### Writings:

Click buttons to reveal abstracts.† denotes undergraduate mentee.

See also, Google Scholar and MathSciNet (subscription required).

- Path-cordial abelian groups
(with Rebecca Patrias)

Submitted, 8 pages.

arXiv:2006.13764

- Gröbner geometry of Schubert polynomials through ice
(with Zachary Hamaker and Anna Weigandt)

Submitted, 22 pages.

arXiv:2003.13719

- Proof of the Cameron and Fon-Der-Flaass periodicity conjecture
(with Rebecca Patrias)

Submitted, 6 pages.

arXiv:2003.13152

- K-theoretic crystals for set-valued tableaux of rectangular shapes
(with Travis Scrimshaw)

Submitted, 19 pages.

arXiv:1904.09674

- Crystal structures for symmetric Grothendieck polynomials
(with Cara Monical and Travis Scrimshaw)

Submitted, 47 pages.

arXiv:1807.03294

- Asymmetric function theory
(with Dominic Searles)

*Schubert Calculus and Its Applications in Combinatorics and Representation Theory*, Springer

Proceedings of the International Festival in Schubert Calculus (Guangzhou, China, 2017), to appear, 38 pages.

arXiv:1904.01358

- Polynomials from combinatorial \(K\)-theory
(with Cara Monical and Dominic Searles)

*Canadian Journal of Mathematics*, to appear, 35 pages.

arXiv:1806.03802

- Derivatives of Schubert polynomials and proof of a determinant conjecture of Stanley
(with Zachary Hamaker, David Speyer, and Anna Weigandt)

*Algebraic Combinatorics***3**(2), 2020, 301-307.

arXiv:1812.00321

- The genomic Schur function is fundamental-positive

*Annals of Combinatorics***24**(1), 2020, 95-108.

arXiv:1810.04727

- Doppelgängers: bijections of plane partitions
(with Zachary Hamaker, Rebecca Patrias, and Nathan Williams)

*International Mathematics Research Notices***2020**(2), 2020, 487-540.

arXiv:1602.05535

- Decompositions of Grothendieck polynomials
(with Dominic Searles)

*International Mathematics Research Notices***2019**(10), 2019, 3214-3241.

arXiv:1611.02545

- Unique rectification in \(d\)-complete posets: towards the \(K\)-theory of Kac-Moody flag varieties
(with Rahul Ilango
^{†}and Michael Zlatin^{†})

*Electronic Journal of Combinatorics***25**(4), 2018, 1-35.

arXiv:1805.02287

- Orbits of plane partitions of exceptional Lie type
(with Holly Mandel)

*European Journal of Combinatorics***74**, 2018, 90-109.

arXiv:1712.09180

- Deformed cohomology of flag varieties
(with Dominic Searles)

*Mathematical Research Letters*,**25**, 2018, 649-657.

arXiv:1410.8070

- Rhombic tilings and Bott-Samelson varieties
(with Laura
Escobar, Bridget Tenner, and Alexander Yong)

*Proceedings of the American Mathematical Society***146**, 2018, 1921-1935.

arXiv:1605.05613

- Promotion of increasing tableaux: frames and homomesies

*Electronic Journal of Combinatorics***24**(3), 2017, 1-14.

arXiv:1702.01358

- Genomic tableaux
(with Alexander Yong)

*Journal of Algebraic Combinatorics***45**, 2017, 649-685.

arXiv:1603.08490

- Resonance in orbits of plane partitions and increasing tableaux
(with Kevin Dilks and Jessica Striker)

*Journal of Combinatorial Theory, Series A***148**, 2017, 244-274.

arXiv:1512.00365

- Equivariant
*K*-theory of Grassmannians II: the Knutson-Vakil conjecture (with Alexander Yong)

*Compositio Mathematica***153**, 2017, 667-677.

arXiv:1508.00446

- Equivariant
*K*-theory of Grassmannians (with Alexander Yong)

*Forum of Mathematics, Pi***5**, 2017, 1-128.

arXiv:1506.01992

*K*-theoretic Schubert calculus and applications

Ph.D. Thesis, University of Illinois at Urbana-Champaign, 2016, 255 pages.

- Proofs and generalizations of
a homomesy conjecture of Propp
and Roby
(with Jonathan Bloom and Dan Saracino)

*Discrete Mathematics***339**, 2016, 194-206.

arXiv:1308.0546

- Genomic tableaux and combinatorial
*K*-theory (with Alexander Yong)

*Discrete Mathematics and Theoretical Computer Science Proceedings***FPSAC`15**, 2015, 37-48. FPSAC 2015, Daejeon, Korea.

- Cyclic sieving of increasing
tableaux and small Schröder paths

*Journal of Combinatorial Theory, Series A***125**, 2014, 357-378.

arXiv:1209.1355

- Generalized graph cordiality
(with Jennifer Wise)

*Discussiones Mathematicae Graph Theory***32**(3), 2012, 557-567.

- A midsummer knot's dream
(with Allison Henrich, Noel MacNaughton, Sneha Narayan, Robert Silversmith, and Jennifer Townsend)

*College Mathematics Journal***42**(2), 2011, 126-134.

arXiv:1003.4494

- Classical and virtual pseudodiagram
theory and new bounds on unknotting numbers and genus
(with Allison Henrich, Noel MacNaughton, Sneha Narayan, and Jennifer Townsend)

*Journal of Knot Theory and Its Ramifications***20**(4), 2011, 625-650.

arXiv:0908.1981

- Large cardinals

Undergraduate Honors Thesis, Oberlin College, 2010

- Zero-divisor ideals and realizable zero-divisor graphs
(with Michael Axtell, Joe Stickles,
*et al.*)

*Involve***2**(1), 2009, 17-27.

- The nilradical and non-nilradical graphs of commutative
rings
(with Abigail Bishop, Thomas Cuchta and Kathryn Boddie)

*International Journal of Algebra***2**(20), 2008, 981-994.

- Effects of temperature, salinity, and air exposure on development
of the estuarine pulmonate gastropod
*Amphibola crenata*(with Islay Marsden and Jan Pechenik)

*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**Gröbner geometry of Schubert polynomials through ice**

AMS Sectional Meeting, Special Session on Combinatorics Related to Geometry and Representation Theory, University of Virginia, Charlottesville, VA, Mar. 2020*K*-theoretic Schubert calculus

Special Colloquium, Indiana University–Purdue University Indianapolis, Feb. 2020*K*-theoretic Schubert calculus

Special Colloquium, University of Massachusetts Lowell, Jan. 2020*K*-theoretic Schubert calculus

Special Colloquium, University of Waterloo, Jan. 2020**Gröbner geometry of Schubert polynomials through ice**

Joint Mathematics Meetings (Denver, CO), Special Session on Combinatorial Structures and Integrable Systems, 15 Jan. 2020*K*-theoretic Schubert calculus

Special Colloquium, Michigan State University, Jan. 2020*K*-theoretic Schubert calculus

Special Colloquium, University of California, San Diego, Nov. 2019*K*-theoretic Schubert calculus

Special Colloquium, University of Auckland, Oct. 2019**Gröbner geometry of Schubert polynomials through ice**

Algebra, Geometry and Combinatorics Day (AlGeCom) XVIII, Washington University in St. Louis, Sept. 2019(poster)*K*-theoretic polynomials

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**(poster)*K*-theory of Grassmannians

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**(poster)*K*-theory of Grassmannians

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