David Jensen

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Dave Jensen with his favorite graph
University of Kentucky
Department of Mathematics
719 Patterson Office Tower
Lexington, KY 40506-0027


Office:  POT 733
Publications and Preprints

Research Papers

33.  The Embedding Theorem in Hurwitz-Brill-Noether Theory
with K. Cook-Powell, Eric Larson, Hannah Larson and Isabel Vogt, submitted.

32.  Sliding Block Puzzles with a Twist: On Segerman's 15+4 Puzzle
with P. Garcia, A. Hanson and N. Owen, submitted.

31.  Tropical Linear Series and Tropical Independence
with S. Payne, submitted.

30.  The Nonabelian Brill-Noether Divisor on M_13 and the Kodaira Dimension of R_13
with S. Payne and G. Farkas, Geometry and Topology (to appear).

29.  Tropical Methods in Hurwitz-Brill-Noether Theory
with K. Cook-Powell, Advances in Mathematics, 398 (2022)..

28.  The Kodaira Dimensions of M_22 and M_23
with S. Payne and G. Farkas, submitted.

27.  A New Lower Bound on Graph Gonality
with M. Harp, E. Jackson, and N. Speeter, Discrete Applied Mathematics, 309 (2022), 172-179.

26.  Scrollar Invariants of Tropical Curves
with K. Sawyer, submitted.

25.  The Motivic Zeta Functions of a Matroid
with M. Kutler and J. Usatine, Journal of the London Mathematical Society, (2020).

24.  Components of Brill-Noether Loci for Curves with Fixed Gonality
with K. Cook-Powell, Michigan Math Journal (2021), 1-27.

23.  Brill-Noether Theory for Curves of a Fixed Gonality
with D. Ranganathan, Forum of Mathematics, Pi, 9 (2021), 1-33.
a video of me speaking about this result can be found here.

22.  Brill-Noether Theory of Curves on P1xP1: Tropical and Classical Approach
with F. CoolsM. D'Adderio and M. Panizzut, Algbebraic Combinatorics 2 (3), 323-341.

21.  Combinatorial and Inductive Methods for the Tropical Maximal Rank Conjecture
with S. Payne, Journal of Combinatorial Theory, Series A, 152 (2017), 138-158.

20.  Gonality of Expander Graphs
with Neelav Dutta, Discrete Mathematics, 341(9) (2018), 2535–2543.

19.  Tropicalization of Theta Characteristics, Double Covers, and Prym Varieties
with Yoav Len, Selecta Mathematica, (2018).

18.  Tropical Independence II:  The Maximal Rank Conjecture for Quadrics
with S. Payne, Algebra and Number Theory, 10(8), (2015).
a video of me speaking about this result can be found here.

17.  Toric Graph Associahedra and Compactifications of M_{0,n}
with R. Ferreira da Rosa and D. Ranganathan, Journal of Algebraic Combinatorics, 43(1), (2015).

16.  Realization of Groups with Pairing as Jacobians of Finite Graphs
with L. Gaudet, D. Ranganathan, N. Wawrykow and T. Weisman, Annals of Combinatorics 22, 781-801 (2018).

15.  Gonality of Random Graphs
with A. Deveau, J. Kainic and D. Mitropolsky,
Involve, a Journal of Mathematics, 9-4 (2016), 715-620.  DOI 10.2140/involve.2016.9.715

14.  The Locus of Brill-Noether General Graphs is not Dense
Portugalia Mathematica, 73 (2016).

13.  Lifting Divisors on a Generic Chain of Loops
with D. Cartwright and S. Payne, Canadian Mathematical Bulletin, 58 (2015)

12