Mikhail Mazin
Assistant Professor

Email: mmazin@math.ksu.edu.
Office: 111 Cardwell Hall.

Most of my work is in the field of Algebraic Combinatorics and its relations to Geometry and Representation Theory. I am particularly interested in Catalan combinatorics, rational parking functions, and combinatorics of affine symmetric groups.

Recently, I started working on a more geometric project. It involves the equivariant K-theory of the space of partial flags and certain operators given by correspondences on this space.

During my PhD studies at the University of Toronto, I worked in the field of algebraic geometry and singularity theory. The title of my thesis was "Geometric Theory of Parshin Residues". This work involved methods from stratification theory and resolution of singularities

Here are my CV and Research Statement.

Published/to appear Papers
  1. Multigraph Hyperplane Arrangements and Parking Functions. M. Mazin.
    (To appear in Ann. Comb., [arxiv.org])

  2. Rational parking functions and LLT polynomials. E. Gorsky, M. Mazin.
    (J. Combin. Theory Ser. A 140 (2016), 123--140, [arxiv.org, preliminary version])

  3. Affine Permutations And Rational Parking Functions. E. Gorsky, M. Mazin, M. Vazirani.
    (Trans. Amer. Math. Soc. 368 (2016), no. 12, 8403--8445, [arxiv.org, preliminary version])

  4. A bijective proof of Loehr-Warrington's formulas for the statistics ctot and mid. M. Mazin.
    (Ann. Comb. 18 (2014), no. 4, pp. 709--722., [arxiv.org, preliminary version])

  5. Compactified Jacobians and q,t-Catalan numbers, II. E. Gorsky, M. Mazin.
    (Journal of Algebraic Combinatorics, 39 (2014), no. 1, 153--186, [arxiv.org, preliminary version])

  6. Compactified Jacobians and q,t-Catalan Numbers, I. E. Gorsky, M. Mazin.
    (Journal of Combinatorial Theory, Series A, 120 (2013), 49--63, [arxiv.org, preliminary version])

  7. Geometric Theory of Parshin's Residues I. Coboundary Operators for Stratified Spaces and the Reciprocity Law for Residues. Mazin, M.
    (Michigan Mathematical Journal, Volume 61, Issue 3 (2012), 651--670, [arxiv.org, preliminary version])

  8. Geometric Theory of Parshin's Residues. Mazin, M.
    (C. R. Math. Acad. Sci. Soc. R. Can. 32 (2010), no. 3, 81--96, [pdf, preliminary version])

Other Materials
  • [arxiv.org] Mazin, M. Geometric Theory of Parshin's Residues II. Toric Neighborhoods of Parshin's Points.
    Preprint (arXiv:0910.2529v1 [math.AG]).
  • Slides from the FPSAC 2014 conference in Chicago. The presentation is about our project with Eugene Gorsky and Monica Vazirani on Affine permutations and parking functions.
  • Extended abstract for the FPSAC 2014 conference in Chicago. (to appear in DMTCS Proceedings, 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014))
  • Poster about generalizations of Pak-Stanley labeling for the IMA workshop on Geometric and Enumerative Combinatorics, 2014.
  • [pdf] M. Mazin. A remark on combinatorics of Hilbert schemes of quasi-homogeneous plane curve singularities.
  • Poster for the AGNES conference in Amherst.

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