News and events

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

    Monday, June 29, 2026 | By

    The Department of Mathematics & Statistics invites students, faculty, and staff to attend the upcoming colloquium with speaker Dr. Basil Nanayakkara on Thursday, July 2nd, from 2:00 PM to 3:00 PM in MCJ 404.  The talk is entitled Zariski cotangent space.

    Abstract

    In algebraic geometry, a scheme is an ordered pair (X, O_X) where X is a topological space and O_X is a sheaf of commutative rings on X such that each point p in X has a neighbourhood that is isomorphic to (specA, O_A) where specA is the prime spectrum of a commutative ring A and O_A is the sheaf on specA induced by the ring structure of A.  It was Oscar Zariski who defined the cotangent space to X at p to be m_p/m_p^2 where m_p is the unique maximal ideal of the stalk O_{X,p} of the sheaf O_X at p.  We will show that this is a sensible definition by constructing an isomorphism between the dual (m_p/m_p^2)* with the tangent space to a smooth manifold at a point as defined in differential geometry.  We will show further that this isomorphism is natural (in the sense of category theory).

  • Ansh Shah Masters Paper Presentation: Monday, June 22, 10:00 AM

    Monday, June 15, 2026 | By

    Ansh Nileshkumar Shah, a Master of Science candidate in the Department of Mathematics and Statistics, will virtually present the Masters Research Project titled On the Diophantine Equation L_n^(k) – L_m^(k) = 2^x 3^y on Monday, June 22, 2026 at 10:00 AM.

    The examination committee includes Supervisor Dr. Omar Kihel and Supervisory Committee Member Dr. Yuanlin Li.

    Students (both graduate and undergraduate) as well as other members of the Brock Community are invited to attend. A Microsoft Teams link to the meeting can be found here: Join the meeting.

    Keywords: Diophantine equations, Generalized Lucas sequences, Linear forms in logarithms, Baker-Davenport reduction method, Transcendental number theory

    Abstract:  In this project, we study methods from transcendental number theory, particularly the theory of linear forms in logarithms of algebraic numbers. This theory, initiated by the groundbreaking work of Alan Baker in the 1960s, provides powerful explicit lower bounds for linear combinations of logarithms of algebraic numbers. Baker’s fundamental contributions, developed in the mid-1960s, led to major advances in Diophantine analysis and were recognized with the award of the Fields Medal in 1970. Since then, this theory has become one of the central tools for the effective resolution of Diophantine equations. Refinements such as Matveev’s theorem provide explicit bounds that are especially useful in modern applications.

    The goal of this work is to apply these methods to the study of a Diophantine equation involving generalized Lucas sequences. More precisely, we investigate the k-generalized Lucas sequence and consider the Diophantine equation L_n^(k) – L_m^(k) = 2^x 3^y where n, m, k, x, and y are nonnegative integers. This problem extends recent work of Kourouma, Rihane and Togbe, who studied the restricted equation L_n^(k) – L_m^(k) = 2 3^y

    To achieve this, we combine several tools from Diophantine approximation. First, we apply Matveev’s theorem on linear forms in logarithms to obtain explicit upper bounds for the variables. Because these bounds are typically very large, we then employ reduction techniques based on a variant of the Baker-Davenport method, as developed by Dujella and Petho, together with Legendre’s criterion. These methods allow us to significantly reduce the bounds and ultimately bring the problem into a computationally tractable range.

    Our main result provides a comprehensive description of the solutions of the equation under specific parametric constraints. For the range n ≤ k, we provide a complete resolution of the problem, mapping out the full behavior of the solution space. On the other hand, for the range n > k, we fully solve the equation for the specific exponents x = 2, 3, 4, 5, and 6, demonstrating that the remaining variables are strictly bounded and yield a finite set of solutions. This gives a resolution of the equation under the specified conditions and represents a natural extension of previously known results.

  • Joyce Khouzam Masters Project Presentation: Friday, June 5, 3:00 PM

    Wednesday, June 03, 2026 | By

    Joyce Khouzam, a Master of Science candidate in the Department of Mathematics and Statistics, will virtually present the Masters Research Project titled Linear Forms in Logarithms and the Extendibility of a D(4)-Pair of Pell Numbers on Friday, June 5, 2026 at 3:00 PM.

    The examination committee includes Supervisor Dr. Omar Kihel and Supervisory Committee Member Dr. Hichem Ben-El-Mechaiekh.

    Students (both graduate and undergraduate) as well as other members of the Brock Community are invited to attend. A Microsoft Teams link to the meeting can be found here: Join the meeting.

