–x“à �ŸŽq (“Œ‹ž�—Žq‘åŠw‘åŠw‰@—�ŠwŒ¤‹†‰È)
The Gordian complex of virtual knots
(ŒÃ‘º ���ƒŽ�, ‘åŽR �i”VŽ�(“Œ‹ž�—Žq‘åŠw), ‰ºàV �¹ŽjŽ�‚Ƃ̋¤“¯Œ¤‹†)
—é–Ø ‚Ü‚èŠG (“Œ‹ž�—Žq‘åŠw‘åŠw‰@—�ŠwŒ¤‹†‰È)
The Gordian complex of non-classical virtual knots by crossing changes
(‰ºàV �¹ŽjŽ�‚Ƃ̋¤“¯Œ¤‹†)
‰F–ì �„Žj (“Œ‹žŠwŒ|‘åŠw‘åŠw‰@‹³ˆçŠwŒ¤‹†‰È)
Sheet number and 11-colorable 2-knot
‹g“c �³–¾ (�é‹Ê‘åŠw‘åŠw‰@—��HŠwŒ¤‹†‰È)
On shortest pathways of unlinking by Xer-diff-FtsK
(�ÎŒ´ ŠCŽ�, Mariel VazquezŽ�, ‰º�ì �q–çŽ�‚Ƃ̋¤“¯Œ¤‹†)
ˆîŠp �„ (‘å�ãŽs—§‘åŠw‘åŠw‰@—�ŠwŒ¤‹†‰È)
—�‚Ý–Ú‚ÌŠiŽq“_•\ަ
•�‘º “Ö (�_ŒË‘åŠw‘åŠw‰@—�ŠwŒ¤‹†‰È)
Cowrithe‚Ì�Å�¬’l‚Æ�Å‘å’l‚ɂ‚¢‚Ä
‰ª�è Œš‘¾ (‹ž“s‘åŠw�”—�‰ð�ÍŒ¤‹†�Š)
$E_6$, $E_8$Œ^•”•ªˆöŽqŠÂ‚Ì•½–Ê‘ã�”‚Æ3ŽŸŒ³‘½—l‘Ì‚Ì�ó‘Ô˜a•s•ϗʂ̑g‚Ý�‡‚킹“I�\�¬‚ɂ‚¢‚Ä
Šâ�Ø ‰ë‰p (�²‰ê‘åŠw‘åŠw‰@�HŠwŒnŒ¤‹†‰È)
3-component surface-links with braid index 4 is ribbon
�¬ŠÚ �’Žq (“Œ‹ž�—Žq‘åŠwŒ»‘㋳—{Šw•”)
Œ‹‚Ñ–Ú‚Ì–{•\Œ»‚ɂ‚¢‚Ä
ŽR’† �m (‘å�ãŽs—§‘åŠw—�Šw•”)
Weights of Markov traces for Alexander polynomials of mixed links
—é–Ø �çˆß (‹ž“s‘åŠw‘åŠw‰@—�ŠwŒ¤‹†‰È)
Brunnian ’êƒ^ƒ“ƒOƒ‹‚Ì•�•Õ$sl_2$•s•ϗʂɂ‚¢‚Ä
“c�_ ŒcŽm (“Œ‹ž�H‹Æ‘åŠw‘åŠw‰@—��HŠwŒ¤‹†‰È)
The maximal degree of the Khovanov homology under twisting
‹´–{ �L�� (“Œ‹ž�—Žq‘åŠw‘åŠw‰@—�ŠwŒ¤‹†‰È)
‹óŠÔŠ®‘S4•”ƒOƒ‰ƒt$K_{3,3,1,1}$“à‚ÌŒ‹‚Ñ–Ú‚Æ—�‚Ý–Ú‚Ì•s•ϗʂɂ‚¢‚Ä
(�Vš —ºŽ�(“Œ‹ž�—Žq‘åŠw)‚Ƃ̋¤“¯Œ¤‹†)
’†�] �N�° (�H“c‘åŠw‘åŠw‰@�HŠwŽ‘Œ¹ŠwŒ¤‹†‰È)
