Takis Sakkalis Professor Mathematics Laboratory Agricultural Univ. of Athens Athens, 118 55 GREECE

Tel: 30-210-529-4117

Fax: 30-210-529-4141

Antispam E-mail: psakkalis AT aua DOT gr

EDUCATION

Ph.D. in Mathematics, University of Rochester, Rochester, NY, July 1986
M.A. in Mathematics, University of Rochester, Rochester, NY, May 1981
B.Sc. in Mathematics, University of Athens, Athens, Greece, June 1979

RESEARCH INTERESTS

Real Algorithmic Algebraic Geometry
Computer Algebra
Computer Aided Geometric Design
Geometric Modeling

ACADEMIC POSITIONS

Professor, Agricultural University of Athens, 24/6/2005 --

Director, Mathematics Laboratory, 8/10/2002 --

Research Affiliate, Massachusetts Institute of Technology, 15/1/2000--

Visiting Associate Professor, Oakland University, Rochester, MI, 5/1/2000--15/8/2000

Associate Professor, Agricultural University of Athens, 22/7/1999 -- 23/6/2005

Visiting Assistant Professor, Dept. of Ocean Engineering , MIT 1996, 1997

Assistant Professor, Agricultural University of Athens 4/5/1994 -- 21/7/1999

Assistant Professor, Oakland University, Rochester, MI 1990 - 1994

Assistant Professor, New Mexico State University, Las Cruces, NM 1988 - 1990

Visiting Scientist, IBM T.J. Watson Research Center, NY 1987 - 1988

Assistant Professor, New Mexico State University, Las Cruces, NM 1986 - 1987

Part-time Instructor, University of Rochester, Rochester, NY 1983 - 1986.

PUBLICATIONS

In Journals and Books

T. Sakkalis, The computation of the index of a Morse function at a critical point, Intern. J. Math. & Math. Sci. Vol. II, No. 4 (1988), 721-726. MR 90a:58026.

T. Sakkalis, Signs of algebraic numbers, Computers and Mathematics, Springer Verlag, (1989), 131-134. MR 90m:12004.

T. Sakkalis and R.T. Farouki, Singular points of algebraic curves, J. Symbolic Computation, 9 (1990), 405-421. MR 91f:14056.

T. Sakkalis, The Euclidean algorithm and the degree of the Gauss map, SIAM J. of Computing, Vol. 19, No. 3 (1990), 538-543. MR 91m:68092.

R.T. Farouki and T. Sakkalis, Pythagorean Hodographs, IBM J. of Research and Development, Vol. 34. No. 5 (1990), 736-752. MR 92a:65063.

T. Sakkalis, On a theorem of H. Hopf, Intern. J. Math. & Math. Sci., Vol. 13, No. 4 (1990), 813-816. MR 91k:57038.

T. Sakkalis, The topological configuration of a real algebraic curve, Bulletin Austr. Math. Soc., Vol. 43, No. 1 (1991), 37-50. MR 92e:14056.

R.T. Farouki and T. Sakkalis, Real rational curves are not "unit speed" , Computer Aided Geometric Design, 8 (1991) 151-157. MR 92d:65034.

T. Sakkalis, On relations between Jacobians and resultants of polynomials in two variables, Bulletin Austr. Math. Soc., 47 (1993), 473-481. MR 94e:12001.

T. Sakkalis and R.T. Farouki, Algebraically rectifiable parametric curves, Computer Aided Geometric Design, 10 (1993) 551-569. MR 95c:65028.

C. Cheng, T. Sakkalis and S. Wang, A case of the Jacobian conjectrure, Journal of Pure and Applied Algebra, Vol. 96 (1994), 15-18. MR 95i:14018a.

D. Polemi and T. Sakkalis, Singular algebraic curves over finite fields, Lecture Notes of Computer Science, Springer Verlag Vol. 793 (1993), 24-37. MR 95i:14053.

R.T. Farouki and T. Sakkalis, Pythagorean-hodograph space curves, Advances in Computational Mathematics 2 (1994), 41-66. MR 95b:50003.

T. Sakkalis and Z. Ligatsikas, Computing the topological degree of polynomial maps, Bulletin Austr. Math. Soc., 56 (1997), 87-94. MR 98g:55002.

T. Maekawa, N.M. Patrikalakis, T. Sakkalis and G. Yu, Analysis and applications of pipe surfaces, Computer Aided Geometric Design, 15 5 (1998), 437-458. MR 99c:68254.

T. Sakkalis, Some applications of the resultant, Bulletin of the Greek Mathematical Society, Vol. 42, (1999), 89-95. MR 2002d:14097.

T. Sakkalis and Ch. Charitos, Approximating curves via alpha shapes, Graphical Models and Image Processing, Vol. 61, No. 3 (1999), 165-176.

T. Sakkalis, G. Shen and N.M. Patrikalakis, Representational validity of boundary representation models, Computer Aided Design, 32 (2000) 719-726.

