Features Required:

1. Event Creation: Users should be able to create events with details such as title, date, time, location, and description.

2. Event Reminder: Users should receive reminders for upcoming events based on their preferred notification settings.

3. Event Invitation: Users should be able to invite others to their events and receive invitations from others.

4. Event Categories: Users should be able to categorize events into different categories, such as personal, work, social, etc.

5. Event Search: Users should be able to search for specific events based on keywords, date, location, etc.

6. Event Sharing: Users should be able to share events with others through various channels, such as email or social media.

7. Event RSVP: Users should be able to RSVP to event invitations and see the list of attendees for their own events.

8. Event Recurrence: Users should be able to set events as recurring (e.g., daily, weekly, monthly).

Design Patterns Involved or Used:

1. Model-View-Controller (MVC) Pattern: The MVC pattern can be used to separate the calendar application into three components: the model (data and business logic), the view (user interface), and the controller (handles user interactions and manages the flow of data).

2. Observer Pattern: The Observer pattern can be used to notify users about upcoming events and event invitations.

3. Factory Pattern: The Factory pattern can be used to create different types of event objects based on user requests, such as one-time events or recurring events.

4. Singleton Pattern: The Singleton pattern can be used to ensure that only one instance of certain classes, such as the event manager or the user authentication manager, is created and shared across the application.

5. Proxy Pattern: The Proxy pattern can be used to handle communication between the application and external services, such as email servers for event reminders.

6. Command Pattern: The Command pattern can be used to encapsulate and decouple actions, such as creating events or sending event invitations, from the specific objects or components that perform those actions.

7. Publish-Subscribe Pattern: The Publish-Subscribe pattern can be used to implement the event notification system, where users subscribe to their events to receive reminders, and publishers send event reminders to the subscribers.

8. Decorator Pattern: The Decorator pattern can be used to add additional features or behaviors to event objects, such as event categories.

9. Strategy Pattern: The Strategy pattern can be used to implement different search algorithms for searching events based on different criteria, such as keywords or date.

10. State Pattern: The State pattern can be used to manage the different states of event interactions, such as creating, editing, or deleting events.

Code: Detailed Implementation of Classes Based on Each Design Pattern Mentioned Above

// User class
class User {
    private String userId;
    private String username;
    private String email;
    // Other attributes and methods

    public User(String userId, String username, String email) {
        this.userId = userId;
        this.username = username;
        this.email = email;
    }

    // Getters and setters
    // Other user-related methods
}

// Event class
class Event {
    private String eventId;
    private User creator;
    private List<User> attendees;
    private String title;
    private LocalDateTime dateTime;
    private String location;
    private String description;
    private boolean isRecurring;
    // Other attributes and methods

    public Event(String eventId, User creator, String title, LocalDateTime dateTime, String location, String description) {
        this.eventId = eventId;
        this.creator = creator;
        this.attendees = new ArrayList<>();
        this.title = title;
        this.dateTime = dateTime;
        this.location = location;
        this.description = description;
        this.isRecurring = false;
    }

    // Getters and setters
    // Methods for adding and removing attendees, setting event as recurring, etc.
}

// EventManager class
class EventManager {
    private List<Event> events;
    // Other attributes and methods

    public EventManager() {
        this.events = new ArrayList<>();
    }

    public void createEvent(Event event) {
        // Add the event to the list of events
    }

    public void inviteAttendee(Event event, User attendee) {
        event.getAttendees().add(attendee);
    }

    // Other event management methods
}

// EventSearchStrategy interface (Strategy)
interface EventSearchStrategy {
    List<Event> searchEvents(List<Event> events, String keyword);
}

// KeywordSearchStrategy class (Strategy)
class KeywordSearchStrategy implements EventSearchStrategy {
    @Override
    public List<Event> searchEvents(List<Event> events, String keyword) {
        // Implement keyword-based event search
    }
}

// DateSearchStrategy class (Strategy)
class DateSearchStrategy implements EventSearchStrategy {
    @Override
    public List<Event> searchEvents(List<Event> events, LocalDate date) {
        // Implement date-based event search
    }
}

// SearchManager class
class SearchManager {
    private EventSearchStrategy searchStrategy;

    public void setSearchStrategy(EventSearchStrategy searchStrategy) {
        this.searchStrategy = searchStrategy;
    }

    public List<Event> searchEvents(List<Event> events, String keyword) {
        return searchStrategy.searchEvents(events, keyword);
    }
}

// ReminderObserver interface
interface ReminderObserver {
    void onReminder(Event event);
}