    Keywords: Linear forms in logarithms, Diophantine equations, Pell numbers

    Abstract:  This paper introduces linear forms in logarithms and determines how it can be used to resolve a concrete problem in number theory. We start by reviewing the tools needed throughout the paper such as: how well rational numbers can approximate real numbers, how continued fractions can make those approximations systematic, and how the Pell equation connects both ideas. From there, Pell numbers are central to the paper.

    Next, we look at Baker’s 1966 theorem and explain why a nonzero expression of the form b_1 log(a_1) + … + b_N log(a_N) cannot be made arbitrarily small and we show the more practical bounds that are due to Matveev and Laurent. We also describe the Dujella-Petho lemma, which uses continued fractions to bring large theoretical bounds down to a range small enough to check by hand or computer.

    As the main application, we walk through the proof of the answer to the question “which Pell numbers P_k can be added to the pair {P_{2n+4}, 4P_{2n+2}} to form a D(4)-triple?”. By reducing the problem to a Pellian equation, parametrizing its solutions, and applying Matveev’s theorem, Laurent’s theorem, and the Dujella-Petho lemma, we see that P_{2n} is the only answer.

  • Thomas Wolf Memorial Event

    Monday, May 04, 2026 | By

    We look forward to gathering tomorrow to remember Thomas Wolf. We will meet at 9:30 a.m. outside the J Block entrance to Pond Inlet, where Dean Berg, colleagues, and Thomas’s family will share a few words in his honour.

    In the event of rain, please proceed directly to the VPMI.

    A commemoration event for professor, friend and colleague of the Faculty of Mathematics and Science, Thomas Wolf will occur on May 5, 2026. The event follows the one-year anniversary of his passing on April 29th, 2025. We will begin the event outside by the entrance to Pond Inlet where a White Spruce tree has been planted in his honour. We are gathering in his memory to celebrate Professor Wolf and launch a new Mathematics and Statistics scholarship – The Thomas Wolf Mathematics Award.

    The event will take place from 9:30 a.m. to 10:30 a.m. meeting outside the entrance to Pond Inlet, where his tree is planted.  Thomas’ family will attend the event and speak to his lasting impact.

    To support the scholarship, a donation link has been created – http://brocku.ca/donate  Select the “In Memory of Thomas Wolf” option from the drop down menu under “Please select the designation of your gift.”  Please consider donating to help support the bright minds applying for the scholarship.

    In addition, we have created website which collects memories of Thomas. Please take a moment to share a photo or story of Thomas that will be included on the site –  https://brocku.ca/mathematics-science/thomas-wolf-tribute/ Approved stories will be read at the event to share in his memory.

  • Mathematics and Statistics Seminar, Dr. Takao Komatsu

    Monday, April 20, 2026 | By

    Students, faculty, and staff are invited to attend the upcoming Mathematics and Statistics Seminar with speaker Dr. Takao Komatsu on Tuesday, April 28, from 2:00 PM to 3:00 PM in GSB 307.  The talk is entitled Some Explicit Values of a q-Eulerian Multiple Zeta Value at Roots of Unity.

    Abstract

    In recent years, the theory of multiple zeta values has seen rapid development, with growing interest in their q-analogues—known as q-multiple zeta values—arising from q-generalizations. These q-analogues recover the classical multiple zeta values in the limit as q -> 1.

    As part of ongoing research into generalized Stirling numbers, Professor Komatsu has investigated finite q-multiple zeta values. In this talk, he will present results expressing these values using Eulerian numbers and derive explicit formulas in the case where q is a primitive root of unity.

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

    Monday, March 09, 2026 | By

    The Department of Mathematics and Statistics invites students, faculty, and staff to attend the upcoming colloquium with speaker Dr. Basil Nanayakkara on Tuesday, March 17, from 2:30 PM to 3:30 PM in MCJ404.  The talk is entitled The Zariski topology on the spectrum of a nil-clean ring.

    Abstract:

    We will show that the clopen subsets of the prime spectrum of a commutative nil-clean ring form a Boolean lattice. This is an interesting mix of topology and abstract algebra.

  • Math, Just Because with Dr. Jean-Jacques Rousseau

    Wednesday, February 04, 2026 | By

    In contribution to Black History Month events on campus, Dr. Jean-Jacques Rousseau will be delivering a math talk at the Black Student Centre on Monday, February 9, from 2:00 PM to 4:30 PM.

    Those interested in the event can find the full details and RSVP on ExperienceBU here.

    Math, Just Because is not a lecture, not a workshop, and certainly not a test! It’s a conversation, an exchange and a math-along. It will touch on how math can help get our money right, explain why we each have unique social media feeds, and show how music is really hearing mathematics.

    But this isn’t “Math, Because It’s Useful.” It’s Math, Just Because: the value of math for its own sake: math for edification, for self-transformation, and ultimately, math for being our best selves. This Black History Month, let’s walk tall knowing that math is ours, and be reminded of how powerful that makes you.

