IPM Calendar 
Tuesday 14 July 2020   Today  
Events for day: Tuesday 31 December 2019    
           10:30 - 12:00     Geometry and Topology Seminar
On Obstructions to Extending Group actions to Bordisms


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


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 $n^{frac{۱۰}{۱۷}+o(۱)}$. ...

           14:00 - 15:00     Weekly Seminar
HEPCo Group
Ultra-light scalar saving the 3+1 neutrino scheme from the cosmological bounds


Farmanieh Building, Seminar Room Class D (3rd floor)


           9:00 - 10:15     Geometry and Topology Seminar
Counting Closed Geodesics on Riemannian Manifolds


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. ...