numbers floating across space

Congratulations to MPhil student in Pure Mathematics, John McCarthy (Supervisors Varghese, Baraglia) who has been admitted with full scholarship to the PhD program at Imperial College (London) to work with Richard Thomas!

Congratulations to PhD student in Pure Mathematics, Hao Guo (Supervisors Varghese, Hang Wang) who has been offered an NSF funded postdoc at Texas A&M which he will accept!

Posted in News | Tagged , ,
Comments Off on Congratulations to John McCarthy and Hao Guo!

Title: A Hecke module structure on the KK-theory of arithmetic groups
When: Friday, 2 March 2018 at 1:10pm in Barr Smith South Polygon Lec theatre 
Speaker: Bram Mesland (Unversität Bonn)

Abstract: Let $G$ be a locally compact group, $\Gamma$ a discrete subgroup and $C_{G}(\Gamma)$ the commensurator of $\Gamma$ in $G$. The cohomology of $\Gamma$ is a module over the Shimura Hecke ring of the pair $(\Gamma,C_G(\Gamma))$. This construction recovers the action of the Hecke operators on modular forms for $SL(2,\mathbb{Z})$ as a particular case. In this talk I will discuss how the Shimura Hecke ring of a pair $(\Gamma, C_{G}(\Gamma))$ maps into the $KK$-ring associated to an arbitrary $\Gamma$-C*-algebra. From this we obtain a variety of $K$-theoretic Hecke modules. In the case of manifolds the Chern character provides a Hecke equivariant transformation into cohomology, which is an isomorphism in low dimensions. We discuss Hecke equivariant exact sequences arising from possibly noncommutative compactifications of $\Gamma$-spaces. Examples include the Borel-Serre and geodesic compactifications of the universal cover of an arithmetic manifold, and the totally disconnected boundary of the Bruhat-Tits tree of $SL(2,\mathbb{Z})$. This is joint work with M.H. Sengun (Sheffield).

Title: Radial Toeplitz operators on bounded symmetric domains
When: Friday, 9 March 2018 at 1:10pm in Lower Napier LG11
Speaker: Raul Quiroga-Barranco (CIMAT, Guanajuato, Mexico) 

Abstract: The Bergman spaces on a complex domain are defined as the space of holomorphic square-integrable functions on the domain. These carry interesting structures both for analysis and representation theory in the case of bounded symmetric domains. On the other hand, these spaces have some bounded operators obtained as the composition of a multiplier operator and a projection. These operators are highly noncommuting between each other. However, there exist large commutative C*-algebras generated by some of these Toeplitz operators very much related to Lie groups. I will construct an example of such C*-algebras and provide a fairly explicit simultaneous diagonalization of the generating Toeplitz operators.

Title: Quantum Airy structures and topological recursion
When: Wednesday, 14 March 2018 at 1:10pm in Ingkarni Wardli B17
Speaker: Gaetan Borot

Abstract: Quantum Airy structures are Lie algebras of quadratic differential operators — their classical limit describes Lagrangian subvarieties in symplectic vector spaces which are tangent to the zero section and cut out by quadratic equations. Their partition function — which is the function annihilated by the collection of differential operators — can be computed by the topological recursion. I will explain how to obtain quantum Airy structures from spectral curves, and explain how we can retrieve from them correlation functions of semi-simple cohomological field theories, by exploiting the symmetries. This is based on joint work with Andersen, Chekhov and Orantin.

 Title: Family gauge theory and characteristic classes of bundles of 4-manifolds
When: Friday, 16 March 2018 at 1:10pm in Barr Smith South Polygon Lec theatre
Speaker: Hokuto Konno (University of Tokyo)

Abstract: I will define a non-trivial characteristic class of bundles of 4-manifolds using families of Seiberg-Witten equations. The basic idea of the construction is to consider an infinite dimensional analogue of the Euler class used in the usual theory of characteristic classes. I will also explain how to prove the non-triviality of this characteristic class. If time permits, I will mention a relation between our characteristic class and positive scalar curvature metrics. 

