083535
URL:https://events.mtu.edu/event/rogers-ramanujan_type_identities
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