$(-2,3,2s+1)$Œ^ƒvƒŒƒbƒcƒFƒ‹Œ‹‚Ñ–Ú‚ÌŠî–{ŒQ‚Ì•\ަ‚Æ$\mathbb{R}$-covered—t‘w�\‘¢‚ɂ‚¢‚Ä
�¡•Ê•{ �F‹K (�L“‡‘åŠw‘åŠw‰@—�ŠwŒ¤‹†‰È)
ƒ`ƒFƒbƒJ�[ƒ{�[ƒh�Ê�F‰Â”\‚ȉ¼‘zŒ‹‚Ñ–Ú‚Ìnormalized arrow polynomial‚ɂ‚¢‚Ä
�¬’¹‹� —S�� (“Œ‹ž�H‹Æ‘åŠw‘åŠw‰@—��HŠwŒ¤‹†‰È)
$\bar{\mu}$ invariant of nanophrases
‘ꉪ ‰p—Y (‘å�ãŽs—§‘åŠw‘åŠw‰@—�ŠwŒ¤‹†‰È)
(2,1)ƒP�[ƒuƒ‹Œ‹‚Ñ–Ú‚Ì—ë”ÔŒW�”‘½�€Ž®
–ì�â •�Žj (‹ž“s‘åŠw�”—�‰ð�ÍŒ¤‹†�Š)
ƒAƒŒƒNƒTƒ“ƒ_�[ƒJƒ“ƒhƒ‹‚Ì$G$‘°‚ƃ‚ƒWƒ…ƒ‰�[•s•ÏŽ®˜_
ˆ°Œ´ ‘�‰î (�L“‡‘åŠw‘åŠw‰@—�ŠwŒ¤‹†‰È)
nƒcƒCƒXƒgƒXƒpƒ“3—tŒ‹‚Ñ–Ú‚ÌŠî–{ƒoƒCƒJƒ“ƒhƒ‹
ŽR–{ ‘ñ�l (�_ŒË‘åŠw‘åŠw‰@—�ŠwŒ¤‹†‰È)
On the Gordian distance by pass moves
ŽsŒ´ ˆê—T (“ú–{‘åŠw•¶—�Šw•”)
‘o‹È“IŒ‹‚Ñ–Ú‚Ì—áŠO“Iƒf�[ƒ“Žè�pƒXƒ��[ƒv�W�‡‚Æ�Å’ZƒXƒ��[ƒv
�ì‰z Œªˆê (‹à‘ò‘åŠw—��HŒ¤‹†ˆæ)
”ñŽ©–¾‚È•½–ʃOƒ‰ƒt‚Ì•s•ϗʂɂ‚¢‚Ä
�¯Œ´ ”¹�l (‘�ˆî“c‘åŠw‘åŠw‰@‹³ˆçŠwŒ¤‹†‰È)
Link-universal subsets of $\mathbb{R}^3$
˜a“c �KŽj˜N (�L“‡‘åŠw‘åŠw‰@—�ŠwŒ¤‹†‰È)
On classification of two-point homogeneous quandle of cyclic type
(“cŠÛ ”ŽŽmŽ� (�L“‡‘åŠw)‚Ƃ̋¤“¯Œ¤‹†)
’JŒû Œ’‘¾ (�_ŒË‘åŠw‘åŠw‰@—�ŠwŒ¤‹†‰È)
On free knots
�¬”© —zŽ™ (‘å�ãŽs—§‘åŠw‘åŠw‰@—�ŠwŒ¤‹†‰È)
‚à‚ë‚ÄŒ^—�‚Ý–Ú‚Ì�\�¬
�¬‘ò �½ (‹îàV‘åŠw‘��‡‹³ˆçŒ¤‹†•”)
Nonminimal bridge positions of torus knots are stabilized
ŽÅ“c Œ«Žj (‘å�ãŽs—§‘åŠw‘åŠw‰@—�ŠwŒ¤‹†‰È)
—L—�ƒUƒCƒtƒFƒ‹ƒg�s—ñ‚Ì“Á’¥•t‚¯
ˆî—t ˜a�³ (“Œ–k‘åŠw‘åŠw‰@—�ŠwŒ¤‹†‰È)
On the enhancements to the Milnor numbers of a class of mixed polynomials