// ReminderManager class (Singleton)
class ReminderManager {
    private static ReminderManager instance;
    private Map<Event, List<ReminderObserver>> observers;

    private ReminderManager() {
        this.observers = new HashMap<>();
    }

    public static synchronized ReminderManager getInstance() {
        if (instance == null) {
            instance = new ReminderManager();
        }
        return instance;
    }

    public void addReminder(Event event, ReminderObserver observer) {
        observers.computeIfAbsent(event, k -> new ArrayList<>()).add(observer);
    }

    public void removeReminder(Event event, ReminderObserver observer) {
        List<ReminderObserver> eventObservers = observers.get(event);
        if (eventObservers != null) {
            eventObservers.remove(observer);
        }
    }

    public void notifyReminders(Event event) {
        List<ReminderObserver> eventObservers = observers.get(event);
        if (eventObservers != null) {
            for (ReminderObserver observer : eventObservers) {
                observer.onReminder(event);
            }
        }
    }
}

// EventCategoriesDecorator class (Decorator)
class EventCategoriesDecorator extends Event {
    private Event event;

    public EventCategoriesDecorator(Event event) {
        super(event.getEventId(), event.getCreator(), event.getTitle(), event.getDateTime(), event.getLocation(), event.getDescription());
        this.event = event;
    }

    @Override
    public List<String> getCategories() {
        List<String> categories = new ArrayList<>(event.getCategories());
        categories.add("Personal");
        return categories;
    }
}

// EventState interface (State)
interface EventState {
    void handleEvent(Event event);
}

// CreatedState class (State)
class CreatedState implements EventState {
    @Override
    public void handleEvent(Event event) {
        // Handle event actions in created state (e.g., inviting attendees, setting recurrence)
    }
}

// OngoingState class (State)
class OngoingState implements EventState {
    @Override
    public void handleEvent(Event event) {
        // Handle event actions in ongoing state (e.g., editing details, adding reminders)
    }
}

// FinishedState class (State)
class FinishedState implements EventState {
    @Override
    public void handleEvent(Event event) {
        // Handle event actions in finished state (e.g., closing event, generating event report)
    }
}

// EventStateContext class
class EventStateContext {
    private EventState currentState;

    public EventStateContext() {
        this.currentState = new CreatedState();
    }

    public void setState(EventState state) {
        this.currentState = state;
    }

    public void handleEvent(Event event) {
        currentState.handleEvent(event);
    }
}

// Main Class
public class EventCalendarApp {
    public static void main(String[] args) {
        // Create users
        User user1 = new User("user1", "john.doe", "john.doe@example.com");
        User user2 = new User("user2", "alice.smith", "alice.smith@example.com");

        // Create event objects
        Event event1 = new Event("event1", user1, "Birthday Party", LocalDateTime.of(2023, 7, 15, 18, 0), "Home", "Join us to celebrate John's birthday!");
        Event event2 = new Event("event2", user2, "Team Meeting", LocalDateTime.of(2023, 7, 20, 14, 30), "Office", "Discuss project updates.");

        // Create event manager
        EventManager eventManager = new EventManager();

        // Create reminder manager
        ReminderManager reminderManager = ReminderManager.getInstance();
        reminderManager.addReminder(event1, new EmailReminderObserver());
        reminderManager.addReminder(event2, new PushNotificationReminderObserver());

        // Create search manager
        SearchManager searchManager = new SearchManager();
        searchManager.setSearchStrategy(new KeywordSearchStrategy());
        List<Event> searchResults = searchManager.searchEvents(eventManager.getEvents(), "birthday");

        // Add event categories using decorators
        Event eventWithCategory = new EventCategoriesDecorator(event1);
        eventWithCategory.getCategories(); // Returns ["Personal"]

        // Set event state and handle actions
        EventStateContext stateContext = new EventStateContext();
        stateContext.setState(new OngoingState());
        stateContext.handleEvent(event1);
    }
}

In this code example, the User class represents a user of the event calendar, the Event class represents an event object, the EventManager class manages the user's events, the SearchManager class uses the Strategy pattern to implement different event search algorithms, the ReminderManager class manages event reminders and uses the Observer pattern to notify users about upcoming events, the EventCategoriesDecorator class adds event categories to events using the Decorator pattern, and the EventStateContext class manages the state of events (created, ongoing, finished) using the State pattern.

Please note that this is a simplified example, and a complete implementation of the Event Calendar involves more complex components, such as event storage and retrieval, event invitations and RSVP management, event synchronization across devices, integration with email and push notification services, and user interface design for creating, viewing, and managing events. Additionally, an Event Calendar application may require backend server components to handle user authentication, event persistence, and real-time event updates. The implementation presented here focuses on the client-side application logic and does not cover the backend server components.