<   Oliver Pechenik: Assistant Professor and NSF Postdoctoral Fellow   >

Writings:

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† denotes undergraduate mentee.
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  1. K-theoretic crystals for set-valued tableaux of rectangular shapes (with Travis Scrimshaw) Down Arrow

    Submitted, 19 pages.
    arXiv:1904.09674
  2. Asymmetric function theory (with Dominic Searles) Down Arrow

    Submitted, 36 pages.
    arXiv:1904.01358
  3. Crystal structures for symmetric Grothendieck polynomials (with Cara Monical and Travis Scrimshaw) Down Arrow

    Submitted, 47 pages.
    arXiv:1807.03294
  4. Polynomials from combinatorial K-theory (with Cara Monical and Dominic Searles) Down Arrow

    Canadian Journal of Mathematics, to appear, 35 pages.
    arXiv:1806.03802
  5. Derivatives of Schubert polynomials and proof of a determinant conjecture of Stanley (with Zachary Hamaker, David Speyer, and Anna Weigandt) Down Arrow

    Algebraic Combinatorics, to appear, 7 pages.
    arXiv:1812.00321
  6. The genomic Schur function is fundamental-positive Down Arrow

    Annals of Combinatorics, to appear, 13 pages.
    arXiv:1810.04727
  7. Doppelgängers: bijections of plane partitions (with Zachary Hamaker, Rebecca Patrias, and Nathan Williams) Down Arrow

    International Mathematics Research Notices, to appear, 54 pages.
    arXiv:1602.05535
  8. Decompositions of Grothendieck polynomials (with Dominic Searles) Down Arrow

    International Mathematics Research Notices 2019(10), 2019, 3214-3241.
    arXiv:1611.02545
  9. Unique rectification in d-complete posets: towards the K-theory of Kac-Moody flag varieties (with Rahul Ilango and Michael Zlatin) Down Arrow

    Electronic Journal of Combinatorics 25(4), 2018, 1-35.
    arXiv:1805.02287
  10. Orbits of plane partitions of exceptional Lie type (with Holly Mandel) Down Arrow

    European Journal of Combinatorics 74, 2018, 90-109.
    arXiv:1712.09180
  11. Deformed cohomology of flag varieties (with Dominic Searles) Down Arrow

    Mathematical Research Letters, 25, 2018, 649-657.
    arXiv:1410.8070
  12. Rhombic tilings and Bott-Samelson varieties (with Laura Escobar, Bridget Tenner, and Alexander Yong) Down Arrow

    Proceedings of the American Mathematical Society 146, 2018, 1921-1935.
    arXiv:1605.05613
  13. Promotion of increasing tableaux: frames and homomesies Down Arrow

    Electronic Journal of Combinatorics 24(3), 2017, 1-14.
    arXiv:1702.01358
  14. Genomic tableaux (with Alexander Yong) Down Arrow

    Journal of Algebraic Combinatorics 45, 2017, 649-685.
    arXiv:1603.08490
  15. Resonance in orbits of plane partitions and increasing tableaux (with Kevin Dilks and Jessica Striker) Down Arrow

    Journal of Combinatorial Theory, Series A 148, 2017, 244-274.
    arXiv:1512.00365
  16. Equivariant K-theory of Grassmannians II: the Knutson-Vakil conjecture (with Alexander Yong) Down Arrow

    Compositio Mathematica 153, 2017, 667-677.
    arXiv:1508.00446
  17. Equivariant K-theory of Grassmannians (with Alexander Yong) Down Arrow

    Forum of Mathematics, Pi 5, 2017, 1-128.
    arXiv:1506.01992
  18. K-theoretic Schubert calculus and applications Down Arrow

    Ph.D. Thesis, University of Illinois at Urbana-Champaign, 2016, 255 pages.
  19. Proofs and generalizations of a homomesy conjecture of Propp and Roby (with Jonathan Bloom and Dan Saracino) Down Arrow

    Discrete Mathematics 339, 2016, 194-206.
    arXiv:1308.0546
  20. Genomic tableaux and combinatorial K-theory (with Alexander Yong) Down Arrow

    Discrete Mathematics and Theoretical Computer Science Proceedings FPSAC`15, 2015, 37-48. FPSAC 2015, Daejeon, Korea.
  21. Cyclic sieving of increasing tableaux and small Schröder paths Down Arrow

    Journal of Combinatorial Theory, Series A 125, 2014, 357-378.
    arXiv:1209.1355
  22. Generalized graph cordiality (with Jennifer Wise) Down Arrow

