Curriculum Vitae Robert H. Lewis Department Of

Curriculum Vitae

Robert H. Lewis Department of Mathematics Fordham University Bronx, NY 10458 [email protected] http://fordham.academia.edu/RobertLewis; http://home.bway.net/lewis/

Education Cornell University, Ithaca NY PhD (mathematics); MA, BA University of North Carolina, Chapel Hill M.S. (computer science)

PhD Thesis Homology Decompositions and Coﬁbrations of Nonsimply Connected Spaces, directed by Peter Kahn (algebraic topology).

Professional - Professor, Fordham University, since 2009. Experience - Associate Professor, Fordham University - Visiting Professor, Department of Mathematics and Statistics, University of New Mexico, spring 2011. - Visiting Professor, Department of Mathematics and Statistics, University of New Mexico, fall 2005. - Consultant in Computer Algebra, Institute for Defense Analysis (Center for Computing Scienes), Bowie MD; spring semester 2005. - Consultant in Computer Algebra, Institute for Defense Analysis (Center for Computing Scienes), Bowie MD; summer 2004. - Consultant in Computer Algebra, Institute for Defense Analysis (Center for Computing Scienes), Bowie MD; summer 2003. - Consultant in Computer Algebra, Institute for Defense Analysis (Center for Computing Scienes), Bowie MD; summer 2002. - Consultant in Computer Algebra, Aerospace Mass Properties Analysis, Inc. (“AMPAC”); 1997-1998. - Consultant in Computer Algebra, Naval Air Warfare Center, Aircraft Division (“NAWCAD”), Warminster PA; 1996. - Assistant professor, Fordham - Assistant professor, Lander College (SC)

Refereed Algebraic Detection of Flexibility of Polyhedral Structures with Applications Publications to Robotics and Chemistry, with Stephen Fox. Fordham Undergraduate Research Journal, April 2012. Computational Study of the 3D Aﬃne Transformation, with B. Palancz, J. Awange, P. Zaletnyik; in: Computational Mathematics: Theory, Methods and Applications. Peter G. Chareton, ed. Nova Science Publishers, New York. January 2010. Linear Homotopy Solution of Nonlinear Systems of Equations in Geodesy, with B. Palancz, J. Awange, P. Zaletnyik. Journal of Geodesy. Springer. Volume 84, Number 1, 79-95. January 2010.

1 Comparing Acceleration Techniques for the Dixon and Macaulay Resultants, Proceedings of the ACA 2007 Conference, Mathematics and Computers in Simulation. Volume 80 Issue 6, February, 2010 Partitioning Multivariate Polynomial Equations via Vertex Separators for Algebraic Cryptanalysis and Mathematical Applications, with Kenneth Koon-Ho Wong, and Gregory V. Bard. IACR (2009). http://magma.maths.usyd.edu.au/magma/citations/topic/CmpCpt/ Heuristics to Accelerate the Dixon Resultant, Mathematics and Computers in Simulation 77, Issue 4, p. 400 – 407, April 2008. Algorithmic Search for Flexibility Using Resultants of Polynomial Systems (with E. Coutsias), in Automated Deduction in Geometry. Lecture Notes in Computer Science, Vol. 4869, p. 68 – 79. Botana, F., Recio, T. (Eds.) Springer, Berlin, 2007. Fermat, Computer Algebra System, in Abstracts (Posters, Short Commun- ications, Mathematical Software) of The International Congress of Mathematicians, Madrid, p. 612. European Mathematical Society, 2006. Solving the Least Squares Method Problem in the AHP for 3 × 3 and 4 × 4 Matrices (with Sandor Bozoki), Central European Journal for Operations Research 13 p. 255 – 270, September 2005. Top Secret Mathematical Topic, Internal publication, Institute for Defense Analysis, 18 pages, April 2005. Note: as of April 2008, this work remains officially “too important to declassify.” Conic Tangency Equations and Apollonius Problems in Biochemistry and Pharmacology (with Stephen Bridgett), Mathematics and Computers in Simulation 61(2) p. 101 – 114, January 2003. Computer Algebra System Fermat, software and documentation, in: Computer Algebra Handbook, J. Grabmeier, E. Kaltofen, V. Weispfenning (editors), Springer- Verlag, 2002. Comparison of Polynomial-Oriented Computer Algebra Systems (with Michael Wester), SIGSAM Bulletin 33(4), p. 5 – 13, Dec. 1999. Solving the Recognition Problem for Six Lines Using the Dixon Resultant (with Peter Stiller), Mathematics and Computers in Simulation 49 (1999) p. 203 – 219. Computer Search for Nilpotent Complexes (with Guy Moore), Experimental Mathematics 6 (1997) p. 239 – 246. Isomorphism Classes and Derived Series of Almost-Free Groups (with Sal Liriano), Experimental Mathematics 3 (1994) p. 255 – 258. Homology and Cell Structure of Nilpotent Spaces, Trans. Am. Math. Soc. 290 (1985) p. 747 – 760. Equivariant Cofibrations and Nilpotency, Trans. Am. Math. Soc. 267 (1981) p. 139 – 155. Two Results Relating Nilpotency and Cofibrations, Proceedings Am. Math. Soc. 72 (1978) p. 403 – 408.

