University of California, Riverside 
Department of Mathematics
Groupoids Seminar
Organizer: Aviv Censor
The UCR Groupoids Seminar started meeting in the Fall 2008 quarter. The seminar's original objective was to focus
attention on a very interdisciplinary and intriguing field of mathematics, in view of the
Groupoidfest 2008 conference hosted at UCR in November 2008.
Being successful in attracting participants and interest, the seminar continues running regularly in 20092010.
The first meeting of the Spring 2010 quarter will be on March 30, 2010.
In Spring 2010, the UCR Groupoids Seminar will meet on Tuesdays at 12:40  2:00 pm
in room 268, Surge building.
Spring 2010
March 30
Speaker: Daniele Grandini
Title: Geometry and Groupoids (cont.)
April 6
Speaker: Daniele Grandini
Title: Geometry and Groupoids, part 4: from Pseudogroups to Groupoids via Germs
April 13
Speaker: Daniele Grandini
Title: Geometry and Groupoids, part 4 (cont.): from Pseudogroups to Groupoids via Germs
April 20
Speaker: Daniele Grandini
Title: Geometry and Groupoids, part 5: Jets
April 27
Speaker: Chris Rogers
Title: Introduction to Differentiable Stacks
May 4
No meeting
May 11
Equivariant Homotopy and Orbifold Invariants
Laura Scull, Fort Lewis College
Abstract
An orbifold is representable if it can be presented as the orbit
space of a manifold by the action of a compact Lie group. A large class of orbifolds is known to be representable.
In this talk I will discuss an ongoing project, joint with D. Pronk of Dalhousie University, to devise a framework for generalizing
results of equivariant homotopy theory to obtain orbifold homotopy invariants for representable orbifolds.
To do this, we represent orbifolds using Lie groupoids where two such groupoids represent the same orbifold if and only if
they are Morita equivalent. A representable orbifold can be obtained from a translation groupoid created from the action of a Lie group
on a manifold. The idea of this project is to examine the notion of Morita equivalence for translation groupoids.
We have used this point of view to develop a method for deciding when equivariant results apply to orbifolds.
I will explain our results and discuss the applications we are currently working with.

May 18
Speaker: Chris Rogers
Title: Introduction to Differentiable Stacks (cont.)
May 25
Speaker: Aviv Censor
Title: Inverse Semigroups and Groupoids
Previous Quarters
Winter 2010
January 7
Organizational meeting
January 14
Speaker: Jacob West
Title: The Fundamental Groupoid Revisited
January 21
Speaker: Julie Bergner
Title: Classical Fixed Point Theory
January 28
Speaker: Julie Bergner
Title: Ringoids in Fixed Point Theory
February 4
Speaker: Chris Carlson
Title: From Manifolds to Orbifolds: A Topological Excursion
Abstract
A manifold is a topological space which is locally diffeomorphic to R^{n}. We will look at the
compatibility condition on the atlas. Orbifolds will be introduced, and the new compatibility
condition will be explored. Several illuminating examples will be discussed. Finally, the
groupoid definition will be introduced.
February 11
Speaker: Daniele Grandini
Title: Geometry and Groupoids, part 1: Orbifolds
Abstract
February 18
Speaker: Daniele Grandini
Title: Geometry and Groupoids, part 2: from Group(oid)s to Orbifolds
Abstract
February 25
Speaker: Daniele Grandini
Title: Geometry and Groupoids, part 2: from Group(oid)s to Orbifolds (cont.)
March 4
Speaker: Daniele Grandini
Title: Geometry and Groupoids, part 3: Pseudogroups
March 11
Speaker: Christopher Walker
Title: Groupoid Cardinality and Egyptian Fractions
Fall 2009
September 24
Organizational meeting
October 1
Speaker: Christopher Walker
Title: Groupoidification of Hall Algebras
October 8
Speaker: Christopher Walker
Title: Groupoidification of Hall Algebras (cont.)