Title: Computing trisections of 4-manifolds
When: Friday, 23 March 2018 at 1:10pm in Barr Smith South Polygon Lec theatre
Speaker: Stephen Tillmann

Abstract: Gay and Kirby recently generalised Heegaard splittings of 3-manifolds to  trisections of 4-manifolds. A trisection describes a 4-dimensional manifold as a union of three 4–dimensional handlebodies. The complexity of the 4–manifold is captured in a collection of curves on a surface, which guide the gluing of the handelbodies. The minimal genus of such a surface is the trisection genus of the 4-manifold. After defining trisections and giving key examples and applications, I will describe an algorithm to compute trisections of 4–manifolds using arbitrary triangulations as input. This results in the first explicit complexity bounds for the trisection genus of a 4–manifold in terms of the number of pentachora (4–simplices) in a triangulation. This is joint work with Mark Bell, Joel Hass and Hyam Rubinstein. I will also describe joint work with Jonathan Spreer that determines the trisection genus for each of the standard simply connected PL 4-manifolds.

Title: Chaos in higher-dimensional complex dynamics
When: Friday, 20 April 2018 at 1:10pm in Barr Smith South Polygon Lec theatre
Speaker: Finnur Larusson

Abstract: I will report on new joint work with Leandro Arosio (University of Rome, Tor Vergata). Complex manifolds can be thought of as laid out across a spectrum characterised by rigidity at one end and flexibility at the other.  On the rigid side, Kobayashi-hyperbolic manifolds have at most a finite-dimensional group of symmetries.  On the flexible side, there are manifolds with an extremely large group of holomorphic automorphisms, the prototypes being the affine spaces $\mathbb C^n$ for $n \geq 2$.  From a dynamical point of view, hyperbolicity does not permit chaos.  An endomorphism of a Kobayashi-hyperbolic manifold is non-expansive with respect to the Kobayashi distance, so every family of endomorphisms is equicontinuous.  We show that not only does flexibility allow chaos: under a strong anti-hyperbolicity assumption, chaotic automorphisms are generic.  A special case of our main result is that if $G$ is a connected complex linear algebraic group of dimension at least 2, not semisimple, then chaotic automorphisms are generic among all holomorphic automorphisms of $G$ that preserve a left- or right-invariant Haar form.  For $G=\mathbb C^n$, this result was proved (although not explicitly stated) some 20 years ago by Fornaess and Sibony.  Our generalisation follows their approach.  I will give plenty of context and background, as well as some details of the proof of the main result.

Title: Index of Equivariant Callias-Type Operators
When: Friday, 27 April 2018 at 1:10pm in Barr Smith South Polygon Lec theatre
Speaker: Hao Guo (University of Adelaide)

Abstract: Suppose M is a smooth Riemannian manifold on which a Lie group G acts properly and isometrically. In this talk I will explore properties of a particular class of G-invariant operators on M, called G-Callias-type operators. These are Dirac operators that have been given an additional Z_2-grading and a perturbation so as to be “invertible outside of a cocompact set in M”. It turns out that G-Callias-type operators are equivariantly Fredholm and so have an index in the K-theory of the maximal group C*-algebra of G. This index can be expressed as a KK-product of a class in K-homology and a class in the K-theory of the Higson G-corona. In fact, one can show that the K-theory of the Higson G-corona is highly non-trivial, and thus the index theory of G-Callias-type operators is not obviously trivial. As an application of the index theory of G-Callias-type operators, I will mention an obstruction to the existence of G-invariant metrics of positive scalar curvature on M.

Title: Index of Equivariant Callias-Type Operators
When: Friday, 4 May 2018 at 1:10pm in Barr Smith South Polygon Lec theatre
Speaker: Tony Licata (Australian National University)

Abstract: The Artin braid group arise in a number of different parts of mathematics.  The goal of this talk will be to explain how basic group-theoretic questions about the Artin braid group can be answered using some modern tools of linear and homological algebra, with an eye toward proving some open conjectures about other groups.


