How can I call a specific file (via php) by referencing the logged-in username?

Try to do this:

<?php global $current_user;?>
<?php if(is_user_logged_in()) :?>
    <?php get_currentuserinfo();?>
    <?php if(is_array( $current_user->roles ) && in_array( 'map_user', $current_user->roles  ) ) : ?>
        <div id="mapContent">
            <?php require("/mapping/".$current_user->user_login.".html/"); ?>
        </div>
    <?php endif; ?>
<?php endif; ?>

Source codex.wordpress.org