California State University, Long Beach is proud to hold the 2007 West Coast Operator Algebra Seminar (WCOAS). There will be 9 talks (4 50-minute long and 5 25-minute long) starting Saturday February 2, 2008 and ending Sunday February 3, 2008. All talks will be held in the Lecture Hall Building room 151 (LH-151).
Parking is free in Lot 4 and Lot 3 in any un-marked spot. See http://daf.csulb.edu/maps/img/maps/2006.gif.
The following is the schedule for Saturday, February 02 2008.
| Time | Activity | Speaker | Title |
|---|---|---|---|
| 09:00am – 09:30am | Breakfast - Registration | ||
| 09:30am – 10:00am | Talk | Martha Gregg | C*-extreme completely positive mappings |
| 10:00am – 10:15am | Break | ||
| 10:15am – 10:45am | Talk | Dan Shiber | CCR Random Matrix Models with Potential |
| 10:45am – 11:00am | Break | ||
| 11:00am – 12:00am | Talk | Jesse Peterson | Group cocycles and the ring of affliated operators |
| 12:00pm – 1:30pm | Lunch | ||
| 01:30pm – 02:30pm | Talk | Adrian Ioana | On the subequivalence relations induced by a Bernoulli action |
| 02:30pm – 02:45pm | Break | ||
| 02:45pm - 03:15pm | Talk | Jason Asher | A Kurosh-Type Theorem for Type III |
| 03:15pm - 03:30pm | Break | ||
| 03:30pm - 04:30pm | Talk | Richard Burstein | Subfactors obtained from Hadamard matrices |
| 06:30pm | Dinner at Ferraro's |
The following is the schedule for Sunday, February 03 2008.
| Time | Activity | Speaker | Title |
|---|---|---|---|
| 09:30am – 10:00am | Talk | Byung Jay Kahng | Fourier transform on locally compact quantum groups |
| 10:00am – 10:15am | Break | ||
| 10:15am – 10:45am | Talk | Kamran Reihani | On K-groups of the crossed products associated with a class of transfomations of tori |
| 10:45am – 11:00am | Break | ||
| 11:00am - 12:00am | Talk | Aviv Censor | Taking Groupoid C*-algebras to the limit |
Let G be a countable group, (X,m) be a non-trivial probability space and denote by S the equivalence relation induced by the Bernoulli action of G on (X,m)^G. I will prove that for any subequivalence relation R of S, there exists a partition X_0,X_1,.. of X^G with R-invariant measurable sets such that the restriction R|X_0 is hyperfinite and R|X_i is strongly ergodic, for i=1,2,..
Let T be a compact Hausdorff space. Raeburn and Taylor associated groupoid C*-algebras to open covers of T, and showed that any element in the Brauer group of T can be realized by such an algebra. We study the asymptotic behavior of the Raeburn-Taylor C*-algebras related to a sequence of open cover refinements. This is accomplished via a limit groupoid G which we construct, along with a groupoid 2-cocycle. Our main result presents the groupoid C*-algebra of G as a certain generalized direct limit of the Raeburn-Taylor algebras. As a special case, our construction produces all UHF C*-algebras as algebras of the form C*(G). This talk is based on joint work with Daniel Markiewicz.
The notion of Fourier transform is among the more important tools in analysis, which has been generalized in abstract harmonic analysis to the level of abelian locally compact groups. The aim of this paper is to further generalize the Fourier transform: Motivated by some recent works by Van Daele in the multiplier Hopf algebra framework, and by using the Haar weights, we define here the (generalized) Fourier transform and the inverse Fourier transform, at the level of locally compact quantum groups. We will then consider the analogues of the Fourier inversion theorem, Plancherel theorem, and the convolution product. Along the way, we also obtain an alternative description of the dual pairing map between a quantum group and its dual.
We will present an extension of the Kurosh-Type Theorem of N. Ozawa to the case of the reduced free product of II_1 factors with non-tracial states. The argument will proceed via a generalization of S. Popa's intertwining-by-bimodules technique.
In this talk, we first review how the Pimsner-Voiculescu exact sequence can be employed to compute the K-groups of the crossed products associated with a general transformation of an n-torus. An error in the literature is addressed regarding the torsion parts of the K-groups of crossed products of Furstenberg transformations. Then for a class of transformations of tori including Furstenberg ones, we explicitly compute the free ranks of the K-groups based on the combinatorial properties of representations of the simple Lie algebra sl_2(C). This leads to finding generating functions and the asymptotic behavior of the sequence of ranks in terms of the dimension of the transformed torus.