Publications Flexibility of Bricard’s Linkages and Other Structures via Resultants and In Print Computer Algebra, with E. Coutsias; accepted by Mathematics and Computers in Simulation. November 2014.

2 Paper Submitted Algebraic Isolation of Outliers in Point Clouds via Expectation Maximization Combined with Likelihood Function of Gaussian Mixture; with J. Awange, B. Palancz, T. Lovas. submitted to IEEE Transactions of Geoscience.

Publications Application of Dixon resultant to maximization of the likelihood function In Preparation of Gaussian mixture distribution, with J. Awange and B. Palancz. Determining Flexibility of Molecules Using Polynomial Systems: Cyclo-Hexane and Cyclo-Octane, with E. Coutsias. International Journal of Quantum Chemistry. Polynomial Systems Arising from Autocatalytic Reactions in Chemistry.

Software Author of computer algebra system Fermat for infinite precision rational arithmetic; modular and finite field arithmetic; polynomial, rational function, and matrix manipulations; and mathematical computer graphics. http://home.bway.net/lewis/

Formal Refereed Computer Algebra System Fermat, software and documentation; Software Published in the CD accompanying Computer Algebra Handbook, J. Grabmeier, E. Kaltofen, V. Weispfenning (editors), Springer- Verlag, 2002. Computer Algebra System Fermat, software and documentation; in CD accompanying “Computer Programming”, July 2002, published by Gruppo Editoriale Infomedia (Italy), R. Boni, editor; Computer Algebra System Fermat, software and documentation; for “Math CD,” Laurent Siebenmann (editor); see http://www.math.washington.edu/˜burdzy/MathCD.html

Web “Mathematics, the Most Misunderstood Subject” Publication (found on the Mathematics Department web site.) There have been more hits on this essay than to the Mathematics Department website, even though it is a subpage to that web site and has existed for less time. For years, it averaged 50 hits per day. In late December 2010, it suddenly attracted 74,000 readers in only two weeks.

Book Abstracts from the 20th Conference on Applications of Computer Algebra, ACA 2014, July 9 - 12, 2014, Fordham University New York, New York. (editor) 67 pages. ISBN: 978-0-692-24793-8

Other Polynomials Everywhere, Sapientia et Doctrina, Inside Fordham. Publications www.fordham.edu/campus resources/public aﬀairs/inside fordham/ march 2 2007/in focus faculty and/sapientia et doctrin 25318.asp Silhouette-based 2D-3D Pose Estimation Using Algebraic Surfaces (with Nazar Khan), submitted to the ICCV 2007 Conference. See also http://www.cs.ucf.edu/ nazar/work/pose estimation/Silhouette-based 2D-3D Pose Estimation using Algebraic Surfaces.pdf

3 Fast Detection of the Nilpotent Part of a Matrix, technical report, NAWCAD. 1996. A Primer on p-adic Rings and Computations, technical report, NAWCAD, 1996. Computer Search for Nilpotent Complexes (with Guy Moore), Notices of the Am. Math. Soc. January 1993. Idemﬁnd, a Program to Detect Similarities in Programming Assignments, technical report, UNC Chapel Hill Computer Science Department, 1980.