    Discussiones Mathematicae Graph Theory 32(3), 2012, 557-567.
  23. A midsummer knot's dream (with Allison Henrich, Noel MacNaughton, Sneha Narayan, Robert Silversmith, and Jennifer Townsend) Down Arrow

    College Mathematics Journal 42(2), 2011, 126-134.
    arXiv:1003.4494
  24. Classical and virtual pseudodiagram theory and new bounds on unknotting numbers and genus (with Allison Henrich, Noel MacNaughton, Sneha Narayan, and Jennifer Townsend) Down Arrow

    Journal of Knot Theory and Its Ramifications 20(4), 2011, 625-650.
    arXiv:0908.1981
  25. Large cardinals Down Arrow

    Undergraduate Honors Thesis, Oberlin College, 2010
  26. Zero-divisor ideals and realizable zero-divisor graphs (with Michael Axtell, Joe Stickles, et al.) Down Arrow

    Involve 2(1), 2009, 17-27.
  27. The nilradical and non-nilradical graphs of commutative rings (with Abigail Bishop, Thomas Cuchta and Kathryn Lokken) Down Arrow

    International Journal of Algebra 2(20), 2008, 981-994.
  28. Effects of temperature, salinity, and air exposure on development of the estuarine pulmonate gastropod Amphibola crenata (with Islay Marsden and Jan Pechenik) Down Arrow

    Journal of Experimental Marine Biology and Ecology 292(2), 2003, 159-176.

Presentations:

