●학력 (Education)

1996년 8월: 경북대학교 대학원 수학과 이학박사
1988년 2월: 경북대학교 대학원 수학과 이학석사
1986년 2월: 경북대학교 자연과학대학 수학과 이학사

● 경력 (Experience)
2010.4 - 현재: 부산대학교 자연과학대학 수학과 교수

2005.4 - 2010.3: 부산대학교 자연과학대학 수학통계학부(수학전공) 부교수

2003.3 - 2004.7: 부산대학교 대학원 수학과장

2003.3 - 2004.2: 부산대학교 자연과학대학 수학통계학부장

1999.3 - 2005.3: 부산대학교 자연과학대학 수학통계학부(수학전공) 조교수
1998.3 - 1999.2: 경북대학교 연구원, 시간강사
1997.3 - 1998.2: 포항공과대학 Pos-Doc.

● 대표논문 (Selected Publications)

○국외학술지 논문

(S)SCI(E)

[1]이상율,박찬녕,임용도, "Symmetric geodesics on conformal compactifications of Euclidean Jordan algebras", BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY /ISSN = 0004-9727, Vol.59, pp.187-201 (1999/02) (AUSTRALIAN MATHEMATICS PUBL ASSOC INC)

[2]이상율, "Matrix presentations of braids and applications", PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY /ISSN = - , Vol.127, Issue.11, pp.3403-3412 (1999/11) (The American Mathematical Society) (한국과학재단)

[3]박찬녕,이상율,장재호, "On the 2-parallel versions of links", CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES /ISSN = 0008-4395, Vol.43, Issue.2, pp.145-156 (2000/03) (CANADIAN MATHEMATICAL SOC)

[4]이상율,박찬녕,임용도, "Knots in S^2 × S^1 derived from Sym(2, R)", FUNDAMENTA MATHEMATICAE /ISSN = 0016-2736, Vol.164, Issue.3, pp.241-252 (2000/09) (POLISH ACAD SCIENCES INST MATHEMATICS)

[5]이상율,박찬녕,서명수, "On adequate links and homogeneous links", BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY /ISSN = 0004-9727, Vol.64, pp.395-404 (2001/10) (AUSTRALIAN MATHEMATICS PUBL ASSOC INC) (학술진흥재단)

[6]이상율, "？n-equivariant goeritz matrices for periodic links", OSAKA JOURNAL OF MATHEMATICS /ISSN = 0030-6126, Vol.40, Issue.2, pp.393-408 (2003/06) (OSAKA JOURNAL OF MATHEMATICS)

[7]이상율,서명수, "The 3-move and knotted 4-valent graphs in 3-space", OSAKA JOURNAL OF MATHEMATICS /ISSN = 0030-6126, Vol.41, Issue.1, pp.119-130 (2004/03) (OSAKA JOURNAL OF MATHEMATICS)

[8]이상율,서명수, "Recurrence formulas for the Alexander polynomials of 2-bridge links and their covering links", JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS /ISSN = 0218-2165, Vol.15, Issue.2, pp.179-203 (2006/02) (WORLD SCIENTIFIC PUBL CO PTE LTD)

[9]이상율,서명수,장희정, "Casson knot invariants of periodic knots with rational quotients", JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS /ISSN = 0218-2165, Vol.16, Issue.4, pp.439-460 (2007/04) (WORLD SCIENTIFIC PUBL CO PTE LTD)

[10]이상율,서명수, "A formula for the delta-unknotting numbers of knots", INTERNATIONAL JOURNAL OF MATHEMATICS /ISSN = 0129-167X, Vol.19, Issue.3, pp.323-338 (2008/03) (WORLD SCIENTIFIC PUBL CO PTE LTD)

[11]이상율, "Invariants of surface links in R-4 via skein relation", JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS /ISSN = 0218-2165, Vol.17, pp.439-469 (2008/04) (WORLD SCIENTIFIC PUBL CO PTE LTD)

[12]이상율,서명수, "Casson knot invariants of periodic knots with rational quotients II", JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS /ISSN = 0218-2165, Vol.17, pp.905-923 (2008/08) (WORLD SCIENTIFIC PUBL CO PTE LTD)

[13]이상율, "Towards invariants of surfaces in 4-space via classical link invariants", TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY /ISSN = 0002-9947, Vol.361, pp.237-265 (2009/01) (AMER MATHEMATICAL SOC)

[14]이상율,서명수, "The genus of periodic links with rational quotients ", BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY /ISSN = 0004-9727, Vol.79, pp.273-284 (2009/04) (AUSTRALIAN MATHEMATICS PUBL ASSOC INC) (학술진흥재단)

[15]서명수,이은주,이상율, "A recursive formula for the Jones polynomial of 2-bridge links and applications ", Journal of the Korean Mathematical Society(대한수학회지) /ISSN = 0304-9914, Vol.46, Issue.5, pp.919-947 (2009/09) (대한수학회)

[16]서명수,이상율,김준오, "The Miyazawa polynomial of periodic virtual links", OSAKA JOURNAL OF MATHEMATICS /ISSN = 0030-6126, Vol.46, Issue.3, pp.769-781 (2009/09) (OSAKA JOURNAL OF MATHEMATICS)

