Wollongong OANCG Seminar
A weekly research seminar hosted at the University of Wollongong on the topics of operator algebras, noncommutative geometry, and related fields. The seminar has been running continuously since 2011.
Key Info
- Regular time: Thursday 3:30 pm Wollongong time (this may vary occasionally and will be noted on the talks below)
- Regular location: 39C.174 - Campus map
- Zoom: Link - Meeting ID: 861 2230 0349 (password provided on request)
- Organisers: Angus Alexander & Alexander Mundey
If you are interested in either giving a talk or being added to the mailing list, please contact the organisers at wollongong.oancg[at]gmail.com.
Talks typically run for around 55 minutes. We welcome speakers ranging from seasoned researchers to graduate students. We hold talks on campus and host remote speakers via Zoom.
Talk Schedule - 2024
Click on "Abstract" to reveal the abstract.
Upcoming talks
- May 2: Eva-Maria Hekkelman (University of New South Wales)
The Joy of MOIsAbstract
Operator integrals appear in various contexts of noncommutative geometry. Proofs of the local index formula, expansions of the spectral action and asymptotics of the heat trace are just a few examples. Thankfully, back in the day, the Soviet school of mathematics cooked up a theory of Multiple Operator Integrals (MOIs) which provides a big toolbox for handling complicated integrals of bounded operators. This is still an active field of research. Sadly, it currently isn't applicable to NCG since our integrals have unbounded operators all over the place. In joint work with Ed McDonald and Teun van Nuland we adapted the theory of MOIs to the framework of abstract pseudodifferential operators Connes–Moscovici/Higson style, which makes MOI theory usable in NCG contexts. We hope this greatly reduces the time noncommutative geometers have to spend fiddling with nasty operator integral analysis. - May 9: Alexander Mundey (University of Wollongong)
TBAAbstract
TBA - May 16: TBA
TBAAbstract
TBA - May 23: Dimitris Gerontogiannis (Leiden University) - Zoom Talk
TBAAbstract
TBA
Recent talks
- April 18: Becky Armstrong (Victoria University of Wellington)
Representing topological full groups in Steinberg algebras and C*-algebrasAbstract
Topological full groups are a useful groupoid invariant that have been used to solve important open problems in group theory. Steinberg algebras are a purely algebraic analogue of groupoid C*-algebras that generalise both Leavitt path algebras and Kumjian–Pask algebras. The Steinberg algebra of an ample Hausdorff groupoid is a quotient of the algebra generated by the inverse semigroup of compact open bisections of the groupoid. Since the topological full group of an ample Hausdorff groupoid sits inside this inverse semigroup, it is natural to ask what the relationship is between the algebra of the topological full group and the Steinberg algebra of the groupoid. In this talk I will present recent results answering this question. (This is joint work with Lisa Orloff Clark, Mahya Ghandehari, Eun Ji Kang, and Dilian Yang.) - April 11: Isaac Bankier (University of Wollongong)
The Groupoid Interpretation of EqualityAbstract
Primary doctrines are a construction presenting a system of first order logic over a base category. Primary doctrines need not have internal notions of equality, however this can be added cofreely, by taking "quotients" by all possible internal equivalence relations. In the proof relevant generalisation of primary doctrines, called primary fibrations, we will see that internal groupoids play the role of equivalence relations. - April 4: Nate Brown (Pennsylvania State University) - Colloquium Talk
Inclusive teaching: a mathematician's viewAbstract
After 20 years of research in theoretical maths, I switched to educational research. Specifically, inequity in STEM education at the university level. In this talk I'll present a representative sample of the body of research demonstrating inequities and their impacts. Correcting course requires a critical examination of higher education from all angles, but in the second half of my talk I'll focus on inclusive teaching as a lever for change. I'll discuss my own journey to becoming a more inclusive teacher and some cornerstones of my approach. - March 28: Arnaud Brothier (University of New South Wales)
Forest-skein categories and groupsAbstract
Vaughan Jones found unexpected connections between subfactor theory and Richard Thompson's group while attempting to construct conformal field theories (CFT). This led to numerous fruitful applications and among others provided a novel way to construct group actions using categories. I am initiating a program strengthening Jones' visionary work where the Thompson group is replaced by a family of groups that I name "forest-skein groups". These groups are interesting on their own, satisfying exceptional properties and having powerful extra-structures for studying them. They are isotropy subgroup of forest-skein categories: categories of planar diagrams mod out by certain skein relations (just like planar algebras are in Jones' subfactor framework).
I will briefly say a word about the story of Jones's discovery and then present forest-skein categories and groups using explicit examples. - March 21: Elizabeth Mabbutt (University of Wollongong)
What is a Sobolev Space and Why Do We Care?Abstract
In simple terms, a Sobolev space is a normed vector space where two functions are “close together” with respect to the Sobolev norm if and only if their derivatives up to order \(m\) are “close together” with respect to the \(L^p\) norm. To understand what this means, a lot of background in functional analysis is required. In this talk, I will explain this background, eventually coming up with a rigorous definition of what a Sobolev space is, and will then show why we care about these spaces. - March 14: Nicholas Seaton (University of Wollongong)
Turning nasty groups into nice onesAbstract
In 2011, an Heuf, Kumjian and Sims provided a classification for Fell algebras. They showed that two such algebras are Morita equivalent over their spectrum \(X\) if and only if they have the same class in the equivariant sheaf cohomology group \(H^2(X)\). This group is nasty, it is very difficult to work with as it is defined using abstract nonsense. In this talk, I will show that this group is isomorphic to a nice group, that is, a direct limit of twists groups. - March 7: Alex Paviour (University of Wollongong)
A glimpse at Axiomatic QFTAbstract
I will discuss the motivation for studying quantum field theory by describing the physical problems it tries to address. I will then describe an influential attempt at a mathematically rigorous basis for QFT, the Wightman axioms, and their physical interpretation. I'll give some physically uninteresting but mathematically challenging examples of quantum fields satisfying these axioms, discuss the benefits and shortcomings of this approach to QFT, and point to some important theorems. - February 29: Angus Alexander (University of Wollongong)
Stationary scattering theoryAbstract
In this talk I will discuss some basic quantities in scattering theory and their physical motivations, as well as how to use the stationary approach to obtain scattering information. - February 22: Aidan Sims (University of Wollongong)
When do \(k\)-graphs embed in their fundamental groupoids, and why does it matter?Abstract
Every graph \(C^*\)-algebra is Morita equivalent to a crossed product by its fundamental group of a \(C^*\)-algebra that is itself Morita equivalent to a commutative AF algebra. It turns out that this is because graphs always embed in their fundamental groupoids. Higher-rank graphs (aka \(k\)-graphs) are a different story. I’ll explain why, starting with what a \(k\)-graph and its fundamental groupoid are. This is joint work with Nathan Brownlowe, Alex Kumjian and David Pask. - Talks from previous years