Isabella Novik

Professor

Department of Mathematics
University of Washington
Box 354350, Seattle, WA 98195

Current Courses

Winter Quarter 2013:

Math 462 (Combinatorics)
Math 582C (Simplicial Complexes)

Research

Interests

Publications

  1. Upper Bound Theorems for homology manifolds, Israel Journal of Mathematics, 108 (1998), 45-82.
  2. The Lower Bound Theorem for centrally symmetric simple polytopes, Mathematika, 46 (1999), 231-240.
  3. A note on geometric embeddings of simplicial complexes in a Euclidean space, Discrete and Computational Geometry, 23 (2000), 293-302.
  4. Lower bounds for the cd-index of odd-dimensional simplicial manifolds, European Journal of Combinatorics 21 (2000), 533-541.
  5. Syzygies of oriented matroids (with Alex Postnikov and Bernd Sturmfels), Duke Mathematical Journal, 111 (2002), 287-317.
  6. Lyubeznik's resolution and rooted complexes, Journal of Algebraic Combinatorics, 16 (2002), 97-101.
  7. A short simplicial h-vector and the Upper Bound Theorem (with Patricia Hersh) , Discrete and Computational Geometry, 28 (2002), 283-289.
  8. Remarks on the Upper Bound Theorem [PS], Journal of Combinatorial Theory Ser. A, 104 (2003), 201-206.
  9. Symmetric iterated Betti numbers [PS], (with Eric Babson and Rekha Thomas), Journal of Combinatorial Theory Ser. A, 105 (2004), 233--254.
  10. Face numbers and nongeneric initial ideals (with Eric Babson), Electronic J. Combin., 11 (2004/06), no.2, Research Paper 25, 23pp. [PDF]
  11. On face numbers of manifolds with symmetry [PS], Advances in Math., 192 (2005), 183-208.
  12. Reverse Lexicographic and lexicographic shifting, (with Eric Babson and Rekha Thomas), Journal of Algebraic Combinatorics, 23 (2006), 107-123. [PDF]
  13. How neighborly can a centrally symmetric polytope be? (with Nati Linial), Discrete and Computational Geometry 36 (2006), no. 2, 273--281. [PDF]
  14. Face ring multiplicity via CM-connectivity sequences (with Ed Swartz), Canadian Journal of Mathematics 61 (2009), no.4, 888-903. [PDF]
  15. A centrally symmetric version of the cyclic polytope (with Alexander Barvinok), Discrete and Computational Geometry, 39 (2008), 76-99. [PDF]
  16. Socles of Buchsbaum modules, complexes and posets (with Ed Swartz), Advances in Mathematics 222 (2009), 2059-2084. [PDF]
  17. Applications of Klee's Dehn-Sommerville relations (with Ed Swartz), Discrete and Computational Geometry, 42, Issue 2 (2009), 261-276. [PDF]
  18. Gorenstein rings through face rings of manifolds (with Ed Swartz), Compositio Mathematica, 145, Issue 4 (2009), 993-1000. [PDF]
  19. Balanced complexes and complexes without large missing faces (with Michael Goff and Steven Klee), Arkiv fur Matematik, 49, Issue 2 (2011), 335-350. [PDF]
  20. Face numbers of generalized balanced Cohen-Macaulay complexes (with Jonathan Browder), Combinatorica, 31(6) (2011), 669-689. [PDF]
  21. Face rings of simplicial complexes with singularities (with Ezra Miller and Ed Swartz), Mathematische Annalen, 351, Issue 4 (2011), 857-875. [PDF]
  22. Face numbers of pseudomanifolds with isolated singularities (with Ed Swartz), Mathematica Scandinavica, 110 (2012), 198-222. [PDF]
  23. Centrally symmetric manifolds with few vertices (with Steve Klee), Advances in Mathematics, 229 (2012), 487-500. [PDF]
  24. Neighborliness of the symmetric moment curve (with Alexander Barvinok and Seung Jin Lee), Mathematika, 59 (2013), 223-249. [PDF]
  25. Centrally symmetric polytopes with many faces (with Alexander Barvinok and Seung Jin Lee), Israel Journal of Mathematics, to appear. [PDF]
  26. Explicit constructions of centrally symmetric k-neighborly polytopes and large strictly antipodal sets (with Alexander Barvinok and Seung Jin Lee), Discrete and Computational Geometry, 49, Issue 3 (2013), 429-443. [PDF]
  27. From flag complexes to banner complexes (with Steve Klee), SIAM J. Discrete Math, to appear. [PDF]

I am on the editorial board of Journal of Algebraic Combinatorics

I am also co-organizing the Combinatorics and Geometry Seminar at the University of Washington together with Sara Billey

Slides

Lectures from Jerusalem Spring School, May 2007: 1, 2.