Isabella Novik

Professor



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

Current Courses

Winter Quarter 2025: Math 402 (Introduction to Modern Algebra)

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), Trans. Amer. Math. Soc., 375 (2022), 4445-4475. [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, 388 (2024), 969-984. [PDF]
  46. Reconstructing simplicial polytopes from their graphs and affine 2-stresses (with Hailun Zheng), Israel Journal of Mathematics, 255 (2023), 891-910. [PDF]
  47. Face numbers: the upper bound side of the story, ICM---International Congress of Mathematicians, Vol. VI. Sections 12-14, 4622-4645, EMS Press, Berlin, (2023). [PDF]; the talk itself can be found here
  48. Neighborly spheres and transversal numbers (with Hailun Zheng), in Open Problems in Algebraic Combinatorics, Proceedings of Symposia in Pure Mathematics, vol. 110, Amer. Math. Soc., Providence, RI, 2024, pp. 113-128. [PDF]
  49. Affine stresses: the partition of unity and Kalai's reconstruction conjectures (with Hailun Zheng), Discrete and Computational Geometry, 72, 928-956 (2024). [PDF]
  50. The merging operation and (d-i)-simplicial i-simple d-polytopes (with Hailun Zheng), Combinatorial Theory, 4 (2024), no. 2, Paper No. 8, 27 pp. [PDF]
  51. Affine stresses, inverse systems, and reconstruction problems (with Satoshi Murai and Hailun Zheng), Int. Math. Res. Not. IMRN, 2024, no. 10, 8540-8556. [PDF]
  52. Transversal numbers of simplicial polytopes, spheres, and pure complexes (with Hailun Zheng), submitted. [PDF]
  53. Determinants of Hodge-Riemann forms (with Matt Larson and Alan Stapledon), submitted. [PDF]
  54. Missing faces of neighborly and nearly neighborly polytopes and spheres (with Hailun Zheng), submitted.[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, Gaku Liu, and Ricky Liu