Presenter: Sara Herke

Finite projective planes are important structures in design theory and geometry. They are well-known to exist for prime power orders but the question of whether or not projective planes can exist for non-prime power orders remains one of the most important unsolved problems in combinatorics. There is an equivalence between finite projective planes and complete sets of mutually orthogonal Latin squares (MOLS). The useful notion of parity of permutations has been extended to Latin squares; in this talk, we consider a direct generalization of the parity of a Latin square to the parity of a set of MOLS. Our results give insight as to why it may be harder to build projective planes of order n >2 when n = 2 (mod 4). This is joint work with Nevena Francetic and Ian Wanless.

### About Pure mathematics seminars

We present regular seminars on a range of pure mathematics interests. Students, staff and visitors to UQ are welcome to attend, and to suggest speakers and topics.

Seminars are held on Tuesdays from 3pm to 3.50pm in Room 67-442 of the Priestley Building (Building 67).

Talks comprise 45 minutes of speaking time plus five minutes for questions and discussion.

#### Information for speakers

Researchers in all pure mathematics fields attend our seminars, so please aim your presentation at a general mathematical audience.

Room 67-442 has a data projector and a whiteboard.

If you wish to use the data projector, contact us a few days in advance of your talk to avoid technical delays on the day - there's a tight turnaround with room bookings.

#### Contact us

To arrange to use the projector, contact Benjamin Burton.

To volunteer to talk or to suggest a speaker, email Clement Maria or Huy Nguyen.