School of Mathematics Seminars
Speaker: Prof. Yorick Hardy | Thursday 25 April
Title: An introduction to multilinear algebra (part 3)
Abstract: This seminar will re-introduce the concept of multilinearity and how tensor products are universal multilinear objects. Concrete examples will be given by considering Kronecker products of matrices. The role of bases and free structures will be considered in more detail, with emphasis on their universal properties and consequences for the tensor product. Finally, tensor products will be considered as a part of an abstract structure leading to the notion of an abstract tensor product. The last part of the seminar will return to symmetric and alternating maps, and show that the determinant of matrices can be viewed (in a multilinear setting) as a universal map.
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Speaker: Prof. Yorick Hardy | Thursday 18 April
Title: An introduction to multilinear algebra (part 2)
Abstract: This seminar will re-introduce the concept of multilinearity and how tensor products are universal multilinear objects. Concrete examples will be given by considering Kronecker products of matrices, and some consequences will be explored including how the determinant of matrices may be viewed (in a multilinear setting) as a universal map. Finally, tensor products will be considered in some other settings and the notion of an abstract tensor product will be considered.
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Speaker: Chinedu Izuchukwu | School of Mathematics, University of the Witwatersrand, Johannesburg | E-mail: chinedu.izuchukwu@wits.ac.za | | Date/Time: Thursday 11 April at 10:15
Title: Fractional Differential Equations: Basics
Abstract: We are familiar with how to find the nth derivative of y with respect to t, i.e., dny(t)/
dtn where n is a positive integer. However, if n is a fraction, it becomes unfamiliar to many. This led to the birth of fractional calculus. We aim to discuss the basic aspects of fractional calculus. We shall begin our discussion with the wellknown gamma functions, then discuss fractional derivatives, and finally, fractional differential equations.
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Speaker: Professor Yorick Hardy | Date: Thursday 14 March 2024
Title: An introduction to multilinear algebra
Abstract: This seminar will introduce the concept of multilinearity and how tensor products are universal multilinear objects. Concrete examples will be given by considering Kronecker products of matrices, and some consequences will be explored including how the determinant of matrices may be viewed (in a multilinear setting) as a universal map. Finally, tensor products will be considered in some other settings and the notion of an abstract tensor product will be considered.
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Speaker: Ronald J. Maartens (Presenter) with Elizabeth Jonck and Kim Lucas | date: Thursday 29 February 2024
Title: Threshold Functions of Random Graphs
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Speaker: Prof. Fabien Pazuki | Affiliation: University of Copenhague, Denmark | Date/Time: Monday 29 January at 10:15 am
Title: Cycloalkanes and elliptic curves
Abstract: The talk aims to explain an unexpected link between a class of molecules composed of carbon and hydrogen atoms, and the theory of elliptic curves over finite fields. The correspondence is topological and doesn't include, so far, any of the crucial geometric features of the cycloalkanes. We will nevertheless explain how modular curves help make this connection, the role of modular polynomials, and give details about explicit computations we performed. The talk is based on joint work with Henry Bambury and Francesco Campagna.