From 2000 till 2005 he has been a research fellow (assegnista di ricerca) at Università degli studi di Brescia; in 2005 he become research associate (ricercatore) in geometry at Politecnico di Bari. From 2008 till 2018 he has been working as a ricercatore confermato at Università degli Studi di Brescia. Since June 2018 he is associate professor in Geometry at Università degli Studi di Brescia.

In 2004 first and ever since 2006 he has been responsible for courses at both undergraduate and graduate level in several Italian universities. He has also been a supervisor for some bachelor and master level dissertations in mathematics.

In the last few years L.Giuzzi has given several communications at international conferences as well as some invited talks at different universities. He has been among the organisers of national ("XVIII congresso UMI", Bari 2007) and international conferences ("Combinatorics 2008", Brescia2008). He has published 26 papers on international refereed journals, 1 book on error correcting codes and holds 1 patent shared with others. His research is mostly concerned with finite geometric structures and designs endowed with a rich automorphism group as well as their applications to coding theory and cryptography. In more detail he is currently interested in:

1. Grassmann geometries and their embeddings
2. unitals [1,3,13,16] and Hermitian varieties over finite fields [M1,Q5,4,5,6,7]
3. codes arising from geometrical constructions [M2,8,12,18]
4. maximal arcs [9,10] and hyperovals [11]
5. graph decompositions and related constructions [15,14,17]
6. cryptography [B1,Q6].