# Full Seminar Archive

Our regular seminar program covers a broad range of topics from applied mathematics, pure mathematics and statistics. All staff and students are welcome.
This page has a complete list of past seminars and a list restricted by year can be accessed via the left-hand menu.

*Peter Donovan - University of New South Wales*

A positive integer $a_0$ determines recursively the sequence$a_0,a_1,a_2,\ldots$ by the Collatz rules $a_{n+1}=a_n/2$ for even $n$ and $a_{n+1}=(3a_n+1)$ for$n$ odd. Massive electronic calculation...

*Stephen Doty - Loyola University Chicago*

The Drinfeld-Jimbo definition of a quantised enveloping algebra by generators and relations is a $q$-analogue of Serre's presentation of a semisimple Lie algebra. The most complicated relations in...

*Stephan Baier - RKM Vivekananda University, India*

The large sieve inequality is of fundamental importance in analytic number theory. Its theory started with Linnik's investigation of the least quadratic non-residue modulo primes on average. These...

*Thomas Gobet - University of Sydney*

The Iwahori-Hecke algebra of the symmetric group is a central object in representation theory and low-dimensional topology. While it is naturally related to reductive groups, it can be defined...

*Caroline Turnage-Butterbaugh - Duke University*

The Riemann zeta-function is a ubiquitous, yet mysterious, function in number theory. The importance of its so-called nontrivial zeros stems from the relationship between the location of these zeros...

*Vinoth Nandakumar - University of Sydney*

The irreducible representations of the general linear Lie algebra in positive characteristic are not well-understood. Lusztig's conjectures, now a theorem of Bezrukavnikov-Mirkovic, describe their...

*Bryce Kerr - University of New South Wales*

This talk concerns some recent results joint with Igor Shparlinski and Kam Hung Yau regarding estimates for multiplicative character sums modulo a prime number. We review the Burgess bound for such...

*Andrew Schopieray - University of New South Wales*

The classical McKay correspondence characterises finite subgroups of SU(2) by associating them with a very restrictive family of graphs.
This can be rephrased in modern language as a classification...

*Matthew Hircock - University of New South Wales*

The numerical range was first studied in 1918 as a useful tool for localising the spectrum of a linear operator on a Hilbert space. The convexity of this localisation limits how much information we...

*Zac Murphy - University of New South Wales*

At first glance, quotient categories might seem like a strange notion to define, but in actuality they turn out to be quite useful constructions. On one hand, they simplify the treatment of certain...