Eylem Zeliha Yildiz : Braids in planar open books and fillable surgeries.
- Geometry and Topology ( 6 Views )We'll give a useful description of braids in $\underset{n}{\#}(S^1\times S^2)$ using surgery diagrams, which will allow us to address families of knots in lens spaces that admit fillable positive contact surgery. We also demonstrate that smooth $16$ surgery to the knot $P(-2,3,7)$ bounds a rational ball, which admits a Stein handlebody. This answers a question left open by Thomas Mark and Bülent Tosun.
Kiran Kedlaya : Census-taking for curves over finite fields
- Number Theory ( 12 Views )With Yongyuan Huang and Jun Bo Lau, we recently completed a census of genus-6 curves over the field F_2, and are working on a similar census in genus 7. This uses Mukai's "flowcharts" for describing canonical curves in this genera. We discuss some of the key features of this classification; some aspects of computational group theory required to convert this classification into tractable computations; and some applications of the results, including relative class number problems for function fields, gonality of curves over finite fields (work of Faber-Grantham-Howe), and cohomology of modular curves (work of Canning-Larson and Bergstrom-Canning-Petersen-Schmitt).
Mark Stern : Introduction to p-harmonic forms, L^p Hodge theory, and L^p cohomology
- Geometry and Topology ( 12 Views )In this talk I will lay the foundations of the geometry of p-harmonic forms and L^p-Hodge theory. As an application, I will give strong evidence for (half of) a conjecture of Gromov on the L^p cohomology of negatively curved symmetric spaces.
Amarjit Budhiraja : Invariant measures of the infinite Atlas model: domains of attraction, extremality, and equilibrium fluctuations.
- Probability ( 12 Views )The infinite Atlas model describes a countable system of competing Brownian particles where the lowest particle gets a unit upward drift and the rest evolve as standard Brownian motions. The stochastic process of gaps between the particles in the infinite Atlas model has a one parameter family {p(a), a > 0} of product form mutually singular stationary distributions. We say that an initial distribution of gaps is in the weak domain of attraction of the stationary measure p(a) if the time averaged laws of the stochastic process of the gaps, when initialized using that distribution, converge to p(a) weakly in the large time limit. We provide general sufficient conditions on the initial gap distribution of the Atlas particles for it to lie in the weak domain of attraction of p(a) for each a. Results on extremality and ergodicity of p(a) will be presented. Finally, I will describe some recent results on fluctuations of the Atlas model from inhomogeneous stationary profiles. This is based on joint work with Sayan Banerjee and Peter Rudzis.