[17]서명수,이상율, "FORMULAS FOR THE CASSON INVARIANT OF CERTAIN INTEGRAL HOMOLOGY 3-SPHERES", JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS /ISSN = 0218-2165, Vol.18, pp.1551-1576 (2009/11) (WORLD SCIENTIFIC PUBL CO PTE LTD)

[18]서명수,이상율, "A formula for the braid index of links", TOPOLOGY AND ITS APPLICATIONS /ISSN = 0166-8641, Vol.157, pp.247-260 (2010/01) (ELSEVIER SCIENCE BV)

[19]임영호,이상율,이경희, "INDEX POLYNOMIAL INVARIANT OF VIRTUAL LINKS", JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS /ISSN = 0218-2165, Vol.19, Issue.5, pp.709-725 (2010/05) (WORLD SCIENTIFIC PUBL CO PTE LTD)

[20]임영호,이상율,이경희, "SIGNATURE, NULLITY AND DETERMINANT OF CHECKERBOARD COLORABLE VIRTUAL LINKS", JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS /ISSN = 0218-2165, Vol.19, Issue.8, pp.1093-1114 (2010/08) (WORLD SCIENTIFIC PUBL CO PTE LTD)

[21]장희정,이상율,서명수, "ON THE Delta-UNKNOTTING NUMBER OF WHITEHEAD DOUBLES OF KNOTS", JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS /ISSN = 0218-2165, Vol.21, Issue.2, pp.1-23 (2012/02) (WORLD SCIENTIFIC PUBL CO PTE LTD)

[22]이상율, "GENERA AND PERIODICITY OF VIRTUAL KNOTS AND LINKS", JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS /ISSN = 0218-2165, Vol.21, Issue.4, pp.1-15 (2012/04) (WORLD SCIENTIFIC PUBL CO PTE LTD)

[23]임영호,이상율, "ON THE INDEX AND ARROW POLYNOMIALS OF PERIDOIC VIRTUAL LINKS", JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS /ISSN = 0218-2165, Vol.21, Issue.6, pp.1250058-1-1250058-21 (2012/05) (WORLD SCIENTIFIC PUBL CO PTE LTD)

[24]임영호,이상율, "A FOUR-VARIABLE INDEX POLYNOMIAL INVARIANT OF LONG VIRTUAL KNOTS", JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS /ISSN = 0218-2165, Vol.21, Issue.9, pp.1250083-1-1250083-18 (2012/08) (WORLD SCIENTIFIC PUBL CO PTE LTD)

[25]이상율,장희정, "The canonical genus for Whitehead doubles of a family of alternating knots", TOPOLOGY AND ITS APPLICATIONS /ISSN = 0166-8641, Vol.159, Issue.17, pp.3563-3582 (2012/11) (ELSEVIER SCIENCE BV)

[26]이상율,김준오,서명수, "ON THE VA-POLYNOMIAL OF PERIODIC VIRTUAL KNOTS", JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS /ISSN = 0218-2165, Vol.22, Issue.5, pp.1350016-1-1350016-20 (2013/04) (WORLD SCIENTIFIC PUBL CO PTE LTD)

[27]정예원,김지언,이상율, "IDEAL COSET INVARIANTS FOR SURFACE-LINKS IN R^4", JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS /ISSN = 0218-2165, Vol.22, Issue.9, pp.1350052-1-1350052-25 (2013/08) (WORLD SCIENTIFIC PUBL CO PTE LTD)

[28]정예원,이상율,김지언, "On the Alexander biquandles of oriented surface-links via marked graph diagrams", JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS /ISSN = 0218-2165, Vol.23, Issue.7, pp.146007-1-146007-26 (2014/06) (WORLD SCIENTIFIC PUBL CO PTE LTD)

[29]이상율,김준오,서명수, "On the virtual Alexander polynomial of periodic virtual knots", JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS /ISSN = 0218-2165, Vol.23, Issue.7, pp.1460011-1-1460011-15 (2014/06) (WORLD SCIENTIFIC PUBL CO PTE LTD)

[30]김지언,정예원,이상율, "On generating sets of Yoshikawa moves for marked graph diagrams of surface-links", JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS /ISSN = 0218-2165, Vol.24, Issue.4, pp.1-21 (2015/04) (WORLD SCIENTIFIC PUBL CO PTE LTD)

[31]김준오,이상율, "Polynomial invariants of flat virtual links using invariants of virtual links", JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS /ISSN = 0218-2165, Vol.24, Issue.6, pp.1-23 (2015/05) (WORLD SCIENTIFIC PUBL CO PTE LTD)

[32]이상율,S. Kamada,정예원, "Applying Lipson's state models to marked graph diagrams of surface-links", JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS /ISSN = 0218-2165, Vol.24, Issue.10, pp.1-18 (2015/09) (WORLD SCIENTIFIC PUBL CO PTE LTD)

[33]이상율,김지언,S. Kamada, "Computations of quandle cocycle invariants of surface-links using marked graph diagrams", JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS /ISSN = 0218-2165, Vol.24, Issue.10, pp.1-35 (2015/09) (WORLD SCIENTIFIC PUBL CO PTE LTD)