Grants Grant from David Halitsky and Family, 2012, for summer research. Fordham University Faculty Fellowship, 2010. Fordham University Faculty Research Grant, 2006. Fordham University Faculty Fellowship 2005. Fordham University Faculty Fellowship 1996. National Science Foundation R.E.U. Grant, 1991. - principal investigator. National Science Foundation R.E.U. Grant, 1989. - principal investigator. National Science Foundation R.E.U. Grant, 1988. - principal investigator. Fordham University Faculty Research Grant, 1987. Fordham University Faculty Fellowship 1987. Cornell University Six-Year PhD Fellowship.

Theses Directed Stephen D. Fox, “Fast Fourier Transforms over Finite Fields”, Undergraduate Honors Thesis, May 2011. Jiazhao Xu, “On the Construction of Finite Three Dimensional Nilpotent Spaces,” Masters Thesis, May 1992. Christopher Snyder, “The Search for Three Dimensional Nilpotent Complexes: An Algorithm”. B.A. Honors Thesis, December 1988.

Undergraduate “Investigation of Protein Structure with Hyperboloids”, Jacob Edison, Research Directed Thomas Klotz. Summer 2012. “Using Diﬀerential Algebra to Solve Diﬀerential Equations”, Daniel White. Summer 2012. “Fast Fourier Transforms over Finite Fields”, Stephen D. Fox. September 2010 - May 2011. “Algorithmic Determination of Molecular Flexibility via Resultants,” Stephen D. Fox. Fordham University Summer Research Fellowship, 2010. Three teams of undergraduates during three summers, 1988, 1989, and 1991, sponsored by the National Science Foundation R.E.U. Program (Research Experiences for Undergraduates). A total of sixteen students. All pursued the topic “Search for Three Dimensional Nilpotent Complexes.” The paper listed above with coauthor Guy Moore describes this project.

4 Sponsored or “Dixon-EDF: A Premier Method for Parametric Polynomial Systems.” Invited Addresses MCAG 12 Conference, Oakland University, Michigan, May 12, 2012. (31 addresses) “Resultant Techniques for Polynomial Systems and Applications to Molecular Flexibility”, Workshop on Algebraic Methods in Systems Biology and Statistics, SAMSI Institute, Research Triangle Park, North Carolina, September 14 – 17, 2008. “Determining Molecular Flexibility Using Resultants of Polynomial Systems,” Odyssey Conference on Computational Chemistry, Edmonton, Alberta. June 2, 2008. “CAS and the Instruction of Mathematics: Where Are We Today?” Invited member of panel, ACA Conference, Oakland University, Michigan, July 21, 2007. “Algorithmic Search for Flexibility Using Resultants,” Department of Mathematics and Computer Science, Seton Hall University, April 10, 2006. “Algorithmic Search for Flexibility Using the Dixon Resultant,” Department of Computer Science, University of New Mexico, December 1, 2005. Top Secret Mathematical Topic, Internal conference, Institute for Defense Analysis, April 2005. “Exploiting Symmetry with the Dixon Resultant”, Applications of Computer Algebra, Lamar University, July 21 – 23, 2004. “Using the Dixon Resultant on Big Problems”, International Symposium on Symbolic and Algebra Computation, Drexel University, August 4 – 6, 2003. Lecture-demonstration “Solving Large Polynomial Systems with the Dixon Resultant”, Applications of Computer Algebra, North Carolina State University, July 28 – 31, 2003. One hour lecture and demonstration, “Computer Algebra System Fermat,” at the conference Computer Algebra for the Working Mathematician, City College of New York, May 15 – 16, 2003. “Computational Geometry via the Dixon Resultant,” AMS Special Session on Computational Algebraic and Analytic Geometry for Low-dimensional Varieties, AMS/MAA meeting, Baltimore, January 18, 2003. “Solving Large Polynomial Systems with the Dixon Resultant,” Center for Computing Sciences, Bowie, MD, July 1, 2002. “Fermat Computer Algebra System,” (demo), Center for Computing Sciences, Bowie, MD, July 1, 2002. “Solving Large Polynomial Systems with the Dixon Resultant,” CBMS Conference, Texas A&M University, May 21, 2002. “Apollonius Meets Computer Algebra,” University of Western Ontario, October 19, 2001. “Comparison of Polynomial-Oriented Computer Algebra Systems,” Solving Equations: Symbolic Computation in Algebra & Geometry, Mt. Holyoke College, June 2000. “The Six-Line Problem and Resultants,” IMACS/ACA Conference, Prague, August 1998.

