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UID:a13c8f88a2f3381561277a28fa1d4530
CATEGORIES:Number Theory Seminar
CREATED:20220127T180747
SUMMARY:Distribution of holonomy on compact hyperbolic 3-manifolds
LOCATION:Zoom
DESCRIPTION:<p>Date: January 25 2:00 - 3:00pm<br />Speaker:&nbsp;<br />Title:&nbsp;<br 
 />The study of hyperbolic 3-manifolds draws deep connections between number
  theory, geometry, topology, and quantum mechanics. Specifically, the close
 d geodesics on a manifold are intrinsically related to the eigenvalues of M
 aass forms via the Selberg trace formula and are parametrized by their leng
 th and holonomy, which describes the angle of rotation by parallel transpor
 t along the geodesic. The trace formula for spherical Maass forms can be us
 ed to prove the Prime Geodesic Theorem, which provides an asymptotic count 
 of geodesics up to a certain length. I will present an asymptotic count of 
 geodesics (obtained via the non-spherical trace formula) by length and holo
 nomy in prescribed intervals which are allowed to shrink independently. Thi
 s count implies effective equidistribution of holonomy and substantially sh
 arpens the result of Sarnak and Wakayama in the context of compact hyperbol
 ic 3-manifolds. I will then discuss new results regarding biases in the fin
 er distribution of holonomy.</p><p>&nbsp;</p>
CONTACT:Lindsay Dever (Bryn Mawr)
X-EXTRAINFO:For zoom information please contact Chris Lutsko: chris.lutsko "at" rutgers
 .edu
DTSTAMP:20260830T164029
DTSTART;TZID=America/New_York:20220201T140000
DTEND;TZID=America/New_York:20220201T150000
SEQUENCE:0
TRANSP:OPAQUE
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