{"id":63,"date":"2023-02-16T15:23:51","date_gmt":"2023-02-16T15:23:51","guid":{"rendered":"https:\/\/academic.csuohio.edu\/soprunov-ivan\/?page_id=63"},"modified":"2026-02-19T10:43:30","modified_gmt":"2026-02-19T15:43:30","slug":"research","status":"publish","type":"page","link":"https:\/\/academic.csuohio.edu\/soprunov-ivan\/research\/","title":{"rendered":"Research"},"content":{"rendered":"\n

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My research is in combinatorial and computational algebraic geometry. I am particularly interested in toric varieties, their applications to sparse polynomial systems, combinatorics and geometry of polyhedra, and coding theory. Recently, I have been also working on geometric inequalities involving mixed volumes.<\/p>\n\n\n

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Publications<\/h2>\n\n\n\n

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  1. On the discrete Heine-Shephard problem for four lattice polygons <\/a> (with D. Gerrity), preprint (2026)<\/li>\n\n\n\n
  2. An algebraic-combinatorial proof of a B\u00e9zout-type inequality for mixed volumes of three-dimensional zonoids <\/a> (with G. Averkov), Discrete & Computational Geometry (2025)<\/li>\n\n\n\n
  3. Binary Triorthogonal and CSS-T Codes for Quantum Error Correction <\/a> (with E. Camps, H. L\u00f3pez, G. Matthews, D. Ruano, and R. San-Jos\u00e9), 60th Annual Allerton Conference on Communication, Control, and Computing, Urbana, Illinois, September 25-27 (2024)<\/li>\n\n\n\n
  4. On the affine permutation group of certain decreasing Cartesian codes <\/a> (with E. Camps, H. L\u00f3pez, and E. Sarmiento), EEE ISIT 2024 International Symposium on Information Theory, Athens, Greece, July 7-12 (2024)<\/li>\n\n\n\n
  5. Mixed volumes of zonoids and the absolute value of the Grassmannian <\/a> (with G. Averkov, K. von Dichter, and S. Richard), preprint (2024)<\/li>\n\n\n\n
  6. The volume polynomial of lattice polygons <\/a> (with J. Soprunova) Proceedings of AMS, vol 152, no 12, (2024), 5313-5325, see GitHub <\/a> for code<\/li>\n\n\n\n
  7. An algebraic characterization of binary CSS-T codes and cyclic CSS-T codes for quantum fault tolerance <\/a> (with E. Camps, H. L\u00f3pez, G. Matthews, D. Ruano, and R. San-Jos\u00e9) Quantum Information Processing, vol 23, article number 230, (2024)<\/li>\n\n\n\n
  8. Relative hulls and quantum codes <\/a> (with S. Anderson, E. Camps, H. L\u00f3pez, G. Matthews, and D. Ruano) IEEE Transactions on Information Theory, (2024), vol 70, issue 5, 3190-3201 <\/li>\n\n\n\n
  9. Pl\u00fccker-type inequalities for mixed areas and intersection numbers of curve arrangements <\/a> (with G. Averkov) International Math Research Notices, vol 2023, issue 18, (2023) 16015\u201316050<\/li>\n\n\n\n
  10. \ud835\udd3dq<\/sub>-zeros of sparse trivariate polynomials and toric 3-fold codes <\/a> (with K. Meyer and J. Soprunova) SIAM Applied Algebra and Geometry, vol 6, issue 3 (2022), see also GitHub <\/a> for code<\/li>\n\n\n\n
  11. Coding theory package for Macaulay2 <\/a> (with T. Ball, E. Camps, H. Chimal-Dzul, D. Jaramillo-Velez, H. L\u00f3pez, N. Nichols, M. Perkins, G. Vera-Mart\u00ednez, and G. Whieldon) Journal of Software for Algebra and Geometry, vol 11 (2021) 117-122<\/li>\n\n\n\n
  12. The dual of an evaluation code <\/a> (with H. L\u00f3pez and R. Villarreal) Designs, Codes and Cryptography, 89, (2021) 1367-1403<\/li>\n\n\n\n
  13. Classification of triples of lattice polytopes with a given mixed volume <\/a> (with G. Averkov and C. Borger) Discrete & Computational Geometry, 66, (2021) 165-202 , see also GitHub <\/a> for data and code<\/li>\n\n\n\n
  14. Inequalities between mixed volumes of convex bodies: volume bounds for the Minkowski sum <\/a> (with G. Averkov and C. Borger) Mathematika 66 (2020) 1003-1027<\/li>\n\n\n\n
