To design a GUI that supports both synchronous and asynchronous learning:

1. Modular design: Create a flexible framework that accommodates different learning modes.

2. Clear navigation: Provide intuitive navigation for both live sessions and self-paced content.

3. Real-time updates: Implement real-time updates for synchronous learning, such as live chats and polls.

4. Asynchronous features: Include features like discussion forums, video recordings, and downloadable resources.

5. User profiles: Allow users to manage their profiles, including preferences for learning modes.

6. Calendar integration: Integrate a calendar for scheduling live sessions and deadlines.

7. Notifications: Implement notifications for upcoming live sessions, new content, and deadlines.

8. Accessibility: Ensure the GUI is accessible on various devices and meets accessibility standards.

9. Analytics: Provide analytics for instructors to track learner engagement in both modes.

10. User feedback: Collect feedback from users to improve the GUI and learning experience.

Synchronous features:

- Live video conferencing

- Real-time chat and Q&A

- Live polls and surveys

- Screen sharing and collaboration tools

Asynchronous features:

- Self-paced video lessons

- Discussion forums and boards

- Downloadable resources and materials

- Quizzes and assessments

- Personalized learning paths

By incorporating both synchronous and asynchronous features, the GUI can support various learning styles and preferences, providing a flexible and effective learning environment.