5 “Solving the Six-Line Problem with Resultants,” IMACS/ACA Conference, Maui, July 1997. IMACS/ACA Conference, Maui, July 1997, member of Computer Algebra Panel. “Fermat, Computer Algebra System,” (demo), University of Delaware, Newark, DE, March 1996. “Hensel’s Lemma, ” City College, New York, Spring 1995. “Finite Dimensional Nilpotent Complexes,” Cornell University, Fall 1987. “Wall Obstructions to Finiteness of Nilpotent Complexes,” Vassar College, Fall 1986. C.U.N.Y. Graduate Center, series of six lectures on Nilpotent Complexes, 1985. “Three Dimensional Nilpotent Complexes,” Cornell University, Spring 1983. “Sorting Algorithms,” University of North Carolina, Charlotte, Spring 1980. “Cofibrations of Nilpotent Complexes,” Davidson College, Spring 1980. “Cofibrations of Nilpotent Complexes,” George Mason University, Virginia, March 1980. “Cofibrations of Nilpotent Complexes,” Youngstown State University, Ohio, February 1980. “Cofibrations and Nilpotency,” Oakland University, Rochester, Michigan, Spring 1978.

Other Talks “Maximizing Likelihood Function for Parameter Estimation in Point Clouds,” Delivered with J. Awange and B. Palancz. ICMS 2014, Seoul, Korea, August 5, 2014. (41 addresses) “Gr¨obnerBasis Applications in Geodesy and Geoinformatics,” with J. Awange and B. Palancz. ICMS 2014, Seoul, Korea, August 5, 2014. Lecture-demonstration “Solving Large Polynomial Systems with the Dixon Resultant and Fermat,”ACA Conference, Fordham University, New York, July 11, 2014. “Computer Algebra Solution of Maximization of Likelihood for Laser Scanning.” ACA Conference, Fordham University, New York, July 9, 2014. “Dixon-EDF: A Premier Method for Parametric Polynomial Systems.” Mathe- matics Seminar, Manhattan College, Bronx, New York, February 27, 2014. “Flexibility of Structures via Computer Algebra.” ACA Conference, Malaga, Spain, July 4, 2013. “Algorithmic Search for Flexibility Using Resultants of Polynomial Systems.” ACA Conference, Houston, Texas, June 27, 2011. “Dixon-EDF: A Premier Method for Parametric Polynomial Systems.” ACA Conference, Vlore, Albania, June 26, 2010. “Resultant Techniques for Polynomial Systems and Applications to Molecular Flexibility.” ACA Conference, Vlore, Albania, June 25, 2010. “Solving Polynomial Systems of Autocatalytic Reactions in Chemistry.” ACA Conference, Montreal, Canada, June 27, 2009. “Determining Flexibility of Molecules Using Resultants of Polynomial Systems.”

