Isabella Novik

Robert R. & Elaine F. Phelps Professor in Mathematics



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

Current Courses

Autumn Quarter 2021: Math 300C

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 Steve 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, 195 (2013), no. 1, 457-472. [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, 27 (2013), no. 2, 1146-1158. [PDF]
  28. Bipartite Rigidity (with Gil Kalai and Eran Nevo), Trans. Amer. Math. Soc., 368 (2016), no. 8, 5515-5545.[PDF]
  29. Bipartite Minors (with Maria Chudnovsky, Gil Kalai, Eran Nevo, and Paul Seymour), Journal Combinatorial Theory, Ser. B 116 (2016), 219-228.[PDF]
  30. Lower bound theorems and a generalized lower bound conjecture for balanced simplicial complexes (with Steve Klee), Mathematika, 62 (2016) 441-477.[PDF]
  31. Face enumeration on simplicial complexes (with Steve Klee). Recent Trends in Combinatorics, 653-686, IMA Vol. Math. Appl., 159, Springer, 2016. [PDF]:
  32. Face numbers of manifolds with boundary (with Satoshi Murai), Int. Math. Res. Not. IMRN, 2017, No. 12, 3603-3646. [PDF]
  33. Simplicial moves on balanced complexes (with Ivan Izmestiev and Steve Klee), Advances in Mathematics, 320C (2017), 82-114. [PDF]
  34. A duality in Buchsbaum rings and triangulated manifolds (with Satoshi Murai and Ken-ichi Yoshida), Algebra & Number Theory, 11-3 (2017), 635-656. [PDF]
  35. Face numbers and the fundamental group (with Satoshi Murai), Israel Journal of Mathematics, 222 (2017), 297-315. [PDF]
  36. A generalized lower bound theorem for balanced manifolds (with Martina Juhnke-Kubitzke, Satoshi Murai, and Connor Sawaske), Mathematische Zeitschrift, 289 (2018), no. 3-4, 921-942. [PDF]
  37. A lower bound theorem for centrally symmetric simplicial polytopes (with Steve Klee, Eran Nevo, and Hailun Zheng), Discrete and Computational Geometry, 61 (2019), no. 3, 541-561. [PDF]
  38. A tale of centrally symmetric polytopes and spheres. Recent Trends in Algebraic Combinatorics, 305-331, Association for Women in Mathematics Series, Vol. 16, Springer, 2019. [PDF]
  39. From acute sets to centrally symmetric 2-neighborly polytopes, SIAM Journal on Discrete Mathematics, 32 (2018), no. 3, 1572-1576. [PDF]
  40. Convex union representability and convex codes (with Amzi Jeffs), Int. Math. Res. Not. IMRN, 2021, no. 9, 7132-7158 [PDF]
  41. Highly neighborly centrally symmetric spheres (with Hailun Zheng), Advances in Mathematics, 370 (2020), 107238. [PDF]
  42. g-vectors of manifolds with boundary (with Ed Swartz), Algebraic Combinatorics, Volume 3 (2020) no. 4, 887-911. [PDF]
  43. New families of highly neighborly centrally symmetric spheres (with Hailun Zheng), submitted.[PDF]
  44. The stresses on centrally symmetric complexes and the lower bound theorems (with Hailun Zheng), Algebraic Combinatorics, Volume 4, (2021) no. 3, 541-549.[PDF]
  45. Many neighborly spheres (with Hailun Zheng), Mathematische Annalen, to appear. [PDF]
  46. Reconstructing simplicial polytopes from their graphs and affine 2-stresses (with Hailun Zheng), submitted. [PDF]
  47. Face numbers: the upper bound side of the story, submitted to the Proceedings of ICM 2022. [PDF]

I am on the editorial boards of Algebraic Combinatorics, Proceedings of the AMS, and SIAM Journal on Discrete Mathematics

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