Posted in Events, Seminars | Tagged ,
Comments Off on Differential Geometry Seminars: Semester 1

Congratulations to our AMSI Vacation Research Scholars, Tobin South and Michael Ucci who received both of the prizes for the best presentation at the recent #AMSIConnect2018 conference.

It is an outstanding achievement for our students that have won all of the available prizes against a field of students from across the country!

University of Adelaide students Michael Ucci and Tobin South  Photo credit: Michael Fotopoulos

University of Adelaide students Michael Ucci and Tobin South
Photo credit: Michael Fotopoulos

Posted in Events | Tagged ,
Comments Off on Congratulations to Michael Ucci and Tobin South!

Congratulations to Mr Michael Hallam (supervisors Varghese and Baraglia) on being awarded the prestigious 2017 B H Neuman prize for the most outstanding student talk presented at the Annual Meeting of the Australian Mathematical Society. He has also been admitted with a full PhD scholarship to the University of Oxford. More information:”

Posted in News | Tagged ,
Comments Off on Michael Hallam wins the 2017 Neumann Prize & Oxford PhD Scholarship

Title: Calculating optimal limits for transacting credit card customers 15:10 Fri 2 Mar, 2018 :: Horace Lamb 1022 :: Prof Peter Taylor :: University of Melbourne Abstract: Credit card users can roughly be divided into `transactors’, who pay off their balance each month, and `revolvers’, who maintain an outstanding balance, on which they pay substantial interest. In […]

Posted in School Colloquium | Tagged
Comments Off on Semester 1: School Colloquiums

Congratulations to Professor of Mathematical Sciences, Yvonne Stokes, on being awarded the 2018 EO Tuck Medal for outstanding research and distinguished service to the field of Applied Mathematics. She is pictured with Professor Peter Taylor from the University of Melbourne. More information: Photo: Mark McGuinness

Posted in News | Tagged ,
Comments Off on 2018 EO Tuck Medal Winner

Seminar: When: Friday, 16 /2/18 Ingkarni Wardli 5.57 3:10-4pm Speaker: Dr Guillermo Gomez, Centre for Cancer Biology, Uni SA Title: Active mechanical relaxation of adherens junctions in the vicinity of apoptotic cells facilitates cell extrusion by promoting epithelial topological transitions. Abstract: Cell extrusion allows the elimination of minorities of cells from the epithelium. Although this […]

Posted in Seminars | Tagged , ,
Comments Off on Dynamics, Modelling and Computation Group Seminars: Semester 1

Mark Girolami Chair of Statistics, Imperial College London, and The Alan Turing Institute presents: Stochastic Modelling of Urban Structure When: Monday 20 November, 11:10am Where: Engineering North N132 Abstract: // Urban systems are complex in nature and comprise of a large number of individuals that act according to utility, a measure of net benefit pertaining to […]

Posted in Events, Seminars | Tagged , , ,
Comments Off on Seminar: Stochastic Modelling of Urban Structure

When:Friday 27 Oct Where: Ingkarni Wardli B17 Presented by Dr Sophie Hautphenne, University of Melbourne Abstract: Markovian binary trees form a general and tractable class of continuous-time branching processes, which makes them well-suited for real-world applications. Thanks to their appealing probabilistic and computational features, these processes have proven to be an excellent modelling tool for […]

Posted in Events, School Colloquium, Seminars | Tagged , ,
Comments Off on Colloquium: The Markovian binary tree applied to demography and conservation biology

Friday 13 October Ingkarni Wardli B17 Professor Mat Simpson, Queensland University of Technology Abstract: Scald burns from accidental exposure to hot liquids are the most common cause of burn injury in children. Over 2000 children are treated for accidental burn injuries in Australia each year. Despite the frequency of these injuries, basic questions about the […]

Posted in School Colloquium | Tagged
Comments Off on Colloquium: Understanding burn injuries and first aid treatment using simple mathematical models