*This seminar series gives visitors and staff members the opportunity to explain the context and aims of their work. These research talks cover any field in the mathematical sciences, and should be presented in a way that is understandable and interesting to a broad audience.* *Seminar information and recordings can be found below and in the SMRI Seminar YouTube playlist.*

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##### SMRI Seminar ‘Homotopy of product systems, K-theory of k-graph algebras, and the Yang-Baxter equations’

**Aidan Sims**, University of Wollongong

**Aidan Sims**

**18 December 2020**

*Abstract:* Higher-rank graphs, or k-graphs, are higher-dimensional analogues of directed graphs. Each k-graph can be described in terms of a coloured graph, called its skeleton, and some factorisation rules that describe how 2-coloured paths pair up into commuting squares. C*-algebras of k-graphs generalise Cuntz-Krieger algebras, and have been the subject of sustained interest essentially because questions about crossed products of C*-algebras by higher-rank free abelian groups are hard, and k-graph algebras constitute a comparably tractable class of examples that could point the way to general theorems. A particularly obstinate question in this vein is that of determining the K-theory of a k-graph algebra, or even just whether the K-theory depends on the factorisation rules, or only on the skeleton. I’ll outline some joint work with James Fletcher and Elizabeth Gillaspy that uses a homotopy argument to establish a surprising link between this question and the question of connectedness (or otherwise) of the space of solutions to a Yang-Baxter-like equation. I won’t assume any background about C*-algebras, k-graphs, or the Yang-Baxter equations, and all are welcome—and people who might know about connectedness (or otherwise) of the spaces of solutions to Yang-Baxter-like equations are especially welcome!

##### SMRI Seminar ‘Piecewise full groups of homeomorphisms of the Cantor set’

**David Robertson**, University of New England

**David Robertson**

**11 November 2020**

*Abstract:* A group G acting faithfully by homeomorphisms of the Cantor set is called piecewise full if any homeomorphism assembled piecewise from elements of G is itself an element of G. They first appeared in the work of Giordano, Putnam and Skau in the context of Cantor minimal systems. Recently they have received significant attention as a source of new examples of finitely generated infinite simple groups. I will present a number of results about these groups obtained in joint work with Alejandra Garrido and Colin Reid.A group G acting faithfully by homeomorphisms of the Cantor set is called piecewise full if any homeomorphism assembled piecewise from elements of G is itself an element of G. They first appeared in the work of Giordano, Putnam and Skau in the context of Cantor minimal systems. Recently they have received significant attention as a source of new examples of finitely generated infinite simple groups. I will present a number of results about these groups obtained in joint work with Alejandra Garrido and Colin Reid.

##### SMRI Seminar Course ‘The geometric approach to cohomology’

**James Borger and Lance Gurney**, Australian National University

**James Borger and Lance Gurney**

**11 November 2020**

*Abstract:* The aim of these two talks is to give an overview of the geometric aka stacky approach to various cohomology theories for schemes: de Rham, Hodge, crystalline and prismatic (due to Simpson and later Drinfel’d). The basic observation is that interesting cohomology theories for schemes can be realised as the (humble) coherent cohomology an associated stack. Interesting aspects of the cohomology theories e.g. comparison theorems, theories of coefficients, perfectness etc can then be naturally expressed and proven in terms of the geometry of the associated stacks. Watch the recordings.

##### SMRI Seminar ‘In praise of small data’

**Tom Bridgeland**, University of Sheffield

**Tom Bridgeland**

**30 January 2020**

*Abstract:* Statistical science has a 200-year history of advances in theory and application. Data science is a relatively newly defined area of enquiry developing from the explosion in the ubiquitous collection of data. The interplay between these fields, and their interactions with science, are a topic of lively discussion among statisticians. This talk will overview some of the current research in statistical science that is motivated by new developments in data science.

*Biography: *Nancy Reid is University Professor and Canada Research Chair in Statistical Theory and Applications at the University of Toronto. Her research interests include statistical theory, likelihood inference, design of studies, and statistical science in public policy. Her main research contributions have been to the field of theoretical statistics. Professor Reid is a Fellow of the Royal Society, the Royal Society of Canada, the American Association for the Advancement of Science, and a Foreign Associate of the National Academy of Sciences. In 2014 she was appointed Officer of the Order of Canada.