Functional Logic Programming:
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There is an annual International Workshop on Functional and Logic Programming. Previous workshops took place in Karlsruhe (1992), Rattenberg/Bavaria (1993), Schwarzenberg/Black Forest (1994, 1995, 1997), Marburg ( 1996), Bad Honnef (1998), Grenoble (1999), Benicassim (2000), Kiel (2001), Grado (2002), Valencia (2003), Aachen (2004), Tallinn (2005), Madrid (2006), Paris (2007), Siena (2008), Brasília (2009), Madrid (2010), Odense (2011), Nagoya (2012).
Papers on functional logic programming have been presented at all conferences related to programming language research.
A couple of years ago, the annual PLILP conference is one of the main conferences related to this subject. You can find a lot of references if you look at the proceedings of past PLILP conferences which are published in the Springer Lecture Notes in Computer Science Series (see PLILP'88-95, ALP/PLILP'96, ALP/PLILP'97, or ALP/PLILP'98).
From 1999, the former ALP and PLILP conferences have been merged and renamed into International Conference on Principles and Practice of Declarative Programming (PPDP). PPDP'99 took place in Paris, PPDP 2000 in Montreal, PPDP 2001 in Florence, PPDP 2002 in Pittsburgh, PPDP 2003 in Uppsala, PPDP 2004 in Verona, PPDP 2005 in Lisboa, PPDP 2006 in Venice, PPDP 2007 in Wroclaw, PPDP 2008 in Valencia.
Another important forum to discuss the integration of functional and logic languages is the International Symposium on Functional and Logic Programming (FLOPS). FLOPS 2001 took place in Tokyo, FLOPS 2002 in Aizu, FLOPS 2004 in Nara, FLOPS 2006 in Fuji Susono, FLOPS 2008 in Ise,
Papers on functional logic programming have been published in various journals related to programming language research. There is a journal with the main focus on the integration of functional and logic programming. This Journal of Functional and Logic Programming is published electronically by the European Association for Programming Languages and Systems (EAPLS).