Are there culinary applications for carrot tops/greens?
I've never had them, but they are indeed edible. Due to the high amount of potassium in them they can be bitter. The World Carrot Museum (lol) even has an entire page for carrot greens, including several recipes.
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They ARE edible and are highly nutritive, rich in protein, minerals and vitamins. The tops of the carrots are loaded with potassium which can make them bitter, so the use of them in food is limited, but there some ideas and recipes below.  The tops are antiseptic and can be juiced and used as a mouthwash.
However, it is edible, so you may mix some in with a mixed lettuce salad. You may also use it for garnish. Combine your common sense and your creative skills, and invent something! That's what makes cooking fun. It is a form of art.  Carrot greens are high in vitamin K, which is lacking in the carrot itself.
Carrot tops are an outstanding source of chlorophyll, the green pigment that studies have shown to combat the growth of tumours. Chlorophyll contains cleansing properties that purify the blood, lymph nodes, and adrenal glands. Scientists have been unable to synthesize chlorophyll in the laboratory, but green plant foods contain sufficient quantities to protect the human body.