    Dr. Jean-Jacques Rousseau is a community math educator whose MATH4AI learning experiences build confidence in non-technical learners through problem-posing, “silly” questions, and real-world applications. He holds a PhD (IHPST, University of Toronto) and an MBA (Schulich School of Business, York University) and completed a three-year postdoc in AI & Trust at York University’s Lassonde School of Engineering. Jean-Jacques is a former Innovation Advisor to the President of Haiti and currently serves as EDID Advisor in the Office of the Vice-President Research at Brock University.

  • Congratulations to Billy Marshall for Major Research Prize

    Wednesday, November 26, 2025 | By

    Dr. Billy Marshall (Department of Mathematics and Statistics) and his team were recently awarded the 2025 Linda G. O’Bryant Noetic Sciences Research Prize (https://noetic.org/prize/).  They share the $100,000 prize with two other groups, all working on conscious AI.

    Of the 56 applicants and 8 finalists, the team lead by Dr. Marshall was selected for contributions in Evaluating Artificial Consciousness through Integrated Information Theory.  Over 3,000 researchers from around the world attended the online awards ceremony.

    We extend our congratulations to Dr. Marshall and his colleagues on their significant achievement.

  • Joshua Mac Intyre Masters Project Presentation: Thursday, November 27, 11:00 AM

    Wednesday, November 19, 2025 | By

    Joshua Mac Intyre, a Master of Science candidate in the Department of Mathematics and Statistics, will virtually present the Masters Research Project titled Nil Clean Group Rings over Metacyclic Groups on Thursday, November 27, 2025 at 11:00 AM.

    The examination committee includes Supervisor Dr. Yuanlin Li and Supervisory Committee Member Dr. Henryk Fukś.

    Students (both graduate and undergraduate) as well as other members of the Brock Community are invited to attend. A Microsoft Teams link to the meeting can be found here: Join the meeting.

    Keywords: Idempotent; group rings; nilpotent; nil clean; Peirce decomposition; Wedderburn-Artin; Metacyclic groups; Fermat numbers

    Abstract:  A ring is called nil clean if each element can be expressed as the sum of an idempotent and nilpotent. This presentation expounds on our work published in Nil clean group rings over metacyclic groups. We will assume at least an undergraduate understanding of group and ring theory but will provide some preliminary information on nil clean rings, group rings, and metacyclic groups. We will justify our comparison between the nil cleanness of ℤ2G, and any group ring RG, where R is a commutative ring and G is a finite group. This comparison will lead to an analysis of ℤ2G, for G up to an order of 20. Then, when considering a nil clean group ring RG over a metacyclic group G, we were able to reduce to the case where G = < a, b | a^{n} = b^{m} = 1, b^{-1}ab = a^{r} >, with m = 2k, n odd, and the center being trivial. We try to break it down a little further to when n is a prime power, calculating n for each m up to 16, and we verify whether most of these candidate group rings are indeed nil clean. Finally, we discuss the results of our investigation and a connection to Fermat numbers.

  • Mathematics and Statistics Seminar Series, Dr. Bernhard Spangl

    Wednesday, November 05, 2025 | By

    Students, faculty, and staff are invited to attend the upcoming event in the Mathematics and Statistics Seminar Series with speaker Dr. Bernhard Spangl on Tuesday, November 11, from 1:00 PM to 2:00 PM.  The talk is entitled Active learning: blending design of experiments and supervised learning

    Abstract

    In this talk I will focus on two research topics: (i) sample size estimation in balanced ANOVA models and (ii) query-by-committee active learning in regression scenarios. Their common aim is to minimize the sample size.

    First, we consider balanced one-way, two-way, and three-way ANOVA models to test the hypothesis that the fixed factor A has no effect. The other factors are fixed or random. We determine the noncentrality parameter for the exact F-test, describe its minimal value by a sharp lower bound, and thus we can guarantee the worst-case power for the F-test. These results allow us to compute the minimal sample size, i.e. the minimal number of experiments needed. Additionally, we provide a structural result for the minimal sample size that we call “pivot” effect (cf. also Spangl et al., 2021).

    Second, we discuss the problem of active learning in regression scenarios. In active learning, the goal is to provide criteria that the learning algorithm can employ to improve its performance by actively selecting data that are most informative. Active learning is usually thought of as being a sequential process where the training set is augmented one data point at a time. We restrict ourselves to a pool-based sampling scenario and investigate a committee-based approach as query strategy for actively selecting instantiations of the input variables x that should be labelled and incorporated into the training set using a real chemometric data set.

     

    Registration link 

    Mathematics and Statistics Seminar Series: Active learning: blending design of experiments and supervised learning with Dr. Bernhard Spangl – ExperienceBU

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