Speaker: Arkadii Slinko
Affiliation: The University of Auckland
Title: Secret sharing schemes (an elementary introduction)
Date: Tuesday, 7 May 2013
Time: 4:00 pm
Location: Room 6115, Owen Glenn Building

Certain cryptographic keys, such as missile launch codes, numbered bank accounts and the secret decoding exponent in an RSA public key cryptosystem, are so important that they present a dilemma. If too many copies are distributed, one may be leaked. If too few, they might all be lost or accidentally destroyed. Secret sharing schemes invented by Shamir (1979) and Blakley (1979) address this problem, and allow arbitrarily high levels of confidentiality and reliability to be achieved. A secret sharing scheme `divides’ the secret S into `shares’ – one for every user – in such a way that S can be easily reconstructable by any authorised subset of users, but an unauthorised subset of users can extract absolutely no information about S. A secret sharing scheme, for example, can secure a secret over multiple servers and it remains recoverable despite multiple server failures.

Secret sharing schemes are a sort of cooperative games where the information and not money is being distributed among players. The set of authorised coalitions of a secret sharing scheme is a simple game so there is a rich connection to the theory of games.

In my talk I will give an elementary introduction to secret sharing.

Speaker: Dr Ben Greiner
Affiliation: University of New South Wales
Title: Bargaining, Asymmetric Information, and Communication – An Experiment
Date: Tuesday, 9 Apr 2013
Time: 12:00 pm
Location: Lab 04, Level 0, Owen Glenn Building

(note the unusual time and venue)

This paper explores the effect of communication on negotiation behavior in a stylized bargaining environment with asymmetric information. In particular, we study an Ultimatum Game in which the total amount to be bargained over (the pie) might be unknown to one party. We systematically vary whether both parties are informed about the pie size (baseline), or only the proposer, or only the responder. In addition, we vary whether there is no communication before the bargaining procedure, or whether the informed party can send a message about the pie size before decisions are made. In one communication condition, the message sender is free to choose the correct or the wrong message (cheap talk), while in the second communication condition the sender can only choose whether to reveal or not to reveal the true pie size (“true talk”). We find that contrary to the theoretical prediction cheap talk has a significant positive effect on efficiency, while true talk is less effective than expected.

Speaker: Kathryn E. Lenz
Affiliation: Department of Mathematics and Statistics, University of Minnesota Duluth
Title: Voting Methods for Municipal Elections: Propaganda, Field Experiments and what USA Voters Want from an Election Algorithm
Date: Tuesday, 19 Mar 2013
Time: 4:00 pm
Location: Room 6115, Owen Glenn Building

Within the past two decades various cities across the USA have experimented with instant run-off voting (IRV) for political elections. These experiments demonstrate a public desire for replacing plurality voting with a better method and they give insight into what voters want from an election algorithm. This talk will briefly review several standard election algorithms, properties and public reaction to them. Examples will be given of IRV city election results, pro-IRV propaganda found on websites, misrepresentations in newspaper opinion pieces and discussions with mathematicians and non-mathematicians. Though disheartening, misinformation about IRV propagating in the public arena and suppression of full IRV election results do provide opportunities for the mathematically minded to engage in civic dialogue and to raise awareness concerning election algorithm options.

Slides are available.

Speaker: Matthias Ehrgott
Affiliation: The University of Auckland
Title: Multiobjective Optimization for Supporting Radiation Therapy Treatment Planning
Date: Tuesday, 5 Mar 2013
Time: 4:00 pm
Location: Room 6115, Owen Glenn Building

The choice of a plan for radiotherapy treatment for an individual cancer patient requires the careful trade-off between the goals of delivering a sufficiently high radiation dose to the tumour and avoiding irradiation of critical organs and normal tissue. To support the treatment planner in this task it is necessary to visualize these trade-offs. The treatment planning problem can be formulated as a multi-objective optimization problem. We present a method to compute the optimal trade-offs for this problem and plot them in three dimensions. Furthermore, by computing a finite set of treatment plans that are well distributed across the entire trade-off surface, we support the treatment planner in identifying the best available plan for the patient under consideration.

Slides are available

Speaker: Dov Samet
Affiliation: Tel Aviv University
Title: Interim agreements: In the footsteps of Zeno, Parkinson, and Nash
Date: Thursday, 14 Feb 2013
Time: 10:30 am
Location: Room 317, Owen Glenn Building

Zeno’s paradoxes of motion, which claim that moving from one point to another cannot be accomplished in finite time, seem to be of serious concern when moving towards an agreement in utility space is concerned. Parkinson’s Law of Triviality implies that such an agreement cannot be reached in finite time. By explicitly modeling dynamic processes of reaching interim agreements, we show that if utilities are von Neumann-Morgenstern, then no such process can bring about an agreement in finite time in linear bargaining problems. To extend this result for all bargaining problems, we characterize a particular path illustrated by Raiffa, and show that no agreement is reached along this path in finite time. When deadlines are set, then agreements are reached exactly at the deadline, proving Parkinson’s Law that work expands so as to fill the time available for its completion.

Speaker: Matthew Ryan
Affiliation: University of Auckland
Title: Freedom of Opportunity: Axiomatic Approaches
Date: Tuesday, 4 Dec 2012
Time: 4:00 pm
Location: Room 6115, Owen Glenn Building

This talk will give a brief and selective overview of the literature on axiomatic characterisations of freedom. Since this literature spans (at least) economics, mathematics, philosophy, politics and statistics, I hope it might be a fruitful area of potential research for the CMSS group. I’ll discuss the main strands of this research and some key results. I’ll also present recent work connecting this literature to that on abstract convexity, including some (hopefully interesting!) open questions.

Link to slides
Survey article by Dowding and van Hees