6 ACA Conference, Montreal, Canada. June 27, 2009. “Application of Symbolic–Numeric Algebra in Geodesy.” ACA Conference, Montreal, Canada. June 28, 2009. “Determining Flexibility of Molecules Using Resultants of Polynomial Systems.” Algebraic Biology Conference, RISC Institute, Austria. July 31, 2008. “Polynomial Equations Arising in Global Positioning Systems and in Nash Equilibria.” ACA 2008 Conference, RISC Institute, Austria. July 29, 2008. “Comparing Acceleration Techniques for Dixon and Macaulay Resultants.” ECCAD Conference, Shepherd University, West Virginia, May 10, 2008. “Comparing Acceleration Techniques for Dixon and Macaulay Resultants.” ACA Conference, Oakland University, Michigan, July 2007. “Algorithmic Search for Flexibility with Resultants of Polynomial Systems.” AMS/MAA Meeting, New Orleans, January 2007. “Algorithmic Search for Flexibility with Resultants.” ADG 2006 Conference, Pontevedra, Spain, August 31, 2006. “Fermat, Computer Algebra System.” International Congress of Mathematicians 2006, Madrid, Spain, August 24, 2006. “Algorithmic Search for Flexibility with Resultants.” ECCAD Conference, Philadelphia, May 5, 2006. “Solving Polynomial Systems with Resultants.” Mathematics Department, University of New Mexico, September 22, 29, 2005. “Groebner Basis Theory.” Mathematics Department, University of New Mexico, December 7, 14, 2005. “Solving the LSM problem in the AHP for 3 × 3 and 4 × 4 matrices” (with S. Bozoki), ORP 3, A EURO conference for young OR researchers, September 21 - 26, 2003. Lambrecht, Germany. “Solving The Least Squares Method Problem In The AHP For 3 × 3 and 4 × 4 Matrices” (with S. Bozoki), The 7th International Symposium on the Analytic Hierarchy Process, August 7 - 9, 2003. Bali, Indonesia. “Solving Large Polynomial Systems with the Dixon Resultant,” SCA 2002 Conference, University of Western Ontario, July 15, 2002. “Solving the Polynomial Signal Processing Equations of Selesnick-Burrus and Little,” ECCAD Conference, LaGuardia Community College, New York, May 18, 2002. “Fermat Computer Algebra System,” (demo), ECCAD Conference, LaGuardia Community College, New York, May 18, 2002. “Apollonius Meets Computer Algebra,” IMACS/ACA Conference, Albuquerque NM, May 29-June 1, 2001. “Comparison of Polynomial-Oriented Computer Algebra Systems,” ISSAC Conference, Vancouver BC, July 28-31, 1999. “Image Analysis and Resultants,” M.A.A. Meeting, Hofstra University, New York, May 5, 1999. “The Six-Line Problem and Resultants,” ECCAD Conference, N. C. State University, April 24, 1999.

7 “Fermat Computer Algebra System,” (demo), ECCAD Conference, Naval Academy, Annapolis, April 1998. “Solving Polynomial Equations with Resultants,” University of Delaware, Newark, DE, October 1996. “Fermat Computer Algebra System,” (demo), ECCAD Conference, I.B.M. Watson Lab, April 1996. “Computer Search for Nilpotent Complexes,” ISSAC Conference, Montreal, July 1995. “Fermat, a Computer Algebra System,” ISSAC Conference, Montreal, July 1995. “Fermat, a Computer Algebra System,” (demo), ECCAD Conference, Newark DE, April 1995. “Isomorphism Classes and Derived Series of Almost-free Groups,” ECCAD Conference, Newark DE, April 1995. “Computer Search for Nilpotent Complexes,” M.A.A. Meeting, New York City, May 1993. “Computer Search for Nilpotent Complexes,” A.M.S. Meeting, San Antonio, January 1993. “Nilpotency and Coﬁbrations,” A.M.S. Meeting, Atlanta, January 1977.

Ongoing Research Polynomial resultants, especially the Dixon method. Projects Apollonius-type sphere, line, and ellipsoid problems in 3D. Computational chemistry, such as ﬂexibility of chemical molecules. Computational Geometry problems, such as the Fermat-Steiner point in 3D. Polynomial G.C.D. algorithms. Matrix normal form algorithms. Computational Algebraic Topology. Implementation of computer algebra systems.

Fordham Service Chair, Department of Mathematics, 1999 - 2005. Web master, Department of Mathematics, 1999 - 2014. Chair of Undergraduate Committee, Department of Mathematics, 2007 - 2013. Assistant Chair, Department of Mathematics, 1990 - 1993.