  • TBA
    AMS Sectional Meeting, Special Session on Special Session on Special Session on Combinatorics Arising from Representations, California State University, Fresno, CA, May 2020
  • TBA
    AMS Sectional Meeting, Special Session on Special Session on Combinatorics of Reduced Decompositions of Elements of Coxeter Groups and Related Topics, California State University, Fresno, CA, May 2020
  • TBA
    AMS Sectional Meeting, Special Session on Recent Advances in Schubert Calculus and Related Topics, Tufts University, Medford, MA, Mar. 2020
  • TBA
    AMS Sectional Meeting, Special Session on Combinatorics Related to Geometry and Representation Theory, University of Virginia, Charlottesville, VA, Mar. 2020
  • Gröbner geometry of Schubert polynomials through ice
    Joint Mathematics Meetings (Denver, CO), Special Session on Combinatorial Structures and Integrable Systems, 15 Jan. 2020
  • Gröbner geometry of Schubert polynomials through ice
    Algebra, Geometry and Combinatorics Day (AlGeCom) XVIII, Washington University in St. Louis, Sept. 2019
  • K-theoretic polynomials (poster)
    FPSAC, Ljubljana, Slovenia, July 2019
  • K-theoretic Schubert calculus
    Elliptic Cohomology Days, University of Illinois at Urbana-Champaign, 11 Jun. 2019
  • Crystal structures for symmetric Grothendieck polynomials
    Geometric Methods in Representation Theory Seminar, University of North Carolina at Chapel Hill, 12 Apr. 2019
  • Dynamics of height 3 plane partitions
    AMS Sectional Meeting, Special Session on Dynamical Systems and Algebraic Combinatorics, University of Hawaii at Manoa, Honolulu, HI, Mar. 2019
  • Taking the long way home
    Undergraduate Math Club, University of Kentucky, 21 Feb. 2019
  • Degenerations of cohomology rings
    Algebra Seminar, University of Kentucky, 20 Feb. 2019
  • Crystal structures for symmetric Grothendieck polynomials
    Combinatorics Seminar, University of Michigan, 15 Feb. 2019
  • Crystal structures for symmetric Grothendieck polynomials
    Combinatorial Algebra meets Algebraic Combinatorics, University of Ottawa, 26 Jan. 2019
  • How to give bad math talks
    REU Seminar, University of Michigan, Aug. 2018
  • Unique rectification in d-complete posets: towards the K-theory of Kac-Moody flag varieties
    OSU Workshop on Schubert Calculus, the Ohio State University, May 2018
  • (K-theoretic) crystals on Grothendieck polynomials
    AMS Sectional Meeting, Special Session on Combinatorial Aspects of Nilpotent Orbits, Northeastern University, Boston, MA, Apr. 2018
  • Taking the long way home: orbits of plane partitions
    Combinatorics Seminar, University of Washington, 28 March 2018
  • Taking the long way home: orbits of plane partitions
    Combinatorics Seminar, Michigan State University, 27 Feb. 2018
  • Orbits of plane partitions of exceptional Lie type
    Joint Mathematics Meetings (San Diego, CA), Special Session on Dynamical Algebraic Combinatorics, Jan. 2018
  • Decompositions of Grothendieck polynomials
    International Festival in Schubert Calculus, Sun Yat-sen University, Guangzhou, China, Nov. 2017
  • Taking the long way home: orbits of plane partitions
    Undergraduate Math Club, University of Michigan, 19 Oct. 2017
  • Deformed cohomology of flag varieties
    Topology, Geometry, and Dynamical Systems Seminar, University of Texas at Dallas, 16 Oct. 2017
  • Decompositions of Grothendieck polynomials
    Algebra and Combinatorics Seminar, University of Texas at Dallas, 13 Oct. 2017
  • Decompositions of Grothendieck polynomials
    Combinatorics Seminar, University of Michigan, 22 Sept. 2017
  • Doppelgänger posets and K-theory
    Capsule Research Talks, University of Michigan, 28 Aug. 2017
  • Schur functions and the Littlewood-Richardson rule
    Graduate Reading Group on the Littlewood-Richardson Rule, Rutgers University, Apr. 2017
  • Decompositions of Grothendieck polynomials
    Algebra Seminar, Rutgers University, Mar. 2017
  • Introduction to symmetric function theory
    Graduate Reading Group on the Littlewood-Richardson Rule, Rutgers University, Mar. 2017
  • Taking the long way home: orbits of plane partitions
    Center for Women in Mathematics at Smith College, Mar. 2017
  • Decompositions of Grothendieck polynomials
    Algebra/Combinatorics/Geometry Seminar, Smith College, Feb. 2017
  • Decompositions of Grothendieck polynomials
    Philadelphia Area Combinatorics & Algebraic Geometry (CAGE) Seminar, University of Pennsylvania, Jan. 2017
  • Decompositions of Grothendieck polynomials
    Combinatorics and Discrete Mathematics Seminar, LaCIM, Université du Québec à Montréal, Dec. 2016
  • K-theoretic Schubert calculus
    Algebra Seminar, Rutgers University, Oct. 2016
  • Taking the long way home: orbits of plane partitions
    AMS Sectional Meeting, Special Session on Algebraic and Enumerative Combinatorics, Bowdoin College, Brunswick, ME, Sept. 2016
  • Rhombic tilings and Bott-Samelson varieties
    AMS Sectional Meeting, Special Session on Combinatorial Aspects of Nilpotent Orbits, Bowdoin College, Brunswick, ME, Sept. 2016
  • Puzzles and Equivariant K-theory of Grassmannians
    Workshop on Equivariant Generalized Schubert Calculus and its Applications, University of Ottawa, Apr. 2016
  • Puzzles and Equivariant K-theory of Grassmannians
    AMS Sectional Meeting, Special Session on Algebraic and Geometric Combinatorics, North Dakota State University, Fargo, Apr. 2016
  • Puzzles and Equivariant K-theory of Grassmannians
