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# Abstract Florent Schaffhauser

**Florent Schaffhauser **will speak on

**The Yang-Mills equations over Klein surfaces**

**Abstract:** In their 1982 seminal paper on 'The Yang-Mills equations over Riemann surfaces', Atiyah and Bott computed the rational Betti numbers of moduli spaces of holomorphic vector bundles of coprime rank and degree over a compact Riemann surface of genus greater than 1 via a gauge-theoretic approach. When the Riemann surface is endowed with a real structure, it is sometimes called a Klein surface and one can construct moduli spaces of Real and Quaternionic vector bundles over it using gauge theory. In a joint work with Melissa Liu (Columbia University), we used this approach to compute the mod 2 Betti numbers of those moduli spaces in the coprime case. In this talk, I would like to give an overview of the general method, comparing it to the original computation of Atiyah and Bott.