Nov

19

2018

The group of isometries G of a compact Riemannian manifold M is a compact Lie group. The symmetry rank of M is defined as the rank of G. For a manifold with positive sectional curvature, we know that the symmetry rank is roughly half the dimension of M by results of Grove and Searle. For the case of a closed, simply-connected, non-negatively curved manifold, it is conjectured that the symmetry rank is roughly two-thirds the dimension of the manifold.

Nov

19

2018

Sw-solutions are local energy solutions, introduced by G. Seregin and V. Sverak in 2017. "S" stands for strong/ Stokes/ split, "w" for weak. This class of solutions inherits good regularity properties from the class of strong solutions, the energy inequality and global existence from the class of weak solutions. It helps simplify the proofs of a number of important properties such as compactness, weak-strong uniqueness and persistence of singularities.

Nov

19

2018

Most microbes are known to live in communities called biofilms, and when life becomes boring, they disperse/detach from the community. Microbial cell dispersal (detachment) from mature biofilm is part of the developmental cycle of microbial biofilms, it can be externally or internally induced, leading to sloughing, erosion or seeding. Talking microbes assist in cell dispersal through a mechanism called quorum sensing, this mechanism is used to coordinate gene expression and behaviour in groups based on population densities.

Nov

20

2018

Nov

26

2018

It is known that near blowup time, the critical norms of strong solutions blow up. At this time, strong solutions cease to exist. However, sw-solutions (or local energy solutions in general) remain in local energy space and coincide the strong solution up to the blowup time. In recent years, a large volume of literature on local regularity near blowup time has been published, including the work of D. Albritton and T. Barker (2018), H. Jia and V. Sverak (2013), W. Rusin and V. Sverak (2011).

The Research Experience for Undergraduates program at OSU is now accepting applications (until Feb. 20, 2019). The program will support 10 undergraduate students for eight weeks from Monday, June 24th, through Friday, August 16th. Participants must be United States citizens or permanent residents. Students from underrepresented groups in mathematics are strongly encouraged to apply.

Participants receive a stipend, travel allowance, and housing allowance. For more information and/or to apply, visit: math.oregonstate.edu/~math_reu/

During the program, we make a point of discussing graduate and career opportunities. We do our best to offer...