SANDRA  SPIROFF

 

University of Mississippi
Department of Mathematics
305 Hume Hall
P.O. Box 1848
University, MS 38677-1848
 

Contact Information

Graduate School

Office: Graduate House, #207
Telephone: (662) 915-7474
FAX: (662) 915-6557
e-mail:  spiroff@olemiss.edu
 

General Information

Assistant Dean of Professional Development & Communication in the Graduate School, and Professor of Mathematics, working in the area of Commutative Algebra. Ph.D earned at the University of Illinois at Urbana-Champaign in 2003, advised by Phillip Griffith. Post-doctoral position at the University of Utah from 2003-2006, mentored by Paul Roberts. Served as a program director at the National Science Foundation from 2020 to 2022. Curriculum vita

Research Software

Automation of the Hilbert-Kunz multiplicity and F-signature calculation for intersection algebras, with G. Johnson*. Software files: hilbert-kunz-and-f-sig.zip Software Instructions: directions for use

Research Publications

  • The Scarf complex and betti numbers of powers of extremal ideals, with S. El Khoury, S. Faridi, and L. Sega, J. Pure & Appl. Alg., to appear.
  • Simplicial resolutions of powers of square-free monomial ideals, with S. Cooper, S. El Khoury, S. Faridi, S. Mayes-Tang, S. Morey, and L. Sega, J. Algebraic Combinatorics, to appear.
  • Powers of graphs and applications to resolutions of powers of monomial ideals, with S. Cooper, S. El Khoury, S. Faridi, S. Mayes-Tang, S. Morey, and L. Sega, Res. Math. Sciences, 9 (2022), no. 2, Paper No. 31, 25pp. ArXiv
  • Morse resolutions of powers of square-free monomial ideals of projective dimension one, with S. Cooper, S. El Khoury, S. Faridi, S. Mayes-Tang, S. Morey, and L. Sega, J. Algebraic Combinatorics, 55 (2022), no. 4, 105--1122. ArXiv
  • Simplicial resolutions for the second power of square-free monomial ideals, with S. Cooper, S. El Khoury, S. Faridi, S. Mayes-Tang, S. Morey, and L. Sega, Women in Commutative Algebra-Proceedings of the 2019 WICA Workshop, Springer and Association for Women in Mathematics, 29, 193-205 ArXiv
  • Ladder determinantal rings over normal domains, with S. Sather-Wagstaff and T. Se, Communications in Algebra, 49 (2021), no. 7, 2804-2828.
  • Generic constructions and semidualizing modules, with S. Sather-Wagstaff and T. Se, Algebras and Representation Theory, 24 (2020), no. 4, 1071-1081.
  • On conditionally defined Fibonacci and Lucas sequences and periodicity, with S. Irby*, Bull. Korean Math. Soc., 57 (2020), no. 4, 1033-1048.
  • Semidualizing modules of 2x2 ladder determinantal rings, with S. Sather-Wagstaff and T. Se, J. Algebra, 538 (2019) 232-252. ArXiv
  • Connectedness and Lyubeznik numbers, with L. Nunez-Betancourt and E. Witt, International Math Research Notices, 2019 (2019), no. 13, 4233-4259. ArXiv
  • On semidualizing modules of ladder determinantal rings, with S. Sather-Wagstaff and T. Se, Illinois J. Math, 63 (2019), no. 1, 165-191. ArXiv
  • Automating the calculation of the Hilbert-Kunz multiplicity and F-signature, with G. Johnson*, Software X, 9 (2019) 35-38. .pdf
  • Computing the invariants of intersection algebras of principal monomial ideals, with F. Enescu, Int. J. Alg. and Comp., 29 (2019), no. 2, 309-332. ArXiv
  • On the structure of S_2-ifications of complete local rings, with S. Sather-Wagstaff, Rocky Mountain Math J., 48 (2018), no. 3, 947-965. ArXiv
  • The tropical semi-ring in higher dimensions, with J. Norton*, Involve Math J., 11 (2018), no. 3, 477-488.
  • Torsion in kernels of induced maps on divisor class groups, with S. Sather-Wagstaff, J. Alg Appl., 14 (2015) 23 pages. ArXiv
  • On invariants of complete intersections, Michigan Math. J., 62 (2013) 209-223.
  • The vanishing of a higher codimension analogue of Hochster's theta invariant, with W.F. Moore, G. Piepmeyer, M.E. Walker, Math. Z., 273 (2013), no. 3, 907-920. ArXiv
  • On zero divisor graphs, with J. Coykendall, S. Sather-Wagstaff, and L. Sheppardson, Progress in Comm. Alg., Vol. 2, de Gruyter, April 2012, 241-299.
  • Five point zero divisor graphs determined by equivalence classes of zero divisors, with F. Levidiotis*, Involve, 4 (2011), no. 1, 53-64.
  • A zero divisor graph determined by equivalence classes of zero divisors, with C. Wickham, Communications in Alg., 39 (2011) 2338-2348; .pdf
  • Hochster's theta invariant and the Hodge Index Theorem, with W. F. Moore, G. Piepmeyer, and M. Walker, Advances in Math, 226 (2010), no. 2, 1692-1714; .pdf
  • Maps on divisor class groups induced by ring homomorphisms of finite flat dimension, with S. Sather-Wagstaff, J. Commutative Algebra, 1 (2009), no. 3, 567-590. ArXiv
  • An algebraic proof of the commutativity of intersection with divisors, with P. Roberts, J. Algebra, 320 (2008) 2165-2180; .pdf
  • Divisor class groups of graded hypersurfaces, with A. Singh, Contemp. Math, 448 (2007) 237-243; .pdf
  • Asymptotic growth of powers of ideals, with C. Ciuperca and F. Enescu, Illinois J. Math, 51 (2007), no. 1, 29-39; .pdf
  • Restriction of divisor classes to hypersurfaces in characteristic p, with Phillip Griffith, J. Algebra, 275 (2004) 801-814; .pdf
  • The limiting behavior on the restriction of divisor classes to hypersurfaces, J. Pure & Appl. Alg, 186 (2004) 77-89; .pdf
     

