How can I get a instance of a generic list with reflection?

var type = Type.GetType(typeof (List<T>).AssemblyQualifiedName);
var list = (Ilist<T>)Activator.CreateInstance(type);

typeof(List<string>).GetGenericTypeDefinition() == typeof(List<>)

var elementType = (
    from iface in myList.GetType().GetInterfaces()
    where iface.IsGenericType
    where iface.GetGenericTypeDefinition() == typeof(IList<>)
    select iface.GetGenericArguments()[0])
        .Single();

void Main()
{
    Parse<Foo>();
}

public static T Parse<T>() where T : new()
{
   var returnObj = new T();
   PropertyInfo[] properties = typeof(T).GetProperties();
   foreach (PropertyInfo p in properties)
   {
     // Get a meaningful property name
     string ins = p.PropertyType.Name;
     switch(ins)
     {
        // populate int
        case "Int32":
           p.SetValue(returnObj, 1 , null);
           break;

        // populate list
        case "IList`1":
           var list = new List<string>();
           // This will throw the exception 'Parameter count mismatch.'
           p.SetValue(returnObj, list, null);
           break;
      }
   }
   return returnObj;
}

public class Foo
{
 public virtual int someInt {get; set;}
 public virtual IList<string> list {get; set;}
}

public class Foo
{
 public virtual int someInt {get; set;}
 public virtual IList<string> this[int key] 
 {
    get{ return null; }
    set 
    {
    }
 }
}

// gets metadata of List<Lecture>.Add method
var addMethod = pi.PropertyType.GetMethod("Add");

// retrieves current LectureList value to call Add method
var lectureList = pi.GetValue(s);

// calls s.LectureList.Add(obj);
addMethod.Invoke(lectureList, new object[] { obj });