IPM Calendar 
Saturday 19 September 2020   Today  
Events for day: Tuesday 22 September 2020    
           14:00 - 15:00     Weekly Seminar
HEPCo Group
Some Aspects of Entanglement Wedge Cross-section



For a given pure state, the entanglement entropy (EE) is a unique measure that characterizes quantum entanglement between two subsystems. However, for mixed states, different quantities which measure quantum or classical correlations between two subsystems have been known, e.g., entanglement of purification and logarithmic negativity. In this talk, first I will review the recent holographic proposals for computing the entanglement wedge cross-section (EWCS) which is dual to entanglement measures for mixed states. Then I will discuss some aspects of EWCS both in static and time-dependent geometries.

           17:30 - 18:30     Mathematics Colloquium
Counting Closed Orbits of Vector Fields


The counting problem for closed geodesics over negatively curved manifolds, and more generally, for closed orbits of Anosov flows is studied extensively in the literature. However, when the metric is not negatively curved, or when the flow of a vector field is not Anosov, closed geodesics/orbits are not isolated and there are some obstacles for defining a well-behaved count function. We discuss some of these obstructions. In particular, we introduce a function which assigns an integer weight to every compact and open subset of the space of closed geodesics for arbitrary Riemannian metrics over closed manifolds.

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