I sent my application to a Professor for a PhD position. His secretary replied:
Dear Mr Singh,
Many thanks for your application.
We will be in contact with you in due course.
What reply should I give to the secretary?
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Don't send any reply. They told you they received your application and will contact you when they're ready. There's nothing for you to say, and any email you send with a non-message will just clutter their inbox and waste their time. Unless you have something of substance to say or a question you need answered, don't send them anything.
Don't send anything. They have explicitly told you that they will contact you.
They are not expecting an acknowledgement. They do not need an acknowledgement. If you didn't get their email, they would expect you to follow up, so the assumption is you received it, until you prove otherwise with a follow up email.
Some may say that it's always a good idea to acknowledge communication. It's true where there may be concern from the sender that the message has not been received, or an acknowledgement has been asked for.
It is almost completely inconsequential if you didn't receive their email, but the consequences of them not receiving your email are far far greater. Which is why it was acknowledged by them.
If the "thank you for your application" message was the first e-mail they sent you, it is worth replying to confirm round-trip communication. It can be a very simple quote of their message with "Thank you" added.
If you have already established that the secretary is sending to the right e-mail address do not clutter their mailbox with a message that adds nothing to their information.
You are not mandated to send any response, however, a thank-you response does not harm. You can reply with something like
Thanks for the acknowledgement. I will wait to hear back from you. Meanwhile, if you need any further information, I'd be happy to provide the same.
It is important to note that in most cases these days "thanks for your application" messages are automated emails generated by the company's online hiring portal. That email is just to confirm that the hiring portal worked as intended and that the company is now able to review your application when they get to it.
Not only do you not need to respond to it, but there is a good chance that if you do respond that your message will go to an unmonitored email address and never be read.
If you need to follow up with the employer, make sure not to rely on that email's reply address to establish a point of contact. Instead see the job listing itself for if it contains contact info.