�ÎŒ´ ŠC (Imperial College London, Department of Mathematics)
Nullification distance between links with small crossing numbers
(joint work with Dorothy Buck)
ŠÝ–{ Œ’Œá (‘å�ã�H‹Æ‘åŠw�HŠw•”)
Simple ribbon fusions for links
(�a’J “N•vŽ�(‘å�ã�H‹Æ‘åŠw), ’Ë–{ ’B–çŽ�(‘å�ã�H‹Æ‘åŠw)‚Ƃ̋¤“¯Œ¤‹†)
�XŒ³ Ѝޡ (�b“ì‘åŠw’m”\�î•ñŠw•”)
Twisted torus knots and essential surfaces
ŸNˆä ‚Ý‚¬˜a (“Œ‹ž�—Žq‘åŠw‘åŠw‰@—�ŠwŒ¤‹†‰È)
Examples of finite type invariants for virtual knots
ˆÉ“¡ “N–ç (“Œ‹ž‘åŠw‘åŠw‰@�”—�‰ÈŠwŒ¤‹†‰È)
Local Aut($F_{n}$)-representations of braids: classification and application
ŽR“c ‚³‚â‚© (“ú–{�—Žq‘åŠw‘åŠw‰@—�ŠwŒ¤‹†‰È)
Minimal unknotting sequences of Reidemeister moves containing unmatched RII moves
(àV“c ŽÀŽ�, —Ñ ’‰ˆê˜YŽ�, —Ñ ”ü˜aŽ�‚Ƃ̋¤“¯Œ¤‹†)
‘�–ì Œ’‘¾ (‘å�ã‘åŠw‘åŠw‰@—�ŠwŒ¤‹†‰È)
4ŽŸŒ³‘½—l‘̂̋ȖÊ�}Ž®‚Ì‹ï‘Ì—á‚Ì�\�¬‚ɂ‚¢‚Ä
�´“c Œb—� (“Œ‹žŠwŒ|‘åŠw‘åŠw‰@‹³ˆçŠwŒ¤‹†‰È)
On links with common sublinks
‰Pˆä ‘ô–ç (“Œ‹ž‘åŠw‘åŠw‰@�”—�‰ÈŠwŒ¤‹†‰È)
“Á•Ê‚ÈL‹óŠÔ‚Æ—�‚Ý–Ú‚Ì�‡�˜‚ɂ‚¢‚Ä
�â–{ �^—��¹ (‘�ˆî“c‘åŠw‘åŠw‰@‹³ˆçŠwŒ¤‹†‰È)
Plane curves in an immersed graph in $\mathbb{R}^2$
(’JŽR Œö‹KŽ�(‘�ˆî“c‘åŠw‹³ˆçŠw•”)‚Ƃ̋¤“¯Œ¤‹†)
’JŒû —T–ƒ (“Œ‹žŠwŒ|‘åŠw‘åŠw‰@‹³ˆçŠwŒ¤‹†‰È)
Interpretations of rack coloring knot invariants in terms of quandles
ˆä�ã •à (“Œ‹ž�H‹Æ‘åŠw‘åŠw‰@�î•ñ—��HŠwŒ¤‹†‰È)
ƒJƒ“ƒhƒ‹‚ð—˜—p‚µ‚½—�‚Ý–Úƒzƒ‚ƒgƒs�[—Þ‚Ì•ª—Þ‚ÉŒü‚¯‚Ä