## UCalgary Peripatetic Seminar: Amolak Ratan Kalra

• Date: 05/06/2022
• Time: 12:00
Lecturer(s):
Amolak Ratan Kalra, University of Calgary
Location:

University of Calgary

Topic:

Categories of Kirchoff Relations

Description:

It is known that the category of affine Lagrangian relations over a field F, of integers modulo a prime p (with p > 2) is isomorphic to the category of stabilizer quantum circuits for p-dits. Furthermore, it is known that electrical circuits (generalized for the field F) occur as a natural subcategory of affine Lagrangian relations. The purpose of this paper is to provide a characterization of the relations in this subcategory — and in important subcategories thereof — in terms of parity-check and generator matrices as used in error detection.

In particular, we introduce the subcategory consisting of Kirchhoff relations to be (affinely) those Lagrangian relations that conserve total momentum or equivalently satisfy Kirchhoff’s current law. We characterize these Kirchhoff relations in terms of parity-check matrices and, study two important subcategories: the deterministic Kirchhoff relations and the lossless relations.

Other Information:

Time: 12:00pm Pacific/ 1:00pm Mountain

Location: Math Sciences Bulding, MS325, University of Calgary