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SUMMARY:Alejandro Calleja (Univ. Complutense\, Madrid)
DTSTART:20250217T110000Z
DTEND:20250217T120000Z
DTSTAMP:20260423T010748Z
UID:GPL/42
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/GPL/42/">Cha
 racter Varieties in Knot Theory</a>\nby Alejandro Calleja (Univ. Compluten
 se\, Madrid) as part of Geometry and Physics @ Lisbon\n\nLecture held in 6
 .2.33 (Seminar Room\, Math\, FCUL).\n\nAbstract\nGiven an algebraic group 
 G and a knot K ⊂ S^3\, we define the G-character variety of K as the mod
 uli space of representations ρ : π1(S^3 − K) → G of the knot group i
 nto G. The importance of these varieties lies in the fact that their study
  provides in a natural way many knot invariants.\n\nIn this talk\, we will
  introduce one of the most important of these invariants\, the E-polynomia
 l\, exposing the techniques used to study them\, as well as the main known
  results\, focusing especially on the case of torus knots. In this context
 \, being able to distinguish when two representations are isomorphic becom
 es crucial. For facing this problem\, we will introduce the configuration 
 space of orbits\, a variety formed by tuples of pairwise non-isomorphic re
 presentations.\n
LOCATION:https://researchseminars.org/talk/GPL/42/
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