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DTSTAMP:20261017T105456
DTSTART;TZID=America/Detroit:20261026T160000
DTEND;TZID=America/Detroit:20261026T170000
SUMMARY:Workshop / Seminar:GLNT: Analytic approaches to factorization of singular moduli
DESCRIPTION:Abstract: In the 1980s\, Gross and Zagier proved factorization formula for norm of difference of singular moduli\, on their way to the Gross-Zagier formula. In that work\, there were two approaches\, one algebraic and one analytic. It turns out that the algebraic approach could produce factorization before taking the norm\, whereas the analytic approach could not. In this talk\, I will report on-going work with Mike Daas\, where we aim to remove the norm through a p-adic analytic approach in the case of Shimura curves.
UID:153219-21915436@events.umich.edu
URL:https://events.umich.edu/event/153219
CLASS:PUBLIC
STATUS:CONFIRMED
CATEGORIES:Mathematics
LOCATION:East Hall - 4088
CONTACT:
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DTSTAMP:20260929T150501
DTSTART;TZID=America/Detroit:20261026T160000
DTEND;TZID=America/Detroit:20261026T170000
SUMMARY:Livestream / Virtual:Long time asymptotics of the generalized soliton gas for the mKdV equation
DESCRIPTION:We analyze a new class of solutions of the modified KdV equation introduced by Dyachenko\, Zakharov\, and Zakharov\, and which can be interpreted as a soliton gas.  These solutions are characterized by a Riemann-Hilbert problem which arises as the limit $N\to \infty$ of a sequence of $2N$-soliton RH problems\, where the solitons display two different triangularity in the jumps. The limiting RH problem belongs to a novel class of problems\, where the jump matrices do not have any zero entry (as opposed to the classical upper/lower triangular setting).\n We show that the initial profile of such a gas solution is approaching a cnoidal wave solution for $x\to \pm \infty$ with different phase shifts\, and we establish an asymptotic description of the gas of solitons for large times that is valid over the entire spatial domain\, in terms of Jacobi elliptic functions\, with slowly modulated phase shifts as time varies from $-\infty$ to $+\infty$.\nThis is a joint work with Ken McLaughlin (Tulane U.) and Robert Jenkins (UCF).\n\n*To request access to the Zoom room\, please contact Nathan Hayford at nhayford [ at ] umich.edu.*
UID:153062-21915026@events.umich.edu
URL:https://events.umich.edu/event/153062
CLASS:PUBLIC
STATUS:CONFIRMED
CATEGORIES:Mathematics
LOCATION:Off Campus Location
CONTACT:
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