The generalized state space of a commutative C*-algebra, denoted SH(C(X)), is the set of positive unital maps from C(X) to the algebra B(H) of bounded linear operators on a Hilbert space H . C*-convexity is one of several noncommutative analogs of convexity which have been discussed in this context. In this paper it is shown that a C*-extreme point of SH(C(X)) satisfies a certain spectral condition on the operators in the range of the associated positive operator-valued measure. If H is finite dimensional, D. Farenick and P. Morenz have shown that every C*- extreme point of SH(C(X)) is multiplicative. However, their method is fundamentally different from the one used here, which enables us to show that C*-extreme maps from C(X) into K+ , the algebra generated by the compact and scalar operators, are multiplicative. It is then possible determine the structure of these maps.
A Hadamard matrix may be used to construct a symmetric commuting square, which gives a subfactor via iteration of the basic construction. Certain Hadamard subfactors arise from the group construction of Bisch and Haagerup. We will discuss methods for computing the principal graphs and standard invariants of these examples.
I will present some results (joint work with Andreas Thom) on cocycles from a group into it's left regular representation and also into the ring of affiliated operators of the group von Neumann algebra. Specifically I will be interested in when a group has positive first l2-Betti number and what does this mean about the structure of certain subgroups when this is the case. I will include a strong generalization of a result of Luck and Gaboriau which states that a finitely generated normal subgroup of a group with positive first l2-Betti number is either a finite subgroup or is of finite index. I will also generalize some classical results of Karrass, Solitar, Griffiths, and Baumslag.
California State University, Long Beach is located at 1250 Bellflower Boulevard Long Beach, California 90840. For your convenince we have provided directions to the seminar from the four major airports (LAX, SNA, LGB, ONT) and large cities.
From Los Angeles International Airport (LAX), Santa Monica, West LA:
Please see the campus map at http://daf.csulb.edu/maps/.
From John Wayne International Airport (SNA), Orange:
Please see the campus map at http://daf.csulb.edu/maps/.
From Orange County:
Please see the campus map at http://daf.csulb.edu/maps/.
From Downtown LA, East LA:
Please see the campus map at http://daf.csulb.edu/maps/.
From Long Beach Airport (LGB)
Please see the campus map at http://daf.csulb.edu/maps/.
From Ontario Internation Airport (ONT):
Please see the campus map at http://daf.csulb.edu/maps/.
Parking: During the weekend parking is free. Please park in Lot 5 directly in front of the LA5 building. See http://daf.csulb.edu/maps/img/maps/2006.gif.
Downtown Long Beach is the entertainment center of this area. Please see http://www.visitlongbeach.com/maps/downtownlongbeach.htm In particular visit the water-front. For specific information please see http://www.ci.long-beach.ca.us/visitors/waterfront.asp. Other sites of interest are:
The CSULB campus offers many interesting peculiar corners. Please visit http://www.csulb.edu/community/v-eventsattractions.html.
Please send the following registration information as soon as possible to gdellaro[at]csulb.edu:
We are expecting support from the NSF. Providing we get the usual support for the conference, we will respect the usual inverse seniority basis. Priority in funding will be given to unsupported graduate students and post-docs. We hope that participants with grants and/or travel money from their home institution will use these to pay as much of their expenses as possible. (Hint: you can increase the probability of getting fully reimbursed for your lodging if you share a room with someone.) We will need original receipts. Also, for non-US-residents, we will need a photocopy of the picture and visa pages of your passport, and your I-94 (if applicable). Do not send these now - just be prepared to give them to us at the conference. Foreign participants must have a B-1 visa to get reimbursement; a B-2 visa or a tourist visa is not good enough. It is at the immigration officer's discretion at the point of US entry which visa (B-1 or B-2) the visitor will receive. You must insist on getting a B-1 visa! We are happy to provide you with a letter of invitation - please let us know if you need one. Note that all of the above applies to Canadians as well.
The conference hotel is the The Guesthouse International Hotel, Long Beach. There is a block of rooms on reserve. Please mention the WCOAS to get the special rate. You can call directly at 562-597-1341 or see http://www.guesthouselb.com/.
