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SUMMARY:Yiannis Sakellaridis
DTSTART:20200530T143000Z
DTEND:20200530T153000Z
DTSTAMP:20260421T085851Z
UID:CARTOON/2
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CARTOON/2/">
 Intersection cohomology & $L$-functions</a>\nby Yiannis Sakellaridis as pa
 rt of Cross Atlantic Representation Theory and Other topics ONline (CARTOO
 N) conference\n\n\nAbstract\nI will report on ongoing joint work with Jona
 than Wang\, relating the intersection complex of the arc space of a spheri
 cal variety to an unramified local $L$-function. This is a broad generaliz
 ation of Tate's thesis ($G=\\mathbb G_m$\, $X=\\mathbb A^1$)\, where the l
 ocal unramified $L$-factors are represented by the characteristic function
  of the integers $\\mathfrak o$ of a non-Archimedean field. For more gener
 al groups $G$ and possibly singular spherical $G$-varieties $X$\, the char
 acteristic function of $X(\\mathfrak o)$ is not the correct object to cons
 ider\, and has to be replaced by a function obtained as the Frobenius trac
 e of the intersection complex of the arc space of $X$. In special cases of
  horospherical\, toric\, affine homogeneous spherical varieties\, or certa
 in reductive monoids\, the relation of this function to $L$-functions was 
 previously described in works of Braverman--Finkelberg--Gaitsgory--Mirkovi
 &cacute\;\, Bouthier--Ng&ocirc\; and myself. Our current work describes th
 ese IC functions in a very general setting\, relating the IC function of t
 he arc space to an $L$-value determined by the geometry of the spherical v
 ariety.\n
LOCATION:https://researchseminars.org/talk/CARTOON/2/
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