My research is in combinatorial and computational algebraic geometry. I am particularly interested in toric varieties and their applications to sparse polynomial systems and to combinatorics and geometry of polyhedra.

What does the picture on the right mean?

  
   
  • Papers and Preprints (You may also look at arXiv and MathSciNet. Note that my last name has two spellings "Soprunov" and "Soprounov"!)

    Global residues for sparse polynomial systems, preprint
    Combinatorial construction of toric residues, (with Amit Khetan) Ann. Inst. Fourier (Grenoble) 55, no. 2 (2005), 511--548
    Toric residue and combinatorial degree, Trans. Amer. Math. Soc., 357 (2005), no. 5, 1963--1975
    Residues and tame symbols on toroidal varieties, Compositio Math. 140 (2004) no. 6, 1593--1613
    On the Gelfond-Khovanskii residue formula, "Topics in Algebraic Geometry and Geometric Modeling", Contemp. Math., 334, AMS (2003), p. 343--349
    Symbols and residues on surfaces , (2001) This paper is a 2-dimensional version of the Compositio paper, but considers arbitrary surfaces. [PDF]
    A short proof of the Prime Number Theorem for arithmetic progressions, (1998) This paper was written in response to Don Zagier's paper "Newman's Short Proof of the Prime Number Theorem" Amer. Math. Monthly 104 (1997), no. 8, 705--708. [PDF]
    Patching theorem in quadratic Serre's conjecture, Fundam. Prikl. Mat. 3 (1997), no. 1, 255--261. (in Russian)

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  • Other

    Global Residues in the Torus, [PDF], slides of my talk at the Union College Mathematics Conference (December 2005)
    Parshin's symbols and residues, and Newton polyhedra, Ph.D. Thesis (2002), advisor Askold Khovanskii
    Computing the global residue in dimension 2, Maple 7 code.
    Computing the toric residue for four 3-simplices, Maple 7 code (with A. Khetan).
    Geometry SOAR 2001, Lecture notes for the SOAR 2001 math summer camp (with K. Kaveh and E. Soprunova)

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