Faculty/Graduate Speaker Session

The origin of chromosomes was a step in the evolution of complex cellular life. In this talk, we model the origin of chromosomes by considering a simple early cell composed of two types of genes: a ``fast gene'' with an advantage for gene-level replication and a ``slow gene'' that replicates more slowly at the gene level, but which confers an advantage for competition between cells. Using a partial differential equation, we will describe how the composition of genes within cells changes in time under within-cell and between-cell competition. We find that the gene-level advantage of fast replicators casts a long shadow on the multilevel dynamics of cell evolution: no level of between-cell competition can produce coexistence of the fast and slow replicators when the two genes are equally needed cell-level reproduction. By introducing a third type of genetic replicator, a "dimer" consisting of a linked pair of the fast and slow gene, we should how a simple chromosome-like dimer can help to promote the long-time coexistence of genes that compete at an individual-level while serving a complementary role for the survival of the cell.
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When introducing numerical methods for solving boundary value problems in a first course on numerical methods, the traditional way is to start with a finite difference approach followed by a separate finite element approach. In this talk, we describe a different way that emphasizes on the connections between the two methods, and the advantage of their simultaneous discussion. Using standard calculus and linear algebra tools, we illustrate the case of a one dimensional boundary value problem discretized on the same set of nodes for both methods.
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Discuss some mathematical problems related to Ductal carcinoma in situ (DCIS) model including direct problem, inverse problem and free boundary problem. DCIS is considered the earliest form of breast cancer. Theoretical and numerical results are presented.
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In this talk I will outline a method using the transpose rule from classical mirror symmetry where if one starts with a Calabi-Yau hypersurface in weighted projective space one can associate to it four distinct manifolds of positive Ricci curvature. This is work in progress.
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Mindfulness is awareness that arises through paying attention, on purpose, in the present moment, without judgement. It has been shown to benefit psychological well being. In this talk, I will share my experience in trying to implement mindfulness in the mathematics lectures.
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The formulation of conjectures and problems are fundamental processes of mathematical activity. In this presentation, I illustrate how we can use interactive geometry software to investigate special problems related to the following problem: The vertices of quadrilateral EFGH are the points of intersection of the consecutive angle bisectors of the angles of a quadrilateral ABCD. What type of quadrilateral is EFGH? Justify your response.
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