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<div>$B3F0L(B<br>
($BEv%a!<%k$r=EJ#<u?.$5$l$?:]$O$4MF<O$/$@$5$$(B)<br>
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$BN)L?4[Bg3X=u65$NB?Me4VBgJe$H?=$7$^$9!%(B<br>
$B2<5-$NDL$j!$(B11$B7n(B16$BF|(B($BLZ(B)$B$KN)L?4[Bg3X?tM}2J3X2JCLOC2q$,9T$o$l$^$9$N$G!$$*CN$i$;$$$?$7$^$9!%(B<br>
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$B$I$&$>$h$m$7$/$*4j$$$$$?$7$^$9!%(B<br>
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$BB?Me4V(B $BBgJe(B<br>
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$BF|;~!'(B 2017$BG/(B11$B7n(B16$BF|(B($BLZ(B) 16:30$B!A(B17:30<br>
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$B>l=j!'(B $BN)L?4[Bg3X$S$o$3!&$/$5$D%-%c%s%Q%9(B(BKC)<br>
$B%&%'%9%H%&%#%s%0(B6$B3,CLOC2q<<(B<br>
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$B%?%$%H%k!'(B The geometry of a phantom circle<br>
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$B9V1i<T!'(B $B2FL\Mx0l(B ($BL>8E209)6HBg3XL>M@65<x(B)<br>
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$B%"%V%9%H%i%/%H!'(B <br>
This is an attempt to apply noncommutative geometry to study $B!H(Bsingular spaces$B!I(B like fractals.<br>
In the first half I will explain what is noncommutative geometry, what is the philosophy behind it, what are basic tools.<br>
In the second half I will present recent work with H. Moriyoshi of Nagoya University. The algebra of continuous functions on the Cantor ternary set contains the algebra A of continuous functions on the circle. The algebra A is called a phantom circle. I will
explain why this is called a phantom circle. Noncommutative geometry is applied to detect this phantom hiding behind the Cantor set.</div>
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<div>************************************<br>
Daisuke TARAMA<br>
Department of Mathematical Sciences<br>
Ritsumeikan University<br>
Address: 1-1-1 Nojihigashi,<br>
Kusatsu, Shiga, 525-8577, Japan<br>
Office: West Wing (WW) 503<br>
E-mail: dtarama [at] fc.ritsumei.ac.jp<br>
************************************<br>
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