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DTSTAMP:20250921T233156Z
DESCRIPTION:Title: Effective Generalization of Hall's Theorem for Limit Gro
 ups and Cube Complexes\n\nAbstract: A finitely generated group G is called
  subgroup separable if every finitely generated subgroup H of G is closed 
 in the profinite topology on G (equivalently\, there is a family of finite
  index subgroups of G intersecting in H). One of the initial motivations f
 or studying residually finite groups and subgroup separable groups was McK
 insey-Malcev algorithm solving the word problem in finitely presented resi
 dually finite groups. Recently\, separability has played a crucial role in
  low-dimensional topology\, namely in the resolutions of the Virtually Hak
 en and Virtually Fibered conjectures.\n\nA celebrated theorem of Marshall 
 Hall implies that finitely generated free groups are subgroup separable an
 d that each their finitely generated subgroup H is a retract of a finite-i
 ndex subgroup K. It also states that K can be obtained from H by a series 
 of free products with infinite cyclic groups. The first statement of the t
 heorem was generalized by Wilton for limit groups. Haglund-Wise proved it 
 for right-angled Artin groups when H is word quasiconvex. We generalize th
 e second statement of Hall's theorem and prove that such K can be obtained
  from H by a series of certain HNN-extentions. This implies that if L is a
  right-angled Artin group\, H a word quasiconvex subgroup of L\, then ther
 e is a finite dimensional representation of L that separates the subgroup 
 H in the induced Zariski topology. As a corollary\, we establish a polynom
 ial upper bound on the size of the quotients used to separate H in L. This
  implies the same statement for a virtually special group L and\, in parti
 cular\, a fundamental group of a hyperbolic 3-manifold. For limit groups t
 his implies similar polynomial bounds and the resolution of the Hanna Neum
 ann conjecture.\n\nThese are joint results with K. Brown and A. Vdovina.\n
 \nWe will gather for teatime in the lounge after the talk and then we will
  go for dinner with Olga. Please let me know if you would be interested in
  joining for dinner.\n\nchristopher.karpinski [at] mail.mcgill.ca\n
DTSTART:20250212T210000Z
DTEND:20250212T220000Z
LOCATION:Room 920\, Burnside Hall\, CA\, QC\, Montreal\, H3A 0B9\, 805 rue 
 Sherbrooke Ouest
SUMMARY:Olga Kharlampovich (CUNY\, Grad Center and Hunter College)
URL:/mathstat/channels/event/olga-kharlampovich-cuny-g
 rad-center-and-hunter-college-363525
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