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<div>$B%?%$%H%k!'(BBV structures on moduli spaces of flat connections
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<div>$B9V1i<T!'(B<span>Pavol Severa $B!J(BUniversity of Geneva$B!K(B</span><br>
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<div><span>Loops (or rather their homotopy classes) on an oriented surface form a Lie algebra, originally discovered by Goldman.
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<div>The Lie bracket is given by a simple formula involving intersection points of two loops.
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<div>This Lie algebra can be interpreted as the Poisson bracket on a moduli space of flat connections (given by the famous Atiyah-Bott symplectic form), if to each loop we assign the trace of the holonomy along the loop.
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<div>Loops come also with another operation, a Lie cobracket discovered by Turaev, given by a very similar formula.
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<div>I will explain what is the corresponding geometric structure on the moduli space.
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<div>I will also try to explain why this structure is interesting and how it relates to the Kashiwara-Vergne problem in Lie theory.
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<span>Based on a joint work in progress with Anton Alekseev, Florian Naef, and Jan Pulmann.</span>
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<div> $B!!(Bhttp://www.ritsumei.ac.jp/accessmap/bkc/<br>
<div> $B!!(Bhttp://www.ritsumei.ac.jp/campusmap/bkc/<br>
<div> $B!!(Bhttp://www.ritsumei.ac.jp/file.jsp?id=227632&f=.pdf<br>
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<div> $B!!B?Me4V(B $BBgJe(B<br>
<div> $B!!(Bdtarama [at] fc.ritsumei.ac.jp<br>
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<div>************************************<br>
<div>Daisuke TARAMA<br>
<div>Department of Mathematical Sciences<br>
<div>Ritsumeikan University<br>
<div>Address: 1-1-1 Nojihigashi,<br>
<div>Kusatsu, Shiga, 525-8577, Japan<br>
<div>Office: West Wing (WW) 606<br>
<div>E-mail: dtarama [at] fc.ritsumei.ac.jp<br>
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