Josh Corey and Ange Mlinko debate whether folks like Anne Winters and Jorie Graham are avant-garde or not. If the discussion ulitimately feels unsatisfying, it's not because both don't make reasonable points, but because the question of who is or is not avant-garde can't be determined on merely formal grounds, i.e. just by reading a text and classifying it one way or the other. Avant-garde is not just a style; it is always also a statement about a work's context of production: the manner in which it appears and circulates, the place it takes within the institutions of art, the extent to which it displays (and demands) a critical awareness of all these things.
That shouldn't be reduced to a crude statement like "Winters and Graham cannot be avant-garde because they are published by Chicago or teach at Harvard." But even if they're not determining, such institutional questions are relevant.
More importantly, the question of avant-garde can't be settled by looking at an individual writer in isolation; fundamental to the idea of avant-garde is, ultimately, the idea of group or movement, one that's hard to reconcile with (and is, perhaps, actively opposed to) the image of a canon in which Poet A jockeys against Poet B for membership in a lineage of heroic greats. Shedding such group allegiances remains one of the prerequistes for being taken seriously as a Great Poet by mainstream critics; but membership in such a community is what allows the avant-garde writer to generate an aesthetic that might differ from the dominant.
I think this is why Jorie Graham has become such a troubling case for those who ally themselves with avant-garde writing. By any measure, Graham is one of the most prominent and successful of American poets. But her style, her surface, is just unconventional enough that it is regarded as "experimental" or even "avant-garde" by many of her mainstream readers--so much so that Graham has occasionally become a punching bag for conservative writers who loathe Language writing and its ilk. The irony is that, while Graham is often praised by critics for her openness to a range of styles, she's never allied herself with any group of experimental writers, and certainly not with Language poets. I imagine that Graham often enrages avant-garde writers because she's often used as a token of stylistic eclecticism ("Oh, yes, we have 'experimental' poets; we have Jorie Graham") in a way that allows for the exclusion of anyone who's doing anything more radical.
That latter strategy is central to Gregory Orr's NYTBR review. But the odd thing is that the more one is an avowed fan of Graham, the more her formal traits seem beside the point: cf. Cal Bedient's Boston Review piece, which reads Graham more as philosopher than poet ("she is more than ever obsessed with the x everyone and everything fundamentally is (or fails to be)").
I perodically come back and try to read Graham, but she just does nothing for me. Orr says she's "ostentatiously thinky," which is nasty on a number of levels (prejudices against smart women and arch academics among them) but probably fundamentally right. Discursivity per se, which Josh is not a big fan of, isn't exactly the problem; it's more like an overdramatized self-consciousness, a sense of a poet trying to "look in" on the process of thought and then constantly reminding you that she's doing it: a trait I see in a funny cross-section of poets ranging from Frank Bidart to Leslie Scalapino. I'd distinguish that from a linguistic self-consciousness because the former is ultimately all about the ego turning in upon itself, while the latter hopefully works toward some awareness of the objective materials that make the ego what it is.