  15. Monomial-Cartesian codes and their duals, with applications to LCD codes, quantum codes, and locally recoverable codes <\/a> (with H. L\u00f3pez and G. Matthews) Designs, Codes and Cryptography, 88, no 8, (2020) 1673-1685<\/li>\n\n\n\n
  16. Wulff shapes and a characterization of simplices via a Bezout type inequality <\/a> (with C. Saroglou and A. Zvavitch) Advances in Mathematics 357 (2019) 106789<\/li>\n\n\n\n
  17. Criteria for strict monotonicity of the mixed volume of convex polytopes <\/a> (with F. Bihan) Advances in Geometry, vol 19, issue 4 (2019) 527-540 <\/li>\n\n\n\n
  18. Generalized multiplicities of edge ideals <\/a> (with A. Alilooee and J. Validashti) Journal of Algebraic Combinatorics, vol 47, issue 3 (2018) 441-472 <\/li>\n\n\n\n
  19. Characterization of simplices via the Bezout Inequality for Mixed volumes <\/a> (with C. Saroglou and A. Zvavitch) Proceedings of AMS, vol 144, no 12, (2016) 5333-5340 <\/li>\n\n\n\n
  20. Bezout Inequality for Mixed volumes <\/a> (with A. Zvavitch) International Math Research Notices , 23 (2016) 7230-7252<\/li>\n\n\n\n
  21. Eventual quasi-linearity of the Minkowski length <\/a> (with J. Soprunova) European Journal of Combinatorics 58 (2016) 107-117<\/li>\n\n\n\n
  22. Multigraded Hilbert function and toric complete intersection codes <\/a> (with M. \u015eahin) Journal of Algebra 459 (2016) 446-467<\/li>\n\n\n\n
  23. Lattice polytopes in coding theory <\/a> Journal of Algebra Combinatorics Discrete Structures and Applications, vol 2, no 2 (2015) 85-94<\/li>\n\n\n\n
  24. Tropical determinant on transportation polytope <\/a> (with S. Gajula and J. Soprunova) Linear Algebra and its Applications, vol 475, no 15 (2015) 28-44<\/li>\n\n\n\n
  25. On dual toric complete intersection codes <\/a> (with P. Celebi Demirarslan) Finite Fields and Their Applications, vol 33 (2015) 118-136<\/li>\n\n\n\n
  26. Toric complete intersection codes <\/a> Journal of Symbolic Computation, 50 (2013) 374-385<\/li>\n\n\n\n
  27. Bringing toric codes to the next dimension <\/a> (with J. Soprunova) SIAM J. Discrete Math. 24, no 2, (2010) 655-665<\/li>\n\n\n\n
  28. Toric surface codes and Minkowski length of polygons <\/a> (with J. Soprunova) SIAM J. Discrete Math. 23, no 1 (2009) 384-400 <\/li>\n\n\n\n
  29. Let me tell you my favorite lattice point problem…<\/a> (with M. Beck, B. Nill, B. Reznick, C. Savage, Z. Xu) Integer points in polyhedra, Contemp. Math. 452, AMS (2008)<\/li>\n\n\n\n
  30. Global residues for sparse polynomial systems <\/a> Journal of Pure and Applied Algebra 209, no 2, (2007) 383-392<\/li>\n\n\n\n
  31. Combinatorial construction of toric residues <\/a> (with A. Khetan) Ann. Inst. Fourier (Grenoble) 55, no 2 (2005) 511-548<\/li>\n\n\n\n
  32. Toric residue and combinatorial degree <\/a> Trans. Amer. Math. Soc. 357, no 5 (2005) 1963-1975<\/li>\n\n\n\n
  33. Residues and tame symbols on toroidal varieties <\/a> Compositio Math. 140, no 6 (2004) 1593-1613<\/li>\n\n\n\n
  34. On combinatorial coefficients and the Gelfond-Khovanskii residue formula <\/a> Topics in Algebraic Geometry and Geometric Modeling, Contemp. Math., 334, AMS (2003) 343-349<\/li>\n\n\n\n
  35. Parshin’s symbols and residues, and Newton polyhedra<\/a> Ph.D. Thesis, University of Toronto (2002)<\/li>\n\n\n\n
  36. Symbols and residues on surfaces<\/a> preprint (2001)<\/li>\n\n\n\n
  37. A short proof of the Prime Number Theorem for arithmetic progressions<\/a> (1998) This paper was written in response to Don Zagier’s paper “Newman’s Short Proof of the Prime Number Theorem”<\/li>\n\n\n\n
  38. Patching theorem in quadratic Serre’s conjecture <\/a> Fundam. Prikl. Mat. 3, no 1 (1997) 255-261 (in Russian)<\/li>\n<\/ol>\n\n\n\n

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