A great talk by Colin Renfrew at the Penn Museum, a must view for anyone interested in Eurasian prehistory. It's good to know that Renfrew holds that the Tocharians originated in West Asia and spread along the Silk Road (south of the Caspian) and not along the steppes. That is also my opinion, and I would perhaps associate them with the J2a/R1b-rich population of eastern Anatolia, Trascaucasia and North Iran, and, perhaps, even related to the Gutians from the Zagros (after Gamkrelidze and Ivanov). That would explain quite well, I believe the anomaly that is the high J2a/R1b frequency in the region.
Also, I would disagree with long-term persistence of Tocharian in Xingiang; it's more likely that this was due to a late migration from somewhere to the west that was eventually swamped by the much more successful wave of the Indo-Iranians that must've involved a J2a/G2a/R1a1 combination. I've made the point before that the vast majority of the territory of Europe and West Asia has shifted language (if not language family) over a span of 2-3 thousand years, so I see no real reason to imagine 2-3 thousand years of linguistic continuity in Xinjiang until the 8th c. AD when Tocharian is first attested.
Here are various abstracts from the Symposium Reconfiguring the Silk Road: New Research on East-West Exchange in Antiquity; hopefully more videos will be uploaded.
James Mallory's talk is also uploaded:
He spends a great deal of his time establishing the (not controversial) idea that Tripolye cultures cannot explain the Yamna phenomenon east of the Dnieper. I will not argue with this, but it is rather a defensive stance of arguing against the spread of Indo-Europeans from the Balkans to the steppe-lands. Positive evidence for the spread of Yamna in the opposite direction is what is needed for the steppe model, and that is what is lacking: with the exception of some clearly Yamna-derived sites in the northern Balkans and Hungary, the links to the rest of the European Indo-Europeans are weak to non-existent.
Moreover, I would argue that the assumption that 3-4,000 years BC there were Indo-European speakers east of the Dnieper is itself suspect. There is no great necessity of explaining how Yamna was Indo-Europeanized from the Balkans, because there is no evidence that it was Indo-European. The first clearly attested Indo-European groups in the European steppe are the Scythians, and they appear in the 1st millennium BC, with both craniology and ancient sources agreeing that they were of eastern origin. So, the inability of the Balkan Tripolye Indo-Europeans of Indo-Europeanizing the Pontic steppe east of the Dnieper is really a non-sequitur, since one must first demonstrate that populations east of the Dnieper spoke Indo-European languages 3,000 years before a single branch of IE (the Iranic) appears in the region from the east.
Mallory also highlights some other substantial problems of the steppe model. Tocharian has IE words for cereals and pigs, and the evidence such as it is suggests that east of the Dnieper there were no domesticated cereals and no evidence of pigs. All this, of course, disappears once we accept that the Tocharians did not move across the steppe lands north of the Caspian, but south of it, from Iran and ultimately the Near East.
Mallory also points out that while he suspects Afanasievo to be linked to the Proto-Tocharians, the sum total of the evidence linking Xinjiang with Afanasievo is meagre. I would also add that, as I've explained above, if one were to establish links between Bronze Age Tarim and Afanasievo, that still leaves a couple of millennia until the first attestation of the Tocharian languages.
Another point of interest is the claim that Indo-Iranians and Tocharians must've been separated in space and time to evolve into so distinctive languages. But, that too is a non-sequitur. We only have to look at the Near East or the Caucasus to witness the co-existence of a handful of language families and dozens of distinct languages. You don't need a large separation to create a new language subfamily, but only a few rivers or high mountains, and Transcaucasia provides both in abundance. I would see Tocharians as the last remnant of the eastern Indo-Europeans, perhaps refugees from further west into Xinjiang itself, with Indo-Iranians pushing them eastward. As for the later steppe cultures that were unquestionably Iranic, these were probably formed after the collapse of the BMAC which sent off Indo-Aryan offshoots south in the 2nd millennium BC, and Iranic ones north, east, and west soon thereafter.