Colloquium Archive 2001
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- Richard Mollin, Department
of Mathematics and Statistics, University of Calgary
1:00PM Friday September 21, 2001
Continued Fractions, Diophantine Equations, Ideals, and Prime-producing Polynomials
- Professor Kirsten Mackenzie-Fleming,
from Central Michigan University
10:00AM Friday, May 4, 2001
Infinite families of non-embeddable quasi-residual designs
- Professor Douglas Stinson, from
University of Waterloo
11:00AM on Wednesday, March 14, 2001
Seeing is Believing
- Alan Ling, Michigan Technological University,
11:00AM on Friday February 2, 2001
Equireplicate Balanced Binary Codes for Oligo Arrays
- Dr. Hadi Kharaghani, University of
Lethbridge
11:00AM on Friday January 19, 2001
On a Class of Strongly Regular Graphs
- Hugh Millington, University of the
West Indies in Barbados, will be giving a series of four colloquia
on January 11 & 12, 2001:
- Dr. Soufiane Noureddine
2:00PM on Monday January 8, 2001
Architecture and Analysis of an Availability Enhancing Middleware
Speaker: Richard Mollin, Department of Mathematics and Statistics, University of Calgary Title: Continued Fractions, Diophantine Equations, Ideals, and Prime-producing Polynomials Date: Friday September 21, 2001 Time: 1:00PM to 1:50PM Room: PE252
Abstract For the uninitiated, we give an overview of the topics in the title, beginning with the notion of a quadratic irrational, moving through the use of continued fraction to solve Pell's equations, to the continued fraction algorithm, using ideal theory, and this author's recent method for finding solutions of dual norm form quadratic Diophantine equations. We explore how sums of two integral squares play a role in determining solutions of Diophantine equations, and examples thereof motivate a discussion of prime producing quadratic polynomials. We start with Euler's polynomial discovered in 1772, through the discovery of ubiquitous results in the literature concerning such optimal prime producing polynomials, which have appeared merely as curiosities. An explanation is given for this prime production by this author's 1996 discovery of the reasons in terms of the class group structure of complex quadratic number fields. We conclude with a presentation of the new prime producing record holders, which have supplanted Euler's polynomial, and give a brief application to cryptography.
Audience ALL ARE WELCOME
Speaker: Professor Kirsten Mackenzie-Fleming, Central Michigan University Title: Infinite families of non-embeddable quasi-residual designs Date: Friday May 4, 2001 Time: 10:00AM to 11:00AM Room: D634
Abstract The parameters 2-(2 
+2,
+1,)
are those of a residual of a Hadamard 2-(4+3,
2+1,
)
design. J.H. van Lint, H.C.A. van Tilborg and J. R.
Wiekma have shown that all 2-(2+2,
+1, )
designs with
< 4 are embeddable. The existence of non-embeddable
Hadamard 2-designs has been determined for the cases
= 5 (J.H. van Lint),
= 6 (V.D. Tonchev), and
= 7 (V.D. Tonchev). In this talk an infinite family
of non-embeddable 2-(2+2,
+1,
)
designs,
= 3(2m)-1, m > 1 is
constructed. Two generalisations of this result will
be discussed.
Audience ALL ARE WELCOME
Speaker: Professor Douglas Stinson, University of Waterloo Title: Seeing is Believing Date: Wednesday, March 14, 2001 Time: 11:00AM to Noon Room: PE254
Abstract Visual Cryptography was introduced at EUROCRYPT'94 by Naor and Shamir. A (t,w) visual threshold scheme is a method to encode a secret image, consisting of black and white pixels, into w shadow images called shares, such that any t of the shares enable the visual recovery of the secret image. The visual recovery consists of xeroxing the shares onto transparencies, and then stacking them. Any t shares will reveal the secret image without any cryptographic computation. However, no information about the image can be obtained by examining any t-1 shares, even with infinite computational resources.
This seemingly impossible problem can be solved if we allow the recovered image to have lower contrast than the original image. It is therefore of interest to construct schemes that minimize this loss of contrast. For example, in a (2,2) visual threshold scheme, the optimal solution involves a 50% loss of contrast.
In this talk, we discuss basic construction methods, and bounds on the contrast, for (t,w) visual threshold schemes. We concentrate on (2,w) schemes, which are the cases of greatest practical interest. For (2,w) schemes, essentially complete results are known.
