Visual Arts/Reviewed: Tim Hawkesworth Recent drawings and paintings. Galleries 2 & 3, Royal Hibernian Academy until Oct 22 01-6612558

Tim Hawkesworth's work is surely the ideal accompaniment to Robert Ballagh's retrospective at the RHA, not least because there's zero chance you'll mistake one for the other. In terms of visual style, they look like opposites: Ballagh's distinctive brand of fine-tuned representation, layered with carefully calculated meaning, as opposed to Hawkesworth's gestural expressiveness in paintings and drawings with no discernible representational image.

Surely those fiercely exuberant displays of thick applied pigment, their surfaces inscribed with myriad squiggles and scrapes, are about freedom from the constraints that are so evident in Ballagh's work? Well, yes and no. They certainly enact freedom from certain kinds of constraint, but they recognise and accept others quite happily. In other words, his work isn't just self-expression in the sense of being arbitrary and spontaneous mark-making.

In everything he does, there is a forward momentum, a sense of his moving toward something, and that something is the overall poise of each piece, a state of teeming liveliness. His struggle is to find and nurture this liveliness within the given structures of painting and drawing. That can mean, paradoxically, standing back, letting the work have its own voice, find its own level, so that it's not expressive in any selfish way at all. It's as if the initial letting go of conventional constraints becomes another kind of letting go entirely.

The gestural language he uses recalls the work of several painters identified with American Abstract Expressionism. They include, most famously, Jackson Pollock, as well as Philip Guston, Mark Tobey and to some extent Willem de Kooning. But for several reasons the American whose work provides the most relevant point of reference is Cy Twombly, someone whose work, like Hawkesworth's, is informed by the Abstract Expressionists but stands at one remove from them. Twombly moved to Italy when he was still in his 20s, and everything he made since that time pursues a dialogue with classical European tradition.

In fact his artistic project has been described as the reconciliation of American Modernism with Old European classical values. While there is an element of truth in that, it's not quite the whole story, and his paintings and sculptures would not prove satisfactory if looked at purely in those terms (the excellent Cy Twombly: A Monograph by Richard Leeman, Thames & Hudson, £60 in UK, provides the best, comprehensive overview).

Rather it is as if he deconstructs both Abstract Expressionism and Classical painting. His work embodies a huge yearning for what both offer, but acknowledges the impossibility of either reconstructing or reconciling them. Yet in exploring this impossibility and loss, he manages to establish another artistic space entirely, a space of exhilarating possibility.

All of which is applicable to Hawkesworth. He was born in Ireland, in Wicklow, and studied history and political science at Trinity before moving to the US to do an MA in fine arts. He has remained there, working and teaching. His trajectory, from the Old World to the New, was the opposite of Twombly's, but there is a similar sense, in his work, of his finding problematic nurture in the notional meeting of the world he'd left behind and the one he found himself inhabiting. He has had to negotiate his own position, and has done so, to some extent warily but also with great commitment and integrity.

As it happens, much of the work in Tim Hawkesworth: Recent Drawings and Paintings was made during, or springs from, a residency at the Ballinglen Arts Foundation in Ballycastle, Co Mayo (a centre established by Americans Margo Dolan and Peter Maxwell). His residency there, a couple of years ago, was significant for him, and seems to have sparked a fruitful engagement with the textures and scale not so much of the north Mayo landscape itself, though that was certainly relevant, as with the density of its accumulated history. A central part of that history involves links with the US.

The written word plays a consistent role in Twombly's work, sometimes legible, often not, implying an urgency of communication and distantly recalling Tobey's calligraphic marks. Hawkesworth, too, uses words, handwritten, and mostly worked over to the point of illegibility and indeed invisibility, in his Mayo drawings. They really are drawings, though his use of oil stick gives them something of the quality of paintings in that he can build up, and scrape through, opaque layers of pigment, so that they have body.

His use of language underlines the fact that the drawings are a language in themselves. One thinks of the handwritten letters that were for generations the primary means of communication linking families on opposite sides of the Atlantic. Appropriately or not, Hawkesworth's Mayo drawings bring to mind a cumulative layering of personal and communal histories. But rather than dwelling on notions of tragedy or disinheritance or loss, he infuses his historical terrain with tremendous generative potential.

One of his smaller paintings is called, intriguingly, Teresa's Brain. It is, for him, quite a specific title, and what we get from the work is a feeling of seething, restless activity. It's not a representation of intricate neural networks, but it powerfully conveys just that idea: a network teeming with energetic life. In the painting, a thick, frenetically agitated layer of creamy white pigment is laid onto and partly merges with underlying layers of darker colour. It's all fantastically busy, but it also achieves that equilibrium referred to earlier, whereby the artist sets it all in motion that then stands back.

In linking Hawkesworth to Twombly, it's important to point out that while there are surely strong affinities and correspondences, such as their shared liking for gestural mark-making judiciously employed, there isn't a notable or obtrusive resemblance between their paintings. It's worth saying, as well, that at a time when there is a certain distrust of an artist's strong, instinctive engagement with a medium, it's refreshing to see Hawkesworth forthrightly demonstrating his commitment to exactly that. After being away for two decades plus, he has returned with a show of beautiful work that acknowledges both the old country and the new entirely on his own terms.