    AMS Sectional Meeting, Special Session on Combinatorial and Computational Commutative Algebra and Algebraic Geometry, University of Utah, Salt Lake City, Apr. 10, 2016
  • Coincidental types, K-theoretic Schubert calculus, and bijections of plane partitions
    AMS Sectional Meeting, Special Session on Algebraic Combinatorics, University of Utah, Salt Lake City, Apr. 9, 2016
  • Puzzles and Equivariant K-theory of Grassmannians
    Combinatorics Seminar, MIT, Cambridge, MA, Feb. 17, 2016
  • Puzzles and Equivariant K-theory of Grassmannians
    Combinatorial Algebra meets Algebraic Combinatorics, University of Western Ontario, Jan. 24, 2016
  • Puzzles and Equivariant K-theory of Grassmannians
    Combinatorics Seminar, University of Michigan, Ann Arbor, Jan. 8, 2016
  • Puzzles and equivariant K-theory of Grassmannians
    Canadian Math Society winter meeting, Scientific Session on Algebraic Combinatorics, Montreal, Dec. 5, 2015
  • Taking the long way home: orbits of plane partitions
    Association for Women in Mathematics Colloquium, UIUC, Dec. 1, 2015
  • Puzzles and Equivariant K-theory of Grassmannians
    Algebraic Geometry/Commutative Algebra Seminar, University of Notre Dame, Notre Dame, IN, Nov. 18, 2015
  • The Belkale-Kumar product on generalized flag manifolds
    AMS Sectional Meeting, Special Session on Algebraic Geometry and Combinatorics, Rutgers University, New Brunswick, NJ, Nov. 15, 2015
  • Knutson-Vakil puzzles compute equivariant K-theory of Grassmannians
    AMS Sectional Meeting, Special Session on Modern Schubert Calculus, Rutgers University, New Brunswick, NJ, Nov. 14, 2015
  • Taking the long way home: orbits of plane partitions
    Oberlin College, Oberlin, OH, Nov. 5, 2015
  • Puzzles and Equivariant K-theory of Grassmannians (poster)
    AlGeCom XII, University of Michigan, Ann Arbor, MI, Oct. 24, 2015
  • Puzzles and Equivariant K-theory of Grassmannians
    Combinatorics Seminar, University of Minnesota, Minneapolis, Oct. 9, 2015
  • Introduction to Schubert calculus
    Student Combinatorics Seminar, University of Minnesota, Minneapolis, Oct. 8, 2015
  • Knutson-Vakil puzzles compute equivariant K-theory of Grassmannians
    AMS Sectional Meeting, Special Session on Combinatorial and Geometric Representation Theory, Loyola University, Chicago, Oct. 3, 2015
  • Equivariant K-theory of Grassmannians
    Formal Power Series and Algebraic Combinatorics (FPSAC), KAIST, Daejeon, South Korea, July 2015
  • Resonance of Plane Partitions
    Illinois REU Seminar, UIUC, June 2015
  • Equivariant K-theory of Grassmannians (poster)
    MAAGC (Mid-Atlantic Algebraic Geometry and Combinatorics), Philadelphia, PA, Apr. 2015
  • Genomic tableaux and equivariant K-theory
    Combinatorics Seminar, University of California Berkeley, Mar. 2015
  • Some things that used to bother me and I now understand better
    AIM workshop on Dynamics in Algebraic Combinatorics, San Jose, CA, Mar. 2015 (Notes by Sam Hopkins)
  • Genomic tableaux and equivariant K-theory
    Algebra and Combinatorics Seminar, Tulane University, Jan. 2015
  • Genomic tableaux and Schubert calculus
    AMS Sectional Meeting, Special Session on Algebraic Combinatorics, University of Wisconsin–Eau Claire, Eau Claire, WI, Sept. 2014
  • Genomic Tableaux and Equivariant K-Theory of Grassmannians
    Algebra–Geometry–Combinatorics Seminar, UIUC, Sept. 2014
  • 'Genomic' Tableaux and Schubert Calculus (poster)
    AlGeCom, UIUC, May 2014
  • Combinatorial Ergodicity
    Algebra–Geometry–Combinatorics Seminar, UIUC, Feb. 2014
  • A homomesy conjecture of J. Propp and T. Roby (poster)
    AlGeCom, Loyola University, Chicago, Nov. 2013
  • Cyclic Sieving of Increasing Tableaux and Small Schröder Paths (poster)
    FPSAC, Paris, France, June 2013
  • Cyclic Sieving of Increasing Tableaux and Small Schröder Paths (poster)
    "Algebra, Combinatorics and Representation Theory: In memory of Andrei Zelevinsky (1953-2013)," Northeastern University, Apr. 2013
  • Cyclic Sieving of Increasing Tableaux and Small Schröder Paths (poster)
    ICERM workshop on Whittaker Functions, Schubert calculus and Crystals, Brown University, Providence, RI, March 2013
  • Cyclic Sieving of Increasing Tableaux and Small Schröder Paths (poster)
    AlGeCom, IUPUI, Indianapolis, Apr. 2013
  • Cyclic Sieving of Increasing Tableaux and Small Schröder Paths
    Algebra–Geometry–Combinatorics Seminar, UIUC, Feb. 2013
  • Iterating the Stern Sequence
    Presentation from a combinatorial number theory course by Bruce Reznick, UIUC, Feb. 2012
  • G-Cordial Graphs
    Combinatorics Seminar, UIUC, Oct. 2010
  • To Infinity and Beyond and Beyond and Beyond: Inaccessibly Infinite Sets
    Undergraduate Honors Thesis presentation, Oberlin College, May 2010
  • Inaccessibly Infinite Sets
    Senior Symposium, Oberlin College, Apr. 2010
  • Classical and Virtual Pseudodiagrams and New Bounds on Unknotting Numbers and Genus
    Joint Math Meetings, Jan. 2010
  • A Midsummer Knot's Dream
    Oberlin College, Nov. 2009
  • Classical and Virtual Pseudodiagrams and New Bounds on Unknotting Numbers and Genus
    Williams College, Aug. 2009
  • The Arrow Polynomial for Virtual Knots
    UnKnot Conference, Denison University, July 2009
  • When One Becomes Two: Splitting Zero-Divisor Graphs of Rings Into Shiny, New Subgraphs (poster)
    Joint Math Meetings, Jan. 2009
  • When One Becomes Two: Splitting Zero-Divisor Graphs of Rings Into Shiny, New Subgraphs
    Undergraduate Research in Mathematics Conference, Bloomington, IN, Aug. 2008