The logo of the Catholic Chaplaincy of the University of York is taken from the crest of the University's coat of arms, a white rose superimposed on the silver and gold cross keys of St Peter. These keys are seen all over the city because York Minster is dedicated to St Peter. The White Rose is, of course, the symbol of Yorkshire; but long before that it was a symbol of Our Lady, the Rosa Mystica, as she is described in the Litany of Loreto. All very apt for the Catholics of the University of York - if rather surprising for a university that was founded very deliberately on secular lines and without even a Faculty of Theology.
But it maybe that whoever designed the arms wanted to suggest that you can't get away from religion quite so easily! Our Lady and St Peter are at the top of the arms. Down below, the university motto suggests there may be a deliberate link.
In limine sapientiae - at the threshold of knowledge or wisdom - is very suitable for a place of learning; but the Latin word limina is also conventionally used to describe a pilgrimage to Rome, ad limina apostolorum, to the doorstep of the apostles St Peter and St Paul; and of course Our Lady is also known as Sedes Sapientiae, the seat of wisdom.
The motto often picks up or puns on one or more of the visual elements in the arms. There's no connection between the motto and the shield but perhaps there is between the motto and the crest.
Deliberate or not, the Catholic students of York are fortunate in their patrons: Our Lady, the Seat of Wisdom; St Peter the Rock on which the Church is founded; and St Thomas More, England's greatest ever witness to the truth.