My research focuses on lucid dreaming and its practical applications. In lucid dreams the dreamer is aware of the fact that he or she is dreaming and can deliberately influence dream content. As eye movements in a dream correspond with actual eye movements, lucid dreams can be successfully verified in a sleep laboratory by using predefined eye signals. Below are some of the questions I have tried to tackle in my research (with the links to the respective publications).
Phenomenology of lucid dreams
How and when do lucid dreams originate? What do lucid dreamers most often do in their lucid dreams? How successful they are with remembering and accomplishing their intentions? What are the main factors influencing the phenomenology of lucid dreams?  How stable is lucid dream frequency over the time?  Can lucidity occur during different stages sleep?  Does it take the same time to accomplish a task in the dream as in the waking state? 
Induction of lucid dreams
Applications of lucid dreams in sports and other areas
How lucid dreams are prevalent among athletes and do athletes use lucid dreams to practice their sports?  How effective lucid dream practice is as compared to mental practice in wakefulness and actual physical practice?  What are other applications of lucid dreams and how often they are used by lucid dreamers? 
Lucidity, mindfulness and well-being
How the levels of lucidity at night are associated with the levels of mindfulness during the day?  Is waking mindfulness associated with the ability to control lucid dreams?  What is the relation between spirituality, mindfulness, dream recall and nightmare frequency?  Is the frequency of lucid dreaming related to better mental health and physical fitness? 
Dream characters in lucid dreams
Are dream characters in lucid dreams able to do maths?  Can they help the dreamer with creative problem solving?  Is there some connection between the “minds” of dream characters and the dreamer?  How frequent are threatening dream characters in lucid dreams and how lucid dreamers deal with them?