October 15
Speaker: Aviv Censor
Title: Topological Groupoids and Haar Systems
October 22
Speaker 1: Aviv Censor
Title: Towards Topological Degroupoidification
Abstract
The groupoidification program led by J. Baez and J. Dolan has been successfully applied to several structures,
such as Hall algebras and Feynman diagrams. In order to expand the scope of groupoidification, with operator
algebras in mind, we take first steps in extending the theory from the realm of discrete groupoids to the
topological setting. In particular we extend the notion of groupoid cardinality, by defining how to measure a
topological groupoid. We also show how to assign measures to continuous groupoid homomorphisms. We demonstrate
our results on groupoids corresponding to open covers, which have been proven useful in the study of continuous
trace C*algebras.
This is a preliminary report on joint work with Daniele Grandini and Christopher Walker.
Speaker 2: Christopher Walker
Title: A Categorification of Hall Algebras
Abstract
In 1990 Ringel first proved that given any simplylaced Dynkin diagram, the Hall algebra of this diagram is
isomorphic to the positive part of Uq(g), where g is the lie algebra associated to the same Dynkin diagram.
Hall algebras turn out to be one of the most natural applications of the Baez/Dolan program of “groupoidification”.
In this talk we will describe the pieces of groupoidification necessary for this example, and then show how to apply
the process to Hall algebras.
October 29
Speaker: Daniele Grandini
Title: Measured Groupoids
November 5
Speaker: Daniele Grandini
Title: Measured Groupoids (cont.)
November 12
Crossed Modules of Hopf Algebras
Yael Fregier, University of Luxembourg
Abstract
Our main goal in this talk will be to translate the diagram relating groups, Lie algebras and Hopf algebras to the
corresponding 2objects, i.e. to categorify it. This will be done by interpreting 2objects as crossed modules and
showing the compatibility of the standard functors linking groups, Lie algebras and Hopf algebras with the concept
of a crossed module. In particular this gives an approach to integrating Lie 2algebras.

November 19
Speaker: Aviv Censor
Title: Can topological & measuretheoretic degroupoidification be made easy?
November 26
Thanksgiving
December 3
Speaker: Edward Burkard
Title: Wedderburn's Theorem for Ringoids
Spring 2009
April 9
Speaker: Julie Bergner
Title: Simplicial Complexes, Simplicial Sets, and Nerves of Groupoids
April 16
Speaker: Julie Bergner
Title: Simplicial Complexes, Simplicial Sets, and Nerves of Groupoids (cont.)
April 23
Speaker: Julie Bergner
Title: Simplicial Complexes, Simplicial Sets, and Nerves of Groupoids (cont.)
April 30
Speaker: Edward Burkard
Title: Ringoids
May 7
Speaker: Christopher Walker
Title: Introduction to Groupoidification
May 14
Groupoids for Classical Field Theories with Symmetry
Joris Vankerschaver, Caltech
Abstract
Einstein's theory of relativity is one of the pinnacles of modern physics.
In this talk, I will focus on some of the particular mathematical structures
underlying this theory. In particular, there is the principle of covariance,
which states that relativity is invariant under arbitrary diffeomorphisms
of spacetime. As a result, not all degrees of freedom are physical. More
specifically, the theory is both overdetermined, in the sense that there
are constraints on the initial data, and underdetermined because of the
aforementioned gauge freedom. I will outline some of our recent work
in dealing with these issues in the case of relativity and other covariant
field theories. Firstly, I will discuss how a simple variational principle
can be used to determine both the constraints and the evolution of the
dynamical variables. Secondly, I will show how some of the constraints
can be seen as the zero level set, not of a momentum map, but of a
groupoid moment map. The talk should be accessible for anyone with a
basic understanding of classical physics. This is joint work with Marco
CastrillonLopez, Jerrold E. Marsden, and Hiroaki Yoshimura.
(Joint meeting with FRG, in Surge 268)

May 21
Speaker: Christopher Walker
Title: Introduction to Groupoidification (cont.)
