Research:

Operator Algebras:

My main research area is C*-algebras, which is a subfield of Functional Analysis. In the past few years I have been focusing on groupoids and their C*-algebras. In my Ph.D. work, Titled "Taking groupoid C*-algebras to the limit", I studied groupoids for open covers, their C*-algebras and limits. This research, which is in part joint work with Daniel Markiewicz, is part of a more ambitious project I hope to pursue: Study the Brauer theory of continuous trace C*-algebras, via carrying out classical results and phenomena from the well developed Brauer theory for fields.
In recent work in progress, I started exploring various connections between groupoid C*-algebras and fractal geometry, in collaboration with Michel Lapidus at UCR.
Simultaneously, I have been working lately with a group led by John Baez at UCR, on a project titled "groupoidification". More specifically, I am working with Daniele Grandini and Christopher Walker on extending the ideas of groupoidification from the discrete setting to the realm of topology and measure theory. Here are slides from recent talks I gave at GPOTS and at Gfest 2009, titled "How to Measure a Groupoid".
I have also been looking into certain roles of groupoids in von-Neumann algebra theory.
Previously, in my M.Sc. thesis, I investigated Lie ideals in nest subalgebras of von-Neumann algebras.

Mathematical Physics:

I have been working together with Guy Tsabary as a side interest, on developing an idea for 3 time dimensions in Special Relativity. This idea evolved into An Alternative Mathematical Model for Special Relativity , published in Il Nuovo Cimento B (see below).

Publications:

Topological and Measure-Theoretic Degroupoidification, with Daniele Grandini and Christopher Walker, in preparation.

Limits of Groupoid C*-algebras arising from Open Covers, with Daniel Markiewicz, Houston Journal of Mathematics, Volume 35 (2009), no. 2, pp. 591-618.

A note about a certain Groupoid C*-algebra Map, with Daniel Markiewicz, preprint.

Taking Groupoid C*-algebras to the Limit, Ph.D. thesis, English, Department of Mathematics, Technion - Israel Institute of Technology, Haifa, Israel, June 2007.

An Alternative Mathematical Model for Special Relativity, with Guy Tsabary, Il Nuovo Cimento B, Volume 120 (2005), Issue 2, pp. 179-196.

Lie Ideals in Nest Subalgebras of von-Meumann algebras, M.Sc. thesis, English, Department of Mathematics, Technion - Israel Institute of Technology, Haifa, Israel, March 2001.

Conference Organization:

Special session on Operator Algebras (with Marta Asaeda and Adrian Ioana), Fall 2009 Western section meeting of the AMS, University of California, Riverside, November 7-8, 2009.

Groupoidfest 2008, University of California, Riverside, November 22-23, 2008.

UCR Operator Algebras Seminar:

The UCR Operator Algebras and related topics seminar meets on Tuesdays at 10:10 - 11:00 in room 268, Surge building.

UCR Groupoids Seminar:

The UCR Groupoids Seminar meets every Thursday at 9:40 - 11:00 am, in Surge 268.

Participation in International Conferences:

AMS Western Section Meeting - Special Session on Operator Algebras at the University of California, Riverside, November 7-8, 2009.
Groupoidfest 2009 at the University of Colorado, Boulder, October 24-25, 2009.
West Coast Operator Algebra Seminar (WCOAS) 2009 at the University of Nevada, Reno, October 17-18, 2009.
GPOTS 2009 (Great Plains Operator Theory Symposium) at the University of Colorado, Boulder, June 2-6, 2009.
Von-Neumann Algebras and Ergodic Theory at UCLA, March 15-18, 2009.
Groupoidfest 2008 at the University of California, Riverside, November 22-23, 2008.
AMS Western Section Meeting - Special Session on C*-algebras, Subfactors and Free Probability at Claremont McKenna College, May 3-4, 2008.
Topics in Von Neumann Algebras at the Banff International Research Station (BIRS), March 23-28, 2008.
West Coast Operator Algebra Seminar (WCOAS) 2008 at the California State University, Long Beach, February 2-3, 2008.
C*-Algebras Associated to Discrete and Dynamical Systems at the Banff International Research Station (BIRS), January 27-February 1, 2008.
Barcelona Conference on C*-Algebras and their Invariants at the Universitat Autonoma de Barcelona, June 11-15, 2007.
35'th Canadian Operator Symposium (COSy) at the University of Guelph, June 5-9, 2007.
Groupoids in Operator Algebras and Noncommutative Geometry at the Institut Henri Poincare, Paris, February 26-March 2, 2007.
GPOTS 2004 (Great Plains Operator Theory Symposium) at Texas A&M University, May 26-May 30, 2004.
CBMS Conference on Graph C*-Algebras at the University of Iowa, May 31- June 4, 2004.

Teaching:

Fall quarter 2009:

Math 260 - Groupoids Seminar, Thursday 9:40-11:00 am, Surge 268
Math 5 - Pre-Calculus. All course materials, including assignments, announcements and grades, can be found on iLearn.
Math 46 - Ordinary Differential Equations. All course materials, including assignments, announcements and grades, can be found on iLearn.

Office Hours: TR 3:30-5:00 pm, 232 Surge Building.

Past:

Here are more details about my past teaching experience.
As a PhD student I was lecturing and prior to that a TA at the Technion, teaching a variety of courses.
My courses have been selected twice and recorded in full for the Technion video library.

Personal:

I am married to Efrat, and father of Ofek, Noga, and Almog.

Contact:

Address : Department of Mathematics, University of California, Riverside CA, 92521, USA

Office : 232 Surge Building.

Phone : 1-951-827-7383

E-mail : avivc@math.ucr.edu