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BEGIN:VEVENT
UID:a13c8f88a2f3381561277a28fa1d4530
CATEGORIES:Number Theory Seminar
CREATED:20220127T180747
SUMMARY:Distribution of holonomy on compact hyperbolic 3-manifolds
LOCATION:Zoom
DESCRIPTION:Date: January 25 2:00 - 3:00pm\nSpeaker: \nTitle: \nThe study of hyperbolic
  3-manifolds draws deep connections between number theory, geometry, topolo
 gy, and quantum mechanics. Specifically, the closed geodesics on a manifold
  are intrinsically related to the eigenvalues of Maass forms via the Selber
 g trace formula and are parametrized by their length and holonomy, which de
 scribes the angle of rotation by parallel transport along the geodesic. The
  trace formula for spherical Maass forms can be used to prove the Prime Geo
 desic Theorem, which provides an asymptotic count of geodesics up to a cert
 ain length. I will present an asymptotic count of geodesics (obtained via t
 he non-spherical trace formula) by length and holonomy in prescribed interv
 als which are allowed to shrink independently. This count implies effective
  equidistribution of holonomy and substantially sharpens the result of Sarn
 ak and Wakayama in the context of compact hyperbolic 3-manifolds. I will th
 en discuss new results regarding biases in the finer distribution of holono
 my.\n \n
X-ALT-DESC;FMTTYPE=text/html:<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:20260830T163541
DTSTART;TZID=America/New_York:20220201T140000
DTEND;TZID=America/New_York:20220201T150000
SEQUENCE:0
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