May 28
Speaker: Aviv Censor
Title: Towards Topological Degroupoidification
Abstract
The groupoidification program led by J. Baez and J. Dolan has been successfully applied to several structures,
such as Hall algebras and Feynman diagrams. In order to expand the scope of groupoidification, with operator
algebras in mind, we take first steps in extending the theory from the realm of discrete groupoids to the
topological setting. In particular we extend the notion of groupoid cardinality, by defining how to measure a
topological groupoid. We also show how to assign measures to continuous groupoid homomorphisms. We demonstrate
our results on groupoids corresponding to open covers, which have been proven useful in the study of continuous
trace C*algebras.
This is a preliminary report on joint work with Daniele Grandini and Christopher Walker.
Winter 2009
January 8
Speaker: Aviv Censor
Title: Groupoids Revisited
January 15
Speaker: Aviv Censor
Title: Groupoid Cohmology and Twisted Groupoid C*algebras (cont.)
January 22
Speaker: Aviv Censor
Title: Groupoid Actions and Equivalence of Groupoids
January 29
Speaker: Vasiliy Dolgushev
Title: The GoldmanMillson Groupoid of a Differential Graded Lie Algebra
Abstract
Many questions of deformation theory give rise to a differential graded (DG) Lie algebra.
To every DG Lie algebra we may assign a groupoid which captures some information about the original question
from deformation theory. In my talk I will explain a construction of this groupoid and give examples.
I will also talk about the GoldmanMillson theorem which says that, under certain assumptions,
quasiisomorphic DG Lie algebras give rise to equivalent groupoids. If I will have time then I will
mention E. Getzler's and A. Henriques' generalizations of these classical constructions.
Febuary 5
Speaker: Aviv Censor
Title: Groupoid Actions and Equivalence of Groupoids (cont.)
Febuary 12
Speaker: Daniele Grandini
Title: Differentiating Lie Groupoids
Febuary 19
Speaker: Daniele Grandini
Title: Differentiating Lie Groupoids (cont.)
Febuary 26
Speaker: Daniele Grandini
Title: Differentiating Lie Groupoids (cont.)
March 5
Speaker: Aviv Censor
Title: Equivalence vs. Similarity of Groupoids
March 12
Speaker: Aviv Censor
Title: Equivalence vs. Similarity of Groupoids (cont.)
Fall 2008
A description of the seminar's objectives can be found in the Groupoid Seminar
Info Page.
September 25
Speaker: Aviv Censor
Title: Groupoids Capture Local Symmetries
October 2
Speaker: Aviv Censor
Title: The Axiomatic Definition and Many Examples
October 9
Speaker: Aviv Censor
Title: Terminology, Properties, and More Examples
October 16
Speaker: Aviv Censor
Title: Some Classification Theorems, Topology and Measure
October 23
Speaker: Julie Bergner
Title: The Fundamental Groupoid
October 30
Speaker: Aviv Censor
Title: Etale Groupoids and their C*Algebras
November 6
Speaker 1: Alex Hoffnung
Title: A Categorification of Hecke Algebras
Speaker 2: Chris Walker
Title: Groupoidified Linear Algebra
November 13
Speaker: Daniele Grandini
Title: Lie Groupoids and Lie Algebroids (part 1)
November 20
Speaker: Daniele Grandini
Title: Lie Groupoids and Lie Algebroids (part 2)
November 21
Special Colloquium:
Groupoid Symmetry for Einstein's Equations?
Alan Weinstein, UC Berkeley
Abstract
The Einstein equations for a Lorentz metric on 4dimensional spacetime may be cast in hamiltonian form, where the
configuration space is the space of riemannian metrics on a 3dimensional manifold. It has been known since work of Dirac
50 years ago that the initial conditions for solutions of these equations are subject to constraints, but our geometric
understanding of these constraints is not complete. It is generally felt that the constraints are related to conservation
laws associated with the action of the group of diffeomorphisms of spacetime, but this group does not act on the initial
data.
In this talk, I will explain ongoing work with Christian Blohmann (Regensburg) and Marco Cezar Fernandes (Brasilia). We
are attempting to show that the initial value constraints for the Einstein equations are associated with the action of a
groupOID related to the groupoid of diffeomorphisms between all pairs of hypersurfaces in spacetime.

November 2223
December 4
Speaker: Aviv Censor
Title: Groupoid Cohmology and Twisted Groupoid C*algebras