    * Indicates University of Mississippi student.

    Inclusion and Equality Initiatives

    • National and Gulf States Math Alliance
    • Elsevier Mathematical Sciences Sponsorship 2019: Promoting Diversity in Mathematics in Mississippi
    • Women in Commutative Algebra: Research Network
      • Banff Workshop 2019 Co-organized with Karen Smith (Michigan); Irena Swanson (Reed); Emily Witt (Kansas). Travel to BIRS is supported by NSF grant NSF-DMS 1934391 and AWM ADVANCE grant NSF-HRD 1500481.
    • AWM Research Symposium 2019 at Rice University in Houston, TX: Special Session in Commutative Algebra co-organized with Adela Vraciu, University of South Carolina.
      • Confirmed speakers include Susan Cooper (Manitoba); Haydee Lindo (Williams); Rebecca R.G. (George Mason); Alexandra Seceleanu (Nebraska-Lincoln); Liana Sega (Missouri-K.C.); Hema Srinivasan (Missouri); Janet Vassilev (New Mexico); Oana Veliche (Northeastern)

    Grants (external)

    Teaching

    I have long been interested in the teaching of mathematics.  As a former high school teacher and teaching assistant, I have taught a variety of courses, using several different instructional methods.  As a Visiting Assistant Professor at the University of Nebraska-Lincoln during the summer of 2007, I team taught an Algebra course for incoming graduate students based on a publication in Communications in Algebra. At Seattle University, I implemented the WeBWorK homework system, a precursor to the now ubiquitous online homework systems. As a graduate student at the University of Illinois, I worked as a Research Assistant, in the area of secondary mathematics teacher education, with Professors Susan Tolman and John Sullivan. Their project, a cooperation between the Mathematics and Education departments at the University and Danville High School, sought to improve teacher preparation.  At the University of Utah, I was an active participant in the Math Circle program for high school students, directed by Peter Trapa. Moreover, I have worked with REU students through the VIGRE grant.  Some of my old course experience is listed in the table below.  An brief summary of my educational experience, is available in this teaching vita.

     

    COURSE(S)

    LEVELS TAUGHT

    INSTRUCTIONAL METHOD

    Calculus I, II, Bus. Calc.

    College & High School

    Calculus and Mathematica, Merit Workshop, Active Learning, Lecture

    College & Intermediate Algebra

    College

    Active Learning/Lecture/Discussion

    Geometry, Algebra, Basic Math

    High School

    Lecture/Active Learning


    Professional Activities (select)