Vjylku

As per Karma theory, certain events of my current life are the fruits of my actions in one or more earlier births. Whose action's fruits am I facing in this birth? Given that it cannot be my current body or mind, it follows that it has to be my Atman. But according to Advaita, only Brahman exists and everything else is the product of Maya. In particular, the seemingly different people we see are all Brahman and seem different only because of Maya. Then how is it possible to determine the me from a previous birth? If one can indeed determine the me from the previous birth then does that not directly imply duality contradicting Advaita?

In fact I do not see how rebirth is even possible in the context of Advaita. Who is getting reborn? There is only Atman which manifests as duality through Maya. One cannot point to someone and say "you will be a great scholar in your next birth". For the statement to be true automatically means duality.

Advaita is true only in the paramarthika stage. We normally are mistaken by the world 'Jagat mithya'. The word 'Jagat' literally means something which is ever-changing.It comes from the root 'gam' which means movement. 'Mithya' here just does NOT mean false. It means :that which is not eternal or is ever-existing'. (Reference : Vivekanander Vedanta-Chinta, Dinesh Chandra Bhattacharya, RMIC).

We get both pleasure and pain because we are deluded by Maya. To cross the ocean of Maya, we need Brahma-Jnana or the knowledge of the never changing eternal truth Which is one with our True Self.To attain that knowledge, we first need'Chitta-suddhi' according to Sri Adi Sankaracharya.For Chitta-Suddhi, we need 'Nishkama-Karma' and 'Ishwara-Upasana'.So long as one has the sense of 'I' and 'My', he has to go on doing good works prescribed by the holy scriptures. So karma is essential to realise 'Advaita' in life.(Reference: Jnani-Guru, Paramahansa Nigamananda Saraswati, Sarasvata Math).

So long as we are ignorant of our True Self, we are Jivatmas. We have basically three bodies- Gross or Sthula,Subtle or Sukshma and Karana or Causal. The subtle body comprises of subtle karmendriyas and subtle jnanendriyas and manas. The causal body is caused by the ignorance that identifies the Self with these gross and subtle bodies. It is the causal body and the subtle body which together are together called Jivatma.This Jivatma dies and is born again and again so long as the true knowledge of the real Self is not obtained. The knowledge of the self destroys the mind which is root of all our ignorance. Being one with our True Self ends our endless journey between births and deaths.

Yes, rebirth is true in duality.When Maya is gone, duality is gone and there is neither birth nor death.

So rebirth and Karma are fully consistent with Advaita (Reference:Jnani-Guru, Paramahansa Nigamananda,Sarasvata Math).

As per Karma theory, certain events of my current life are the fruits of my actions in one or more earlier births.

Yes

Whose action's fruits am I facing in this birth?

Your own.

Given that it cannot be my current body or mind, it follows that it has to be my Atman.

By this reasoning you are saying you are not responsible for anything you did yesterday or anything before current moment.

In particular, the seemingly different people we see are all Brahman and seem different only because of Maya. Then how is it possible to determine the me from a previous birth?

If you can identify yourself as doer of a task among many people, you performed yesterday, then you may very well also identity yourself among many people of your previous birth tasks.

If one can indeed determine the me from the previous birth then does that not directly imply duality contradicting Advaita?

This contradiction seems to even arises if you think you can identify yourself as doer of a task you performed yesterday among many. Because according to Advaita, only one exists. Even in this every moment this contradiction arises. You may simple say, if Advaita is true, why are there so many people.

In fact I do not see how rebirth is even possible in the context of Advaita. Who is getting reborn?

Again, I really do not see your argument here. What's the problem with rebirth? It's just like going from yesterday to today or childhood to youth to old age. If you take yourself as the same person yesterday and today, what is wrong with rebirth? Like Krishna says:

देहिनोऽस्मिन्यथा देहे कौमारं यौवनं जरा।

तथा देहान्तरप्राप्तिर्धीरस्तत्र न मुह्यति।।2.13।।

Are Advaita and Karma theory completely contradictory?

There's nothing like 'complete' contradiction or 'slight' contradiction. It's either contradiction or no contradiction. Anyhow, answering the question. No there is no contradiction in karma theory and Advaita.

What is Karma really?

Karma essentially are the vasanas because one only performs karma out of vasanas and not without it. Vasistha also says:

जन्तुर्_यद्_वासनो राम तत् कर्ता भवति क्षणात् ।

अन्य-कर्मान्य्_अभावश्_चेत्य्_एतन्_न_एव_उपपद्यते ॥१४॥
(14, 9, 2 YV)

Objection: This is not always the case. Some actions are performed based on circumstances (or bhagya).

Answer: This is not true. The circumstances (or bhagya) also are a result of past karmas.

यद्_एव तीव्र~संम्वेगाद्_दृढम् कर्म कृतम् पुरा ।

तद्_एव दैव-शब्देन पर्यायेण_इह कथ्यते ॥१६॥
(16, 9, 2 YV)

What are vasanas really? Vasanas are nothing other than Manas.

यद्_दैवम् यानि कर्माणि कर्म साधो मनो हि तत् ।

मनो हि पुरुषस्_तस्माद्_दैवम् न_अस्ति_इति निश्चयः ॥१८॥
(18, 9, 2 YV)

The above mentioned theory is karma theory. This is as true as saying area of square is side^2.

Now, Advaita only says that this Manas is unreal. And by neglecting this Manas everything gets neglected from Manas down to Karma. There is simply no contradiction. It seems there's a contradiction because we try to question the unreality of karmas while presuming the existance of Manas. When you say karmic theory is false, its as good as saying area of square is not side^2. Karma theory is said to be false according to Advaita only because of lack of better words. And when it is said false, it is assumed you also neglect the Manas along with it.

So, when you say "Why am I getting the fruits of karma? The one that performed karma in the past life was not me because everything is one", you are using Advaita to claim "Only Atman exist" and the same time saying "I enjoy". You cannot say "I enjoy" in light of Advaita because Atman never enjoys nor does action. Remember all the Manas idea gets neglected in light of Advaita. On the other hand if you take the responsibility of fruits you are enjoying, you also need to acknowledge your actions of the past.