Groupoid Fest '98



Participants

Valentin Deaconu vdeaconu@math.unr.edu Doug Drinen drinen@asu.edu Igor Fulman ifulman@math.ucalgary.ca Jiang-Hua Lu jhlu@math.arizona.edu Steve Kaliszewski kaz@math.la.asu.edu Alex Kumjian alex@unr.edu Paul Muhly muhly@math.uiowa.edu David Pask davidp@frey.newcastle.edu.au Alan Paterson mmap@olemiss.edu John Quigg quigg@math.la.asu.edu Jacqui Ramagge jacqui@frey.newcastle.edu.au Nandor Sieben nandor.sieben@asu.edu Jack Spielberg jss@math.la.asu.edu Belisario Ventura bventura@wiley.csusb.edu Alan Weinstein alanw@math.berkeley.edu Dana Williams dana.williams@dartmouth.edu

Schedule

All talks will be held in room PSA 203 of the Math Building (Bateman Physical Sciences Center, A wing), which is on the northeast corner of Tyler Mall and Palm Walk. You can use a chalk board (sorry, no big chalk, but we do have big erasers!) and/or a transparency projector. Saturday Sunday 9:30-10:30 Weinstein Ramsay 10:30-11:00 Kumjian Fulman 11:00-11:30 -break- -break- 11:30-12:00 Deaconu Pask 12:00- 2:00 -lunch- Ramagge (12:00-12:30) 2:00- 3:00 Paterson -lunch- (12:30- 2:00) 3:00- 3:30 Lu 3:30- 4:00 -break- 4:00- 4:30 Drinen 4:30- 5:00 Sieben 6:00- Tombstone Brewery

Abstracts

Deaconu: Cohomology of topological graphs and pimsner algebra Abstract: We use the long exact sequence of Kumjian to compute the sheaf cohomology of the groupoid \Gamma associated to a topological graph. We show that certain twisted groupoid C*-algebras associated to \Gamma are isomorphic to Pimsner algebras. Drinen: Isomorphism of graph groupoids Abstract: For a row-finite directed graph E, Kumjian, Pask, and Raeburn defined its graph C*-algebra C*(E). If E has no sinks, then C*(E) \cong C*({G}_E), where {G}_E is the graph groupoid, a construction of Kumjian, Pask, Raeburn, and Renault. We investigate some graph transformations which preserve the graph groupoid. Fulman: Ideals in the algebra of a one-sided dynamical system Abstract: We use a spectral theorem for bimodules (an analog of the theorem by Muhly and Solel) to describe ideals in the non-selfadjoint algebra arising from a one-sided dynamical system. Unlike in the case considered by Muhly and Solel, in our case the groupoid arising is not r-discrete. Kumjian: C*-algebras of multigraphs Abstract: Building on recent work of G. Robertson & T. Steger, we consider certain C*-algebras associated to multigraphs. Under mild assumptions the C*-algebra of a multigraph may be seen to be isomorphic to the C*-algebra of a groupoid associated to the multigraph. Lu: Hopf algebras coming from groupoids Pask: Semigroup actions on graph algebras Paterson: Asymptotic morphisms and the analytic index map for Lie groupoids Abstract: We will discuss the construction of a canonical asymptotic morphism {T_{\epsilon}} in E(C_{0}(A(G)^{*}), C^{*}(G)) associated with a Lie groupoid G. When G is a trivial groupoid, this asymptotic morphism is the Connes-Higson asymptotic morphism. For general G, the asymptotic morphism induces the analytic index map on the groupoid. Ramsay: Local action groupoids Abstract: The title refers to groupoids with the property that every point in the space of units has a neighborhood to which the restriction of the groupoid is isomorphic to a groupoid arising from an action of a group on that neighborhood. Most of the talk will be about results on the case in which the group is always the circle. These results were obtained by El Sayed Sallam in his Ph.D. work, extending some results of Baum, Brylinski and MacPherson on delocalized cohomology to such groupoids. Sieben: Fell bundles over inverse semigroups and r-discrete groupoids Abstract: Fell bundles over inverse semigroups are introduced and shown to be closely related to Fell bundles over r-discrete groupoids. Twisted semidirect product bundles are characterized as homogeneous Fell bundles. Weinstein: Toward normal forms for proper groupoids and Lie algebroids

Saturday Night

For Saturday night, we have reserved space at the Tombstone Brewery so we can gather. You'll be able to order your own food and drinks --- it's minimally organized, in keeping with my understanding of the spirit of the conference. The Tombstone Brewery is about 100 yards north of the Best Western, on the same side of the street (Scottsdale Road). From campus, this is about 1 mile north on Rural Road (the eastern boundary of campus), across the bridge over the ``river'', under the freeway bridge, and then immediately on the left. (When Rural Road crosses the river it becomes Scottsdale Road.) Address: 710 E. Gilbert. Phone: (602) 967-2337.

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S. Kaliszewski / Department of Mathematics / Arizona State University
Tempe, Arizona U.S.A. 85287-1804