# Seminar: Theory Seminar Special

## 23 May 2018

Time: 2:30 - 4:30pmVenue: BR.:3.01 Queen Mary University of London

Prof Prakash Panagaden (McGill University and the Alan Turing Institute) is giving a Theory Seminar Special, which will be in the form of a 2-hour seminar with a good amount of background material.

Note the seminar is on *Wednesday at 2:30pm, at the Computer Science building* (i.e. not in our usual seminar room).

Title: Quantitative equational reasoning

Speaker: Prof. Prakash Panangaden

Host: Pasquale Malacaria

http://theory.eecs.qmul.ac.uk/seminars/

Abstract:

Reasoning with equations is a central part of mathematics. Typically we think of solving equations but another role they play is to define

algebraic structures like groups or vector spaces. Equational logic was formalized and developed by Birkhoff in the 1930s and led to a subject

called universal algebra. Universal algebra was used in formalizing concepts of data types in computer science. In this talk I will present

a quantitative analogue of equational logic: we write expressions like s=_\epsilon t with the intended interpretation "s is within \epsilon of

t". It turns out that the metatheory of equational logic can be redeveloped in this setting. Perhaps this seems like sterile theory but

what makes it come alive is some striking examples. A notion of distance between probability distributions called the Kantorovich metric

(frequently called the Wasserstein metric) has become important in the theory of probabilistic systems and in parts of machine learning. It

turns out that this metric emerges naturally as the "free algebra" of some simple equational axioms in our extended sense.

This is joint work with Radu Mardare and Gordon Plotkin.

**Directions, if coming from outside QMUL**

Queen Mary is on Mile End Road, with nearest tube stations being Stepney Green (closest one to the seminars) and Mile End. The seminar is in the

Peter Landing Building, 3rd-floor teaching rooms: https://goo.gl/maps/nSVqvkDhuCx