# 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.

Kam Hung Yau - UNSW
For any sufficiently small real number $\varepsilon >0$, we obtain an asymptotic formula for the number of solutions to $\lVert \alpha n + \beta \rVert < x^{\varepsilon}$ ($\lVert \cdot \... Danesh Jogia and Timothy McMahon - Australian Signals Directorate Number theory has had a special relationship with cryptography since the mid-seventies when the Diffie-Hellman and RSA algorithms were published. With the existence of a quantum computer becoming... Igor Shparlinski - UNSW We outline some new bounds on bilinear sums with Kloosterman sums and also with some similar sums. In particular, these bounds improve some recent results of V. Blomer, E. Fouvry, E. Kowalski, Ph.... Alexander Fish - University of Sydney We will show how polynomial walks can be used to establish a twisted recurrence for sets of positive density in$\mathbb{Z}^d$. In particular, we will demonstrate that if$Γ ≤ GL_d(\mathbb{Z})$is... Tim Trudgian - UNSW Canberra Very little is known about the distribution of primitive roots of a prime$p$. Grosswald conjectured that the least primitive root of a prime p is less than$\sqrt{p} - 2$for all$p> 409$. While... Wadim Zudilin - Radboud University Nijmegen (Netherlands) and the University of Newcastle (NSW, Australia) In 2003, Fernando Rodriguez-Villegas conjectured fourteen congruences modulo$p^3$that relate hypergeometric sums truncated at$p-1$to the Fourier coefficients$a(p)$of weight 4 modular forms.... Bryce Kerr - UNSW This talk concerns some recent results of the author about incomplete Gauss sums modulo primes. We outline the methods used for obtaining new quantitative bounds and discuss how these results fit in... Joseph Gunther - University of Wisconsin-Madison On a hyperelliptic curve over$\mathbb{Q}$, there are infinitely many points defined over quadratic fields: just pull back rational points of the projective line through the degree two map. But for... Debargha Banerjee - IISER Pune If we start with mod$p\$ objects, it may or may not have lifts to characteristic zero objects. Buium introduced differential modular forms in a new geometry by using a close analogy with function...

James Borger - ANU
The classical theory of canonical lifts for elliptic curves gives a canonical way of lifting ordinary'' elliptic curves in positive characteristic to characteristic zero. I'll explain a new point...