[34]이상율, "Polynomial invariants for virtual marked graphs and virtual surface-link theory I", JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS /ISSN = 0218-2165, Vol.26, Issue.12, pp.1-35 (2017/10) (WORLD SCIENTIFIC PUBL CO PTE LTD)

[35]정예원,이상율,A. Kawauchi,S. Kamada, "Polynomial of an oriented surface-link diagram via quantum A2invariant", TOPOLOGY AND ITS APPLICATIONS /ISSN = 0166-8641, Vol.231, pp.159-185 (2017/12) (ELSEVIER SCIENCE BV)

[36]김지언,이상율,S. Kamada,A. Kawauchi, "Presentation of immersed surface-links by marked graph diagrams", JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS /ISSN = 0218-2165, Vol.27, Issue.10, pp.1-10 (2018/08) (WORLD SCIENTIFIC PUBL CO PTE LTD)

[37]S. Kamada,A. Kawauchi,김지언,이상율, "Biquandle cohomology and state-sum invariants of links and surface-links", JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS /ISSN = 0218-2165, Vol.27, Issue.11, pp.1-37 (2018/08) (WORLD SCIENTIFIC PUBL CO PTE LTD)

[38]이상율,조혜란,송현종, "Derivation of Schubert normal forms of 2-bridge knots from (1,1)-diagrams", JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS /ISSN = 0218-2165, Vol.28, Issue.8, pp.1-30 (2019/07) (WORLD SCIENTIFIC PUBL CO PTE LTD)

[39]셰이크 모드 이브라힘,이상율, "Diquandles and invariants for oriented dichromatic links", JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS /ISSN = 0218-2165, Vol.30 Issue.7 pp.1 - 25 (2021/06) (WORLD SCIENTIFIC PUBL CO PTE LTD) 

[40] 장희정,이상율, "Crossing number of an alternating knot and canonical genus of its whitehead double", TOPOLOGY AND ITS APPLICATIONS /ISSN = 0166-8641, Vol.301 pp.1 - 30, (2021/09)(ELSEVIER SCIENCE BV)

[41] 이상율,Cao, J,Garcia-Ferreira, S,Hattori, Y,Kou, H,"Special issue for the proceedings of the Third Pan-Pacific International Conference on Topology and Applications (PPICTA)", TOPOLOGY AND ITS APPLICATIONS /ISSN = 0166-8641, Vol.301,(2021/09) (ELSEVIER SCIENCE BV)

[42] 정수현, 김지언, 이상율,"Polynomial and signature invariants for pseudo-links via Goeritz matrices", JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS /ISSN = 0218-2165, Vol.31 Issue.10

pp.1 - 33, (2022/09) (WORLD SCIENTIFIC PUBL CO PTE LTD)

[43] 김지언,이상율,Mohd Ibrahim Sheikh, "Presentations of diquandles and diquandle coloring invariants for solid torus knots and links", JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS /ISSN = 0218-2165, Vol.33 Issue.02 pp.1 - 43, (2024/02) (WORLD SCIENTIFIC PUBL CO PTE LTD)

○국내학술지 논문

SCOPUS

[1]이상율, "On the Minkowski units of 2-periodic knots", Bulletin of the Korean Mathematical Society /ISSN = 1015-8634, Vol.38, Issue.3, pp.475-486 (2001/08) (대한수학회)

[2]이상율, "On the Alexander polynomials of periodic links and related topics", Trends in Mathematics /ISSN = 1229-1404, Vol.7, Issue.1, pp.75-86 (2004/06) (Information Center for Mathematical Science) (한국과학재단)

학진등재

[1]이상율, "SL(2,C)-representation varieties of periodic links", East Asian Mathematical Journal /ISSN = 1226-6973, Vol.19, Issue.2, pp.317-335 (2003/06) (대한수학회)

[2]이상율, "Symmetry of graphs associated with permutations on Z_n", East Asian Mathematical Journal /ISSN = 1226-6973, Vol.20, Issue.1, pp.109-117 (2004/06) (대한수학회)

[3]이상율, "Homology 3-spheres obtained by surgery on even net diagrams", Communications of the Korean Mathematical Society /ISSN = 1225-1763, Vol.27, Issue.4, pp.815-834 (2012/10) (대한수학회)

[4]이상율,김근영, "Representations of n-fold Cyclic Branched Coverings of (1,1)-knots up to 10 Crossings as Dunwoody Manifolds", East Asian mathematical journal(구. Pusan Kyongnam Mathematical Journal) /ISSN = 1226-6973, Vol.38 Issue.1 pp.107 - 127 (2022/02) (영남수학회)

그 외

[1]이상율,박찬녕, "The paralell version of criteria for periodic links", The Youngnam Mathematical Journal /ISSN = - , Vol.2, pp.81-91 (1995/12) (영남수학회)

[2]이상율,임용도, "On the intersection of two torus knots", East Asian Mathematical Jornal /ISSN = 1226-6973, Vol.16, Issue.1, pp.61-69 (2000/06) (대한수학회 부산경남지부)

● 대학원생(Graduate student)