jQuery, AJAX, and PHP post from front end

I have a form that passes field values to jQuery, which validates the fields and creates the variables being sent in data: {} in the snippet below.

$.ajax({
        type: "POST",
        url: "<?php bloginfo('stylesheet_directory'); ?>/process.php",
        dataType: "json",
        data: {
            "title":title,
            "goals":goals,
            "progress":progress,
            "categories":categories,
            "tags":tags,
            "video":video,
            "audio":audio,
        },
        success: function() {
            //get permalink for post from php and go to it
        }
    });

process.php is not receiving any data, or it's not posting the data. I'm not sure why. Here is process.php

    <?php

        $user_submitted_title = sanitize_text_field($_POST['user_submitted_title']);
        $user_submitted_progress = $_POST['user_submitted_progress'];
        $user_submitted_goals = $_POST['user_submitted_goals'];
        $user_submitted_categories = $_POST['user_submitted_categories'];
        $user_submitted_tags = sanitize_text_field($_POST['user_submitted_tags']);
        $user_submitted_video = sanitize_text_field($_POST['user_submitted_video']);
        $user_submitted_audio = sanitize_text_field($_POST['user_submitted_audio']);

        $user_post = array(
            'comment_status' => 'open',
            'post_author'    => $user_ID,
            'post_category'  => array($user_submitted_categories),
            'post_content'   => '<h2>Project Progress</h2>' . $user_submitted_progress . '<h2>Project Goals</h2>' . $user_submitted_goals,
            'post_status'    => 'publish',
            'post_title'     => $user_submitted_title,
            'post_type'      => 'post',
            'tags_input'     => $user_submitted_tags
        );

        $user_post_id = wp_insert_post($user_post);
        add_post_meta($user_post_id, 'wpcf-video', $user_submitted_video);
        add_post_meta($user_post_id, 'wpcf-audio', $user_submitted_audio);

        $user_post_redirect = get_permalink($user_post_id);

    ?>

I need to figure out why nothing posts when I use the form, and I need to figure out how to send $user_post_redirect back to jquery so I can redirect to it. Can someone please help?