Flower Hour

Speaker: (Western)

"Mathematical Biology Seminar"

Time: 11:00

Room: WSC 187

PhD Thesis Defence

Speaker: Marwa Tuffaha (Western)

"Mutational Bias Shifts and Severe Environmental Stress Promote Mutator Emergence"

Time: 10:00

Room: MC 204

This thesis explores how elevations in mutation rates, also known as the rise of mutators, can be affected by two main factors: mutational biases and harsh environmental challenges. We show here that shifts in mutational biases -especially reductions or reversals- increase an organism's access to previously under-sampled mutations, resulting in higher frequencies of beneficial de novo mutations. Through a discrete-time mathematical model and simulations, we demonstrate that this enhanced access facilitates the rise of mutator strains with larger fitness effects. We also consider how evolutionary rescue can promote mutator lineages under abrupt or gradual environmental stress. Using branching processes and deterministic models, supported by simulations, we show that de novo mutators are likely to hitchhike due to evolutionary rescue events when the wildtype mutation rate is intermediate, while pre-existing mutators in the populations have a significant advantage when mutation costs are minimal due to low wildtype mutation rates. Unsurprisingly, the stronger a mutator is, the more effective it is if the wildtype mutation rate is low, while its relative advantage decreases in populations where the wildtype itself is a mutator. Finally, by analyzing cancer mutational data, we show that our theoretical predictions apply to human cancer. We find that non-hypermutated tumors exhibit a reversal of germline mutation biases such that a similar mutation spectrum across tissues shows signs of positive selection in cancer genes, whereas hypermutated tumors potentially access cancer-driver mutations through their high mutation rates without the need for bias shifts. Altogether, these findings underscore the important role that mutational biases and severe environmental stresses have on mutator emergence in asexual organisms, point to mechanisms of adaptive evolution and drug resistance development, and suggest possible therapeutical implications for the treatment of cancer.

PhD Thesis Defence

Speaker: Prakash Singh (Western)

"Maximal torus in Hofer geometry and Embeddings in S^2 \times S^2"

Time: 09:00

Room: MC 204

This talk consists of two parts: In the first part, we will discuss geometric properties of the group of Hamiltonian diffeomorphisms (Ham(M)) associated to a closed symplectic manifold (M,\om) with respect to the Hofer metric. This group, although infinite dimensional, exhibits properties similar to compact Lie groups. Pushing this philosophy, it has been observed, classically, that when the symplectic manifold is endowed with a toric action, the centralizer of this action plays the role of a maximal torus in Ham(M). In this talk, we present results that support the Hofer geometric arguments supporting this philosophy. We also present some results w.r.t the intrinsic Hofer geometry on this centraliser. In the second part of the talk, we will discuss the embedding space of two disjoint standard symplectic balls of capacities (sizes) c1 and c2 in $S^2\times S^2$ with respect to any symplectic form. The set of admissible capacities for such embeddings is subdivided into polygonal regions in which the homotopy type of the embedding space is constant. We present these sets of all stability chambers. We also present the homotopy type of the relevant embedding spaces in some of these chambers.

Colloquium

Speaker: Olguta Buse (Indianapolis)

"Homotopic stability chambers in irrational blow up ruled surfaces"

Time: 15:30

Room: MC 107

We will give a gentle introduction to questions about the homotopy type of symplectomorphism groups of ruled symplectic 4-manifolds. Expanding results from the nineties on minimal rational ruled surfaces, several strides have been made in more recent years in the cases of blow-ups of such manifolds. We focus on understanding at large how such groups behave as we deform the symplectic forms within the cohomology cone in the case of irrational ruled surfaces with arbitrarily many blow ups. Using improved inflation techniques and a better understanding of the spaces of $J$ holomorphic curves, we will introduce a chamber structure on the reduced symplectic cone of such manifolds, so that the symplectomorphisms groups remain homotopically the same within the chambers. We will then discuss how an instance of such extremal ray limiting behaviour yields nontrivial symplectic isotopies, contrasting to the minimal cases. This is joint work with Jun Li.