| Friday 19 April 2024 | |
| Events for day: Tuesday 31 December 2019 |
| 10:30 - 12:00 Geometry and Topology Seminar On Obstructions to Extending Group actions to Bordisms School MATHEMATICS Motivated by a question of Ghys, we talk about cohomological obstructions to extending group actions on the boundary $partial M$ of a $3$-manifold to a $C^0$-action on $M$. Among other results, we show that for a $3$-manifold $M$, the $mathbb{S}^1 imes mathbb{S}^1$ action on the boundary does not extend to a $C^0$-action of $mathbb{S}^1 imes mathbb{S}^1$ as a discrete group on $M$, except in the trivial case $M cong mathbb{D}^2 imes mathbb{S}^1$. Using additional techniques from 3-manifold topology, homotopy theory, and low-dimensional dynamics, we find group actions on a torus and a sphere that are not nullbordant, i.e. they admit ... 10:30 - 11:30 Lecture Cops and Robbers on Graphs of Bounded Diameter School MATHEMATICS The game of Cops and Robbers is a well known game played on graphs. In this talk we consider the class of graphs of bounded diameter. We improve the strategy of cops and previously used probabilistic method which results in an improved upper bound for the cop number of graphs of bounded diameter. In particular, for graphs of diameter four, we improve the upper bound from $n^{frac{۲}{۳}+o(۱)}$ to $n^{frac{۳}{۵}+o(۱)}$ and for diameter three from $n^{frac{۲}{۳}+o(۱)}$ to $n^{frac{۱۰}{۱۷}+o(۱)}$. ... 9:00 - 10:15 Geometry and Topology Seminar Counting Closed Geodesics on Riemannian Manifolds School MATHEMATICS Associated with every closed oriented smooth manifold $M$, let $R_M$ denote the space of all pair $(L,g)$, where $g$ is a Riemannian metric on $M$ and $L$ is a real number which is not the length of any closed $g$-geodesics. A locally constant geodesic count function $pi_M:R_M ightarrow mathbb{Z}$ is defined which virtually counts the number of closed $g$-geodesics of length less than $L$ at $(L,g)in R_M$. In particular, when $g$ is negatively curved, $pi_M(L,g)$ is precisely the number of prime closed $g$-geodesics which have length smaller than $L$. The asymptotic growth of the number of closed $g$-geodesics may subsequently be studied. ... |