<html><head><meta http-equiv="Content-Type" content="text/html charset=iso-2022-jp"></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; "><div><br></div><div><div><span style="font-size: 15px; "> $B3'MM!"(B</span></div><div><span style="font-size: 15px; "><br></span></div><div><span style="font-size: 15px; ">$B8&5f=82q$N$40FFb$G$9!#(B</span></div><div><span style="font-size: 15px; ">$BB?$/$NJ}$N$4;22C$r$*BT$A$7$F$*$j$^$9!#(B</span></div><div><span style="font-size: 15px; "><br></span></div><div><div style="font-family: 'MS Gothic', monospace, sans-serif; "><span style="font-size: 15px; "> $BBh#22s6e=#9gF1%;%_%J!<(B</span></div><div style="font-family: 'MS Gothic', monospace, sans-serif; "><span style="font-size: 15px; "><br></span></div><div style="font-family: 'MS Gothic', monospace, sans-serif; "><span style="font-size: 15px; ">$BF|;~(B: 2013$BG/(B11$B7n(B9$BF|!JEZ(B) 16:00 - 17:00 $B!J%F%#!<%?%$%`(B: 15:30 - 16:00$B!K(B</span></div><div style="font-family: 'MS Gothic', monospace, sans-serif; "><span style="font-size: 15px; "><span style="font-family: 'MS Gothic'; ">$B>l=j(B: $B</;yEgBg3XM}3XIt(B220$B<<!JM}3XIt#19f4[$H#29f4[#23,$N(B</span><span style="font-family: 'MS Gothic'; ">$BEO$jO-2<$K$"$k3,CJ65<<!K(B</span></span></div><div><span style="font-size: 15px; "><font face="MS Gothic, monospace, sans-serif">$B9V1i<T(B</font><span style="font-family: 'MS Gothic'; ">: Scott A. Wolpert $B;a(B (University of Maryland, College Park)</span></span></div><div style="font-family: 'MS Gothic', monospace, sans-serif; "><span style="font-size: 15px; "><span style="font-family: 'MS Gothic'; ">$BBjL\(B: </span><span style="font-family: 'MS UI Gothic', Osaka, Arial, sans-serif; ">PSL<span class="GINGER_SOFATWARE_correct" grcontextid="(:0" ginger_sofatware_markguid="798dc5c4-603e-4eee-aef2-6174f126b8e7" ginger_sofatware_uiphraseguid="0ce8744e-4b2d-47e5-9283-ce6185e1dcbd">(</span>n<span class="GINGER_SOFATWARE_correct" grcontextid=";:1" ginger_sofatware_markguid="ebd54f3b-21e8-427c-9462-382fd5a63b0d" ginger_sofatware_uiphraseguid="0ce8744e-4b2d-47e5-9283-ce6185e1dcbd">;</span>R) surface group representations and projective twist-bulge deformations</span></span></div><div><span style="font-family: 'MS UI Gothic', Osaka, Arial, sans-serif; font-size: 15px; ">$BMW;](B: </span></div><div><span style="font-family: 'MS UI Gothic', Osaka, Arial, sans-serif; font-size: 15px; "><div class="yiv2071368009MsoNormal" style="padding: 0px; ">We consider projective PSL<span class="GINGER_SOFATWARE_correct" grcontextid="(:0" ginger_sofatware_markguid="98692722-cab4-418a-97de-fe6b08380ca1" ginger_sofatware_uiphraseguid="02777d15-bc99-402b-a8fa-7a85caf1e930">(</span>n<span class="GINGER_SOFATWARE_correct" grcontextid=";:1" ginger_sofatware_markguid="fc308a9b-e7c4-40b7-a714-8f549937be94" ginger_sofatware_uiphraseguid="02777d15-bc99-402b-a8fa-7a85caf1e930">;</span>R) representations of the fundamental group of a surface with finite topology. The