Articles from:July 2026

  • Department of Mathematics and Statistics Colloquium: Dr. Basil Nanayakkara

    Monday, July 27, 2026 | By

    The Department of Mathematics & Statistics invites students, faculty, and staff to attend the upcoming colloquium with speaker Dr. Basil Nanayakkara on Thursday, August 6th, from 2:00 PM to 3:00 PM in MCJ 404.  The talk is entitled What is a natural map?

    Abstract

    Mathematicians use the term ‘natural map’ informally.  For example, if A is a ring and I is an ideal of A, then the map A → A/I given by a → a + I is said to be natural.  As another example, if V is a vector space, then there is a natural map from V to its double dual V ∗∗. (Thus, V and V∗∗ are naturally isomorphic when V is finite dimensional.)  Also, if X is a topological space and Y is a subspace of X, then the quotient map X → X/Y is natural. There are many other examples one can give.

    We will discuss the definition of natural transformations in category theory, and show that the maps mentioned above are indeed natural. If time permits we will show that the dual of the Zariski cotangent space at a point of a smooth manifold is naturally isomorphic to the tangent space at that point.

  • Maham Taqi Masters Paper Presentation: Monday, July 20, 10:00 AM

    Wednesday, July 15, 2026 | By

    Maham Taqi, a Master of Science candidate in the Department of Mathematics and Statistics, will virtually present the Masters Research Paper titled Lifetime Probability of Default Estimation for Consumer Loans under IFRS 9: A Comparative Study of Survival and Competing-Risks Models on Monday, July 20, 2026 at 10:00 AM.

    The examination committee includes Supervisor Dr. Syed Ejaz Ahmed and Supervisory Committee Member Dr. Jan Vrbik.

    Students (both graduate and undergraduate) as well as other members of the Brock Community are invited to attend. A Microsoft Teams link to the presentation can be found here: Join the meeting.  Please join with your camera and microphone turned off.

    Keywords: IFRS 9; lifetime probability of default; survival analysis; competing risks; discrimination; calibration

    Abstract: Lifetime probability of default (PD) estimation is an important component of expected credit loss measurement under IFRS 9. In consumer loan portfolios, modelling must account for both loan default and early prepayment over the contractual maturity. This study compares survival and competing-risk models for estimating lifetime PD in 36-month and 60-month loan cohorts. Model performance is evaluated using time-dependent AUC and Brier score, while calibration is assessed against the empirical Aalen–Johansen default cumulative incidence function. The research emphasizes the importance of evaluating lifetime credit-risk models across two contractual horizons, with particular attention to whether discrimination and calibration lead to the same model conclusions.  Discrimination is found to be similar across models, whereas calibration reveals meaningful differences between modelling approaches. These results suggest that calibration is more informative than discrimination, and that competing-risk methods provide a more appropriate framework for IFRS 9 lifetime PD estimation and expected credit loss measurement.

  • Department of Mathematics & Statistics Colloquium: Dr. Alfred Geroldinger

    Wednesday, July 08, 2026 | By

    The Department of Mathematics & Statistics invites students, faculty, and staff to attend the upcoming colloquium with speaker Dr. Alfred Geroldinger on Monday, July 20th, at 10:00 AM in GSB 308.  The talk is entitled On the arithmetic of Krull monoids with torsion class group.

    Abstract

    Let H be a Krull monoid (e.g. the multiplicative monoid of nonzero elements of a Krull domain).  Then every non-invertible element can be factored into irreducible elements.  If a = u_1 … u_k with k in N_0 and irreducibles u_1, …, u_k, then k is a factorization length and the set L(a) of all factorization lengths of a is called the length set of a.

    The system of length sets is an infinite family of finite subsets of N_0.  Its structure depends only on the class group of H and the distribution of prime divisors in the classes.  We provide an overview of current knowledge regarding length sets and present new results (joint work with David J. Grynkiewicz and Guoqing Wang) for torsion class groups.