Department of Mathematics & Computer Science is pleased to have one of the worlds leading experts in Cryptography on campus and invites all interested to attend this very interesting talk for general audiences.
Speaker: Alan Ling, Michigan Technological University Title: Equireplicate Balanced Binary Codes for Oligo Arrays Date: Friday February 2, 2001 Time: 11:00 to 12:00 Room: D633
Abstract In the manufacture of oligo arrays for DNA hybridization experiments, manufacturing defects must be detected and their position determined. The design of manufacturing protocols for such oligo arrays leads to a combinatorial problem, requiring certain binary codes which have an additional balance property. In this talk, constructions using block designs and packings for these codes, within a range of interest in a practical manufacturing application, are developed. The focus is on equireplicate codes, constant weight codes in which every bit position is a one equally often.
Department of Mathematics & Computer SCience is pleased to have one of the most vibrant experts in "Designs, Codes and Cryptography" on campus and invites all interested to attend this talk.
Speaker: Dr. Hadi Kharaghani Title: On a Class of Strongly Regular Graphs. Date: Friday January 19, 2001 Time: 11:00AM Room: C589
Abstract This talk is a report of my study leave. I have given this talk a few times for general audience and I am sure everyone can follow this talk. The talk is about a construction method for a symmetric (0,1)-matrix H with zero diagonal of order 936 in such a way that H2 has 375 on its main diagonal and 150 elsewhere. A little of finite field theory, finite group theory, computer search and hard work are the main ingredients of the construction method.
Audience ALL ARE WELCOME
Speaker: Hugh Millington, from the University of the West Indies in Barbados Title: Towards a New Axiomatization of the Foundations of Mathematics Date: Thursday January 11, 2001 Time: 11:00AM Room: C589
Abstract The proposed axiomatization uses a lambda-calculus formalism, together with an hierarchy of membership relations and a set of non-existential axioms, to generate set-theoretic universes.
Audience Persons with a first course in axiomatic set theory, and some exposure to formal languages.
Speaker: Hugh Millington, from the University of the West Indies in Barbados Title: Unbounded Category Theory Date: Thursday January 11, 2001 Time: 3:00PM Room: C589
Abstract A formalism for Category Theory is put forward in which a priori considerations of size do not appear.
Audience Some acquaintance with the central ideas and constructions of category theory is advisable.
Speaker: Hugh Millington, from the University of the West Indies in Barbados Title: On the consistency of Morse-Kelley Class Theory Date: Friday January 12, 2001 Time: 11:00AM Room: C589
Abstract Assuming the consistency of the Theory of Predicates we use translation to give a finitistic proof that Morse-Kelley Class theory is consistent.
Audience This requires some familiarity with formal languages and the axiomatization of MK, but should be otherwise largely self-contained.
Speaker: Hugh Millington, from the University of the West Indies in Barbados Title: Set Theory in a lambda calculus extension of Lukasiewicz Logic Date: Friday January 12, 2001 Time: 2:00PM Room: C589
Abstract The talk sketches a formal treatment of the foundations of mathematics in a lambda calculus extension of Lukasiewicz logic, with a special comment on its significance for the consistency of axiomatic set theory.
ALL ARE WELCOME
Speaker: Dr. Soufiane Noureddine Title: Architecture and Analysis of an Availability Enhancing Middleware Date: Monday January 8, 2001 Time: 2:00 to 2:50PM Room: PE256
Abstract The availability of IT systems is becoming increasingly more important. With therising complexity of software applications and the underlying architectures, ensuring a certain degree of availability is no more a trivial task. In this talk a novel architecture that enhances the availability of running (distributed) software applications is introduced. The main idea of the approach is based on the provision of programming abstractions, which reduce the failure susceptibility of applications, on the exploitation of the distributed environment in order to provide mechanisms for an availability enhancing load migration, and on the provision of mechanisms for active monitoring and for dynamic reconfiguration. A model is developed for the architecture in order to quantitatively assess the benefits of load migration and to evaluate component scheduling algorithms. The modeling effort also includes the introduction of new adequate performability measures for the architecture. The usefulness of these parameters is made plausible by virtue of analytic techniques.
ALL ARE WELCOME