# PIMS lectures

Title: Climate Change – does it all add up?

Speaker: Chris Budd, University of Bath, UK and the Royal Institution, UK

Date and time:
05 May 2015,
4:30pm -
5:30pm

Location: David Turpin Building (DTB), Room A104

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Climate change has the potential to affect all of our lives. But is it really happening, and what has maths got to do with it?

In this talk I will take a light hearted view of the many issues concerned with predicting climate change and how mathematics and statistics can help make some sense of it all. Using audience participation I will look at the strengths and weaknesses of various climate models and we will see what the math can tell us about both the past and the future of the Earth's climate and how mathematical models can help in our future decision making.

All are welcome. No heavy duty maths will be involved, but you will learn about chaos, catastrophes and tipping points. Please bring a questioning mind.

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Title: Eigenvalues, Determinants, and Distribution of Rank: Towards Taussky Unification

Speaker: Shaun Fallat, University of Regina

Date and time:
01 Apr 2015,
3:30pm -
4:30pm

Location: Cornett A225

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Abstract:

In 1958, Olga Taussky-Todd proposed an exploration into potential unified treatments of a list of properties shared by various classes of “positive matrices”. For instance, item (4) on her original list sought explanations concerning the fact that both positive semidefinite symmetric matrices and matrices with all minors nonnegative (aka. totally nonnegative matrices) have all real nonnegative eigenvalues.

In this talk, I will offer a new perspective concerning item (4) on Taussky’s list by way of analyzing the spectrum of tridiagonal matrices and provide a brief outline of the associated history and theory along these lines. In addition, I will highlight other important similarities shared by these classes of matrices including: eigenvalue interlacing, classical determinantal inequalities, and a notion of rank distribution known as shadowing.

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Title: Total Domination in Graphs and Transversals in Hypergraphs

Speaker: Michael A. Henning, University of Johannesburg

Date and time:
19 Mar 2015,
3:30pm -
4:30pm

Location: Cornett A229

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Abstract:

The total domination number of a graph G is the minimum cardinality of a set S of vertices so that every vertex of G is adjacent to a vertex in S, while the transversal number of a hypergraph H is the minimum cardinality of a subset of vertices in H that has a nonempty intersection with every edge of H. In this talk, we survey recent results on total domination in graphs. Perhaps much of the recent interest in total domination in graphs arises from the fact that total domination in graphs can be translated to the problem of finding transversals in hypergraphs since the transversal number of the open neighorhood hypergraph of a graph is precisely the total domination number of the graph. We explore this transition from total domination in graphs to transversals in hypergraphs and discuss several recent results on total domination in graphs obtained using transversals in hypergraphs that appear difficult to obtain using purely graph theoretic techniques.

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Title: Algorithmic Mechanisms for Privacy, Truthfulness and Social Welfare

Speaker: Sampath Kannan, University of Pennsylvania

Date and time:
26 Feb 2015,
7:00pm -
8:00pm

Location: ECS 660

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PIMS Distinguished Lecture by Sampath Kannan Chair in the **Department of Computer and Information Science** at U Penn.

Mechanism design is the problem of computing an optimal allocation of resources under criteria such as social welfare or revenue. The problem is more challenging than algorithm design because the inputs have to be elicited from selfish agents who may be able to derive an advantage by lying. A standard approach to overcome this challenge is to design incentive-compatible mechanisms where truth-telling is a dominant strategy or at least a Nash equilibrium. In this work we are concerned with another reason that strategic agents may lie - to protect the privacy of their data. This is a relatively new concern in the field of mechanism design. What is needed are mechanisms that are incentive-compatible and protect the privacy of data. We show that if the goal is social welfare then this is possible - nearly optimal social welfare can be achieved in general while protecting the privacy of the data. One the negative side, the exponential mechanism is not always computationally efficient. Efficiency has to be proved on a problem-by-problem basis.

In the last part of the talk we briefly describe how even when privacy is not a goal in itself, it can be used as a tool to design (nearly) incentive- compatible mechanisms where none were known to exist. We also show an example where we need to greatly relax the notion of privacy in order to have a realizable mechanism at all.

This is joint work with Zhiyi Huang. The last part is joint work with Jamie Morgenstern, Ryan Rogers, Aaron Roth, and Steven Wu.

There will be refreshments after the talk.

Additional information is available on the Pacific Institute for the Mathematical Sciences (PIMS) website: <a href="http://www.pims.math.ca/scientific-event/150226-pudlsk">http://www.pims.math.ca/scientific-event/150226-pudlsk</a>

Title: Bose Bush bound revisited: elementary considerations and further prospects

Speaker: Rahul Mukherjee, Indian Institute of Management Calcutta

Date and time:
19 Feb 2015,
3:30pm -
4:30pm

Location: COR A229 (Cornett Building)

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Orthogonal arrays have numerous applications in various disciplines including statistics, engineering and cryptography. We will revisit the celebrated Bose-Bush bound on orthogonal arrays and examine how an elementary approach, based on a certain mean-variance inequality, can lead to a possibly stronger version of this bound. Further prospects, including extension to mixed-level orthogonal arrays and a connection with multivariate analysis, will be indicated.

Additional information is available on the Pacific Institute for the Mathematical Sciences (PIMS) website: <a href="http://www.pims.math.ca/scientific-event/150219-pudlrm">http://www.pims.math.ca/scientific-event/150219-pudlrm