T. Sakkalis, G. Shen and N.M. Patrikalakis, Topological and geometric properties of interval solid models, Graphical Models, 63, 163-175 (2001).

G. Shen, T. Sakkalis and N.M. Patrikalakis, Boundary representation model rectification, Graphical Models, 63, 177-195 (2001).

J. Wallner, T. Sakkalis, T. Maekawa, H. Pottmann and G. Yu, Self-intesection of offset curves and surfaces, International Journal of Shape Modeling, Vol. 7, No. 1, 1-21 (2001).

G. Shen, T. Sakkalis and N.M. Patrikalakis, A Rectification algorithm for manifold boundary representation models. Idmme'2002-Selected papers book. P. Chedmail, G. Cognet, C. Fortin, C. Mascle and J. Pegna, Editors. Kluwer Publishing Company, (129-138) 2002.

R.T. Farouki, M. al-Kandari and T. Sakkalis, Hermite interpolation by rotation-invariant spatial Pythagorean-hodograph curves, Advances in Computational Mathematics, 17: 369-383 (2002). MR 2003e:65011.

R.T. Farouki, M. al-Kandari and T. Sakkalis, Structural invariance of spatial Pythagorean hodographs, Computer Aided Geometric Design, 19 (2002) 395-407. MR 2003g:65019.

T. Sakkalis, Polynomial remainders and plane automorphisms, Bulletin Austr. Math. Soc, 68 (2003), No. 1, 73-79. MR 2005a:14085.

C. Cheng and T. Sakkalis, Power linear maps of nilpotency index two, Communications in Algebra, Vol. 32, No. 7 (2004), 2635-2637. MR 2005f:14116.

T. Sakkalis, T. J. Peters and J. Bisceglio Isotopic Approximations and Interval Solids, Computer Aided Design, 36 (11), (2004), 1089-1100.

T. Sakkalis, A note on proper polynomial maps, Communications in Algebra, Vol. 33, No. 9 (2005), 3359-3365. MR 2006g:14096.

T. J. Peters, J. Bisceglio, D.R. Ferguson, C.M. Hoffmann, T. Maekawa, N.M. Patrikalakis, T. Sakkalis and N.F. Stewart Computational Topology for Regular Closed Sets (within the I-TANGO project), On-line Journal Topology Atlas Invited Contributions, Vol. 9, No. 1, pp. 12 (2004).

K.H. Ko, T. Sakkalis and N.M. Patrikalakis, Resolution of multiple roots of nonlinear polynomial systems, International J. of Shape Modeling, Vol 11, No. 1 (2005) 121-147.

K. Abe, J. Bisceglio, D.R. Ferguson, T. J. Peters, A.C. Russell and T. Sakkalis, Computational topology for isotopic surface reconstruction, Theoretical Computer Science., 365 (2006) 184-198.

R.T. Farouki and T. Sakkalis, Rational space curves are not "unit speed", Computer Aided Geometric Design, 24 (2007) 238-240.

T. Sakkalis, The fundamental theorem of algebra: An elementary proof, Bulletin of the Greek Mathematical Society , Vol. 53, (2007), 131-134.

K.H. Ko, T. Sakkalis and N.M. Patrikalakis, A reliable algorithm for computing the topological degree of a mapping in R^2, Applied Mathematics and Computation, 196 (2008) 666-678.

T. Sakkalis, R.T. Farouki and L. Vaserstein, Non-existence of rational arc length parameterizations for curves in R^n, J. Computational and Applied Mathematics, 228(2009) 494-497.

L. Vaserstein, T. Sakkalis and S. Frisch, Polynomial parametrization of Pythagorean tuples , Int. J. Number Theory, Vol. 6 (6) (2010), 1261-1272.

R.T. Farouki and T. Sakkalis, Rational rotation-minimizing frames on polynomial space curves of arbitrary degree , J. Symbolic Computation, Vol. 45 (8) (2010), 844-856.

R.T. Farouki and T. Sakkalis, Equivalence of distinct characterizations for rational rotation-minimizing frames on quintic space curves, Computer Aided Geometric Design, 28 (2011) 436-445.

R.T. Farouki and T. Sakkalis, A complete classification of quintic space curves with rational rotation--minimizing frames, J. Symbolic Computation, Vol. 47 (2) (2012), 214-226.

T. Sakkalis and R.T. Farouki, Pythagorean-hodograph curves in Euclidean spaces of dimension greater than 3, J. Computational and Applied Mathematics, 236 (2012) 4375-4382.

R.T. Farouki, C.Y. Han, P. Dospra and T. Sakkalis, Rotation-minimizing Euler-Rodrigues rigid-body motion interpolants, Computer Aided Geometric Design, 30 (2013) 653-671.

