For example in the following list: "Technology Entrepreneurship, and Advanced Leadership" simplified to "Tech Entrepreneurship, and Adv. Leadership"
The answer is a matter of style/choice outlined by Clare in the question's comments.
I used the following style guide: http://public.oed.com/how-to-use-the-oed/abbreviations/
The Oxford Dictionaries' page "Punctuation in abbreviations", which catalogues British and American styles, says:
If the abbreviation consists only of the first part of a word, then you should put a period at the end:
Wed. (= Wednesday)
Dec. (= December)
Unless you are working to a style guide with different rules, this is the rule you should follow, since the rule is the same in both British and American English, and Adv is clearly the first part of Advanced.
Adv. (with a full stop) is the correct way to punctuate this abbreviation.
In your specific example (which looks like a title, a headline or a heading to me),
Technology Entrepreneurship, and Advanced Leadership
Tech. Entrepreneurship, and Adv. Leadership
with a full stop at the end of each abbreviation.
If you are following a different style guide that says to not put a full stop after the abbreviation, then you would write it like so:
Tech Entrepreneurship, and Adv Leadership
In your original example, you mixed styles. Whatever style you are following you should apply consistently.
If it is indeed a title, a headline or a heading, it doesn't get a full stop at the end, however, if you were to include it in a sentence, it would:
The talk called Tech. Entrepreneurship, and Adv. Leadership was attended by 200 people.
This should only be done for reasons of space; normally you would not abbreviate these words in a full sentence.
Note: some abbreviations such as ad for advertisement have become naturalised, so should not be spelt with a full stop.