# Seminars & Colloquia Calendar

## Homology systole over mod 2 coefficients and systolic freedom

#### Lizhi Chen, Lanzhou University, China

Location: ** Hill 525**

Date & time: Tuesday, 24 October 2017 at 3:30PM - 4:30PM

### Abstract: I am going to talk about problems around homology systole over mod 2 torsion coefficients. Given a Riemannian metric defined on a closed manifold, we define mod 2 homology systole to be the infimum of volumes of cycles representing nontrivial classes in homology group with mod 2 coefficients. Gromov conjectured that there would be systolic rigidity for mod 2 homology systoles, similar to homotopy 1-systolic inequalities on aspherical manifolds. However, later work shows that counterexample exists. In the talk, different aspects related to this conjecture will be explained. In particular, there are two types of motivations to study this problem. The first motivation is based on Gromovâ€™s essential systolic inequality on aspherical manifolds. Another recent motivation is from quantum information theory.

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