Exceptional Overall Chair of the twentieth annual ACA Conference (Applications of Services Computer Algebra), held at Fordham University, July 9 - 12, 2014. There were 140 registrants from ﬁfteen countries. Organized a conference for faculty and students about professional science masters degrees. Invited three outside speakers. The conference was attended by several deans and faculty from other departments, as well as Fordham Trustee Lilian Wu. May 6, 2010. Consultant and reviewer of the Department of Mathematics at Iona College, at the invitation of the Provost of Iona College. December 10, 2010.

Professional Overall Chair, ACA 2014 Conference, held at Fordham University, Activity July 2014. There were 140 registrants from ﬁfteen countries. Session Cochair, Computer Algebra in Chemistry and Physics, ACA

8 Conference, Vlore, Albania, June 2010. Session Cochair, Elimination Theory and Applications, ACA Conference, Montreal, June 2009. http://aca2009.etsmtl.ca/sessions/elimination.html Session Cochair, Chemistry and Computer Algebra, ACA Conference, Montreal, June 2009. http://aca2009.etsmtl.ca/sessions/chemistry.html Member, Steering Group, ACA Conferences, since 2007. Frequent referee for Applied Mathematics and Computation. Frequent referee for Computers and Mathematics with Applications. Frequent referee for Mathematics and Computers in Simulation. Frequent referee for Journal of Computational and Applied Mathematics. Frequent referee for Journal of Symbolic Computation. Frequent referee for talks at conferences (ISSAC, ACA, PASCO). Frequent reviewer for various text book publishers.

Mathematical Judge, senior high level, Tri-County Science and Technology Fair, April 24, Outreach Activity 2010, held at White Plains High School, White Plains, New York. Judge, senior high level, Tri-County Science and Technology Fair, April 12, 2008, held at Kennedy Catholic High School, Katonah, New York. One fifty minute lecture to Stuyvesant High School advanced math students (30 students) on the R.S.A. cryptosytem, February 2002. One fifty minute lecture to Regis High School advanced math students (30 students) on the R.S.A. cryptosytem, December 2001. Two fifty minute lectures to Bronx High School of Science advanced math clubs (120 students) on the R.S.A. cryptosytem, March 2001.

Courses Taught College Mathematics Applied Calculus I Applied Calculus II Linear Mathematics Finite Mathematics Computer Literacy Mathematical Methods in Business I Mathematical Methods in Business II Calculus and Analytic Geometry I Calculus and Analytic Geometry II Calculus and Analytic Geometry III Calculus and Analytic Geometry IV (recitation) Mathematical Modeling Introduction to Discrete Mathematics Algorithmic Mathematics Introduction to Computer Science (Undergraduate) Computer Programming in PL/I Applied Computer Science Data Structures Linear Algebra Ordinary Diﬀerential Equations Computer Architecture

9 Compiler and Assembler Design Theory and Design of Programming Languages Mathematical Structures Real Analysis (Undergraduate) Complex Analysis (Undergraduate) Topology (Undergraduate) Abstract Algebra (Undergraduate) Topics in Applied Mathematics (Undergraduate) Independent Study in Chaos and Fractals (Undergraduate) Introduction to Computer Science (Graduate) Analysis of Algorithms (Graduate) Abstract Algebra I (Graduate) Abstract Algebra II (Graduate) Numerical Analysis (Graduate) Topology (Graduate)

References Professor Evangelos Coutsias, Stony Brook University, NY. Professor Michael Barnett, CUNY and Princeton University (chemistry). Professor Peter Stiller, Texas A. and M. University. Professor Erich Kaltofen, North Carolina State University. Doctor Anthony Hearn, Rand Corporation. Professor John Little, College of the Holy Cross. Professor Manfred Minimair, Seton Hall University. Professor David Saunders, University of Delaware. Professor Gilbert Baumslag, City College of New York. Doctor Michael Wester, University of New Mexico. Professor William Singer, Fordham University.