# Winter of Disconnectedness (AMSI Workshop)

## Monday, 25th Jul 2016 — Friday, 5th Aug 2016

Harbourview Function Center and University of Newcastle

For details please visit the the "Winter of Disconnectedness" AMSI meeting website.

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# CARMA Seminar

## Thursday, 28th Jul 2016

V205, Mathematics Building

# Dr Faustin Adiceam

(University of York)

# On the minimum of a positive definite quadratic form over non-zero lattice points. Theory and applications.

Let $\Sigma_d^{++}(\R)$ be the set of positive definite matrices with determinant 1 in dimension $d\ge 2$. Identifying two $SL_d(\Z)$-congruent elements in $\Sigma_d^{++}(\R)$ gives rise to the space of reduced quadratic forms of determinant one, which in turn can be identified with the locally symmetric space $X_d:=SL_d(\Z)\backslash SL_d(\R)\slash SO_d(\R)$. Equip the latter space with its natural probability measure coming from the Haar measure on $SL_d(\R)$. In 1998, Kleinbock and Margulis established very sharp estimates for the probability that an element of $X_d$ takes a value less than a given real number $\delta>0$ over the non-zero lattice points $\Z^d\backslash\{ \bm{0} \}$.

This talk will be concerned with extensions of such estimates to a large class of probability measures arising either from the spectral or the Cholesky decomposition of an element of $\Sigma_d^{++}(\R)$. The sharpness of the bounds thus obtained are also established for a subclass of these measures.

This theory has been developed with a view towards application to Information Theory. Time permitting, we will briefly introduce this topic and show how the estimates previously obtained play a crucial role in the analysis of the perfomance of communication networks.

This is work joint with Evgeniy Zorin (University of York). Dr Adiceam is a visitor of Dr Mumtaz Hussain.

# CARMA Seminar

## Thursday, 28th Jul 2016

V205, Mathematics Building

# Dr David Simmons

(University of York)

# Unconventional height functions in Diophantine approximation

The standard height function $H(\mathbf p/q) = q$ of simultaneous approximation can be calculated by taking the LCM (least common multiple) of the denominators of the coordinates of the rational points: $H(p_1/q_1,\ldots,p_d/q_d) = \mathrm{lcm}(q_1,\ldots,q_m)$. If the LCM operator is replaced by another operator such as the maximum, minimum, or product, then a different height function and thus a different theory of simultaneous approximation will result. In this talk I will discuss some basic results regarding approximation by these nonstandard height functions, as well as mentioning their connection with intrinsic approximation on Segre manifolds using standard height functions. This work is joint with Lior Fishman.

Dr Simmons is a visitor of Dr Mumtaz Hussain.

# Number Theory Down Under

## Friday, 23rd Sep 2016 — Tuesday, 27th Sep 2016

(Location to be decided)

For details please visit the the conference website.

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# Tools and Mathematics: Instruments for Learning

## Tuesday, 29th Nov 2016 — Thursday, 1st Dec 2016

(Location to be decided)

Please visit the workshop web page for further information.

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# Australasian Conference on Combinatorial Mathematics and Combinatorial Computing

## Monday, 12th Dec 2016 — Friday, 16th Dec 2016

University House

For details, please visit the conference web page.

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# APCO Workshop

## Friday, 16th Dec 2016 — Saturday, 17th Dec 2016

University House

For details, please visit the APCO web page.

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# International Conference on Fixed Point Theory and Its Applications

## Monday, 24th Jul 2017 — Friday, 28th Jul 2017

Harbourview Function Centre [Newcastle, NSW]

The conference is in the planning stages, and information will be added to the conference page as it becomes available.

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