# Giornata di Combinatoria per festeggiare gli 80 anni di Dan
Hughes

La giornata, organizzata in collaborazione con il Dipartimento di Metodi e
Modelli Matematici per le Scienze Applicate, si svolgerà
giovedì 31 gennaio 2008 presso il Dipartimento di Matematica "G.
Castelnuovo" (Università di Roma "La Sapienza" - Piazzale Aldo
Moro, 5 - Roma) in aula Picone.
In apertura (ore 10,30) verrà offerto ufficialmente a Dan il volume
speciale di *Designs, Codes and Cryptography* edito da D. Ghinelli,
J. Hirschfeld e D. Jungnickel per il suo 80mo compleanno.

### Programma

- Ore 11
- James Hirschfeld: Dan's Career

Abstract: *I would survey some of Dan Hughes mathematics and also speak
about his influence through the conferences he organised.*
- Ore 12
- Antonio Pasini: Polar spaces of infinite rank

Abstract: *Many properties of polar spaces of finite rank fail to hold
in polar spaces of infinite rank. For instance, in a polar space of
infinite rank it can happen that maximal singular subspaces have different
dimensions; every polar space of infinite rank contains singular subspaces
that cannot be obtained as intersections of any family of maximal singular
subspaces, whereas in a polar space of finite rank every singular
subspace is the intersection of a finite number of maximal singular
subspaces. In this lecture I will discuss peculiar properties of polar
spaces of infinite rank, to test how far them can drug us from the
familiar world of polar spaces of finite rank. In particular, I will
consider the following open problem: is it true that, in polar space of
infinite rank, we can always find at least one pair of mutually disjoint
maximal singular subspaces?*
- Ore 15
- Dieter Jungnickel: Latin Squares from Euler to Now

Abstract: *This talk is meant to be entertaining: I shall review some
highlights in the history of Latin squares (which actually starts before
Euler), from Euler to very recent developments. Magic squares and puzzles
will also show up. No previous knowledge in the area is needed.*