R.T. Farouki, P. Dospra and T. Sakkalis, Scalar-vector algorithm for the roots of quadratic quaternion polynomials, and the characterization of quintic rational rotation-minimizing frame curves, J. Symbolic Computation, Vol. 58 (2013), 1-17.

R.T. Farouki and T. Sakkalis, Corrigendum to "Rational rotation-minimizing frames on polynomial space curves of arbitrary degree'' [J. Symbolic Comput. 45 (2010) 844-856], J. Symbolic Computation, Vol. 58 (2013), 99-102.

Kwanghee Ko and T. Sakkalis, Orthogonal projection of points in CAD/CAM applications: an overview, J. of Computational Design and Engineering, Vol. 1, No. 2 (2014), 116-127.

C. Cheng and T. Sakkalis, On new types of rational rotation-minimizing frame space curves, J. Symbolic Computation, Vol. 74 (2016), 400-407.

T. Sakkalis, Jacobians of quaternion polynomials, Bulletin of the Greek Mathematical Society , Vol. 61 (2017), 31-40.

T. Sakkalis, Kwanghee Ko and Galam Song, Roots of quaternion polynomials; theory and computation. Theoretical Computer Science,, Vol. 800 (2019), 173-178.

R. T. Farouki and T. Sakkalis, Construction of rational curves with rational arc lenghts by direct integration. Computer Aided Geometric Design 74, article 101773 (2019).

T. Sakkalis, Polynomials and degrees of maps in real normed algebras, Communications in Mathematics, 28 (2020), 43-54.

In Proceedings of Conferences

T. Sakkalis and R.T. Farouki, Rectification of parametric curves, Computer Aided Geometric Design: From Theory to Practice, NTUA, Athens, Greece, (1995), 97-102.

G. Shen, T. Sakkalis and N.M. Patrikalakis, Manifold boundary representation model rectification, Proceedings of the 3rd International Conference on Integrated Design and Manufacturing in Mechanical Engineering, C. Mascle, C. Fortin, J. Pegna, editors. Page 199 and CDROM. Montreal, QC, Canada. May 2000. Presse internationale Polytechnique, Montreal, Canada, May 2000. http://www.congresbcu.com/idmme-csme2000.htm

N.M. Patrikalakis, T. Sakkalis and G. Shen, Boundary representation models: validity and rectification, invited paper in Proceedings of The 9th IMA Conference on the Mathematics of Surfaces, University of Cambridge, September 2000. R. Cipolla and R. Martin, editors. pp. 389-409. London, UK, Springer Verlag, 2000.
G. Shen, T. Sakkalis and N.M. Partikalakis, Interval methods for B-rep model verification and rectification, Proceedings of the ASME 26th Design Automation Conference, Baltimore, MD, September 2000. P. 140 and CDROM. NY, ASME 2000.

G. Shen, T. Sakkalis and N.M. Partikalakis, Analysis of boundary representation model rectification, Proceedings of the Sixth ACM Solid Modeling Symposium, D.C. Anderson and K. Lee, editors. Ann Arbor, Michigan, June 2001. pp. 149-158. NY: ACM, 2001.

T. Sakkalis and T.J. Peters, Ambient isotopic approximations for surface reconstruction and interval solids, 8th ACM Symposium on Solid Modeling and Applications. G. Elber and V. Shapiro, Editors. Seattle Washington, June 16-20, (2003) 176-184.

D. Ferguson, C. Hoffmann, T. Maekawa, N. Patrikalakis, T. Peters, T. Sakkalis and N. F. Stewart, Accurate Numerical Intersection of Geometric Objects, 5th International Congress on Industrial and Applied Mathematics (ICIAM 2003). Sydney, Australia, July 2003.

K.H. Ko,T. Sakkalis and N.M. Patrikalakis, Nonlinear Polynomial Systems: Multiple Roots and their Multiplicities, Shape Modeling International Conference, SMI 2004. F. Giannini and A. Pasko, Editors. Genoa, Italy, June 2004. Los Alamitos, CA: IEEE Computer Society Press, (2004), 87-98.

H. Mukundan, K.H. Ko, T. Maekawa, T. Sakkalis and N.M. Patrikalakis, Tracing Surface Intersections with a Validated ODE System Solver, Proceedings of the Ninth EG/ACM Symposium on Solid Modeling and Applications. G. Elber, N.M. Patrikalakis and P. Brunnet, Editors. Genoa, Italy, June 2004. Eurographics Press (2004), 249-254.

K. Abe, J. Bisceglio, T.J. Peters, A.C. Russell, D.R. Ferguson and T. Sakkalis, Computational Topology for Reconstruction of Surfaces with Boundary: Integrating Experiments and Theory, International Conference on Shape Modeling and Applications (SMI'05) . MIT, June 15-17, 2005. IEEE Computer Society Press, (2005) 288-297.

Technical Reports

T. Sakkalis, On the zeros of a polynomial vector field, IBM RC-13303, (1987).