# 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.

*Harry Denman - University of New South Wales*

In Analysis, Brouwer's fixed point theorem and the contraction mapping theorem are the cornerstone of fixed point theorems. Brouwer's fixed point theorem states that every continuous function f on a...

*Robert Tan - University of New South Wales*

In classical probability theory, the expectation of a random variable \( X \) on a probability space \( (\Omega, \mathcal{F}, \mathbb{P}) \) is defined to be the integral of a random variable, when...

*Alex Patterson - University of New South Wales*

Let $f$ be a polynomial over a field $F$ and let $f^{(n)}$ denote the $n$-th iterate of $f$. An active research area in the field of arithmetic dynamics is to investigate the properties of $f^{(n)}$...

*Daniel Tanios - UNSW Sydney*

The advent of information systems and their subsequent ubiquity have made cryptography an important field and an active area of research. New technological and computational challenges to...

*Matthew Di Meglio - University of New South Wales*

Chebotarev’s density theorem is a deep result in the intersection of algebraic number theory, Galois theory and analysis. This presentation will explain the statement of Chebotarev’s theorem through...

*Emily Cliff - University of Sydney*

A vertex algebra describes the symmetries of a two-dimensional conformal field theory (CFT), while a factorization algebra (introduced by Beilinson and Drinfeld) over a complex curve consists of...

*Jesse Burke - University of Sydney*

The local ring of an algebraic variety at a point is a commutative Noetherian local ring, and every finitely generated module over such a ring has a minimal free resolution (to be defined in talk)....

*Richard Garner - Macquarie University*

The Catalan numbers $1,1,2,5,14,42, \cdots$ are well known to be the solution to many different counting problems; Stanley in his 2015 book lists 214 such problems. The two ur-examples of families...

*Simon Macourt - University of New South Wales*

Exponential sums were first introduced 200 years ago by Gauss. Since then, bounds on such sums have been an interesting item of study and have found several applications. We will give an introduction...

*Peng Gao - Beihang University*

Let $\mathcal{D}$ be the set of non-square quadratic discriminants and $\chi_D=(\frac {D}{\cdot})$ be the Kronecker symbol. The mean square estimation \begin{align*}\sum_{\substack {|D| \leq X \\ D \...