The festival and the public conference will run <em>concurrently</em> with each other. <em>To concur </em>is a verb and cannot be used along with another verb, in this case the verb <em>to run</em>. The verb <em>to run</em> is the main verb and this is linked to a compound subject which has two heads: <em>festival </em>and <em>public conference. </em>The two events will take place simultneously or concurrently, therefore an adverb derived from to concur has to be used. <em>To concur</em> means to take place at the same time.