goal is to use generalizations of the Fenchel-Nielsen twist deformation to understand the geometry of the representation space. For PSL<span class="GINGER_SOFATWARE_correct" grcontextid="(:0" ginger_sofatware_markguid="b861e936-4c78-4fe0-a7ae-beef24aaa49e" ginger_sofatware_uiphraseguid="95b57318-a656-4d5b-a53d-9f8186374714">(</span>n<span class="GINGER_SOFATWARE_correct" grcontextid=";:1" ginger_sofatware_markguid="41125784-3ee5-4c8b-b3c2-07f46c7a107e" ginger_sofatware_uiphraseguid="95b57318-a656-4d5b-a53d-9f8186374714">;</span>R) representations of compact surfaces, we review basic results <span class="GINGER_SOFATWARE_correct" grcontextid="for:2" ginger_sofatware_markguid="0d3008eb-9d34-4a02-a448-e93113fc286b" ginger_sofatware_uiphraseguid="95b57318-a656-4d5b-a53d-9f8186374714">for</span> the Hitchin component, including results of Benzecri, Goldman, <span class="GINGER_SOFATWARE_correct" grcontextid="Labourie:3" ginger_sofatware_markguid="0cb76764-e983-4261-831e-2ea37b6c7008" ginger_sofatware_uiphraseguid="95b57318-a656-4d5b-a53d-9f8186374714">Labourie</span> and Bonahon-Dreyer. We discuss the <span class="GINGER_SOFATWARE_correct" grcontextid="Labourie:0" ginger_sofatware_markguid="bfa740f8-1321-49f0-807f-60572912f321" ginger_sofatware_uiphraseguid="37cf7fee-42cb-4e73-ac16-82b821f6473a">Labourie</span> & Fock-Goncharov positivity condition for the $B!H(Bflag curve$B!I(B. The twist-bulge deformation for PSL<span class="GINGER_SOFATWARE_correct" grcontextid="(:0" ginger_sofatware_markguid="4be04cae-aeae-4b8d-9689-0a9e0dc265f3" ginger_sofatware_uiphraseguid="fe76075f-945e-4e0e-b021-6b548da4872f">(</span>3<span class="GINGER_SOFATWARE_correct" grcontextid=";:1" ginger_sofatware_markguid="e27afb24-53b5-469d-9396-b666d216d9b7" ginger_sofatware_uiphraseguid="fe76075f-945e-4e0e-b021-6b548da4872f">;</span>R) representations is described and we present the formula of our student Terence Long for the twist-bulge derivative of a generalized cross ratio. </div><div class="yiv2071368009MsoNormal" style="padding: 0px; "><br></div><div class="yiv2071368009MsoNormal" style="padding: 0px; ">$B%j%s%/!'(B<a href="http://www2.math.kyushu-u.ac.jp/~weng/WolpertKJS.pdf">http://www2.math.kyushu-u.ac.jp/~weng/WolpertKJS.pdf</a></div><div class="yiv2071368009MsoNormal" style="padding: 0px; "><br></div><div class="yiv2071368009MsoNormal" style="padding: 0px; ">$BEvF|(B12:00$B0J9_!"M}3XIt#19f4[$H#29f4[$N8<4X$,$H$b$K2r>{$5$l$^$9!#(B</div><div class="yiv2071368009MsoNormal" style="padding: 0px; "><br></div><div class="yiv2071368009MsoNormal" style="padding: 0px; "><div style="font-family: Helvetica; ">$B!!>.]$(B</div><div style="font-family: Helvetica; "><div>$B</;yEgBg3XBg3X1!(B $BM}9)3X8&5f2J(B $B?tM}>pJs2J3X@l96(B</div><div>$B")(B890-0065$B!!</;yEg;T7485(B1-21-35<br>TEL: 099-285-8031<br></div><div>E-MAIL: <a href="mailto:obitsu@sci.kagoshima-u.ac.jp">obitsu@sci.kagoshima-u.ac.jp</a></div></div></div></span></div></div></div></body></html>