BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:John Quigg (Arizona State University) DTSTART:20200819T190000Z DTEND:20200819T200000Z DTSTAMP:20260420T053058Z UID:NYC-NCG/17 DESCRIPTION:Title: Baum-Connes\, coactions\, and the Tilde Problem\nby John Quigg (Arizo na State University) as part of Noncommutative geometry in NYC\n\n\nAbstra ct\nTrouble with the Baum-Connes Conjecture (with coefficients) can in som e way be blamed upon the existence of groups for which the reduced-crossed -product functor is not exact. The full crossed product is exact but doesn 't fix the conjecture. Efforts to fix the conjecture have focused upon the ``minimal exact crossed product''\, whose existence is known through abst ract nonsense\, but a construction remains elusive. Baum\, Guentner\, and Willett propose a candidate formed in part by tensoring with a fixed actio n. Our contribution to the [BGW] ``exotic crossed product'' program involv es composing the full crossed product with coaction functors\, hoping that the shift to coactions will add new insights. In particular\, we replace the [BGW] candidate by tensoring with a fixed coaction. For a long time we had a hard time proving that our functor is exact. The ``natural'' approa ch involves embedding into ``tilde multiplier algebras'' (which I'll defin e in the talk). But we can't see how to prove that this gives an exact fun ctor\, and we call this the Tilde Problem. To get around this\, we initial ly proved exactness of our coaction functor another --- extremely unsatisf ying --- way: a long odyssey through equivariant C*-correspondences\, ``na tural'' Morita equivalence\, crossed-product duality\, and --- the final h umiliation --- appealing to exactness of the [BGW] crossed-product functor itself\, completely thwarting our goal of doing everything within the rea lm of coactions. Fortunately\, we recently saw how to use our incomplete k nowledge of the tilde functor to prove exactness of our coaction functor.\ nThis is joint work with Steve Kaliszewski and Magnus Landstad.\n LOCATION:https://researchseminars.org/talk/NYC-NCG/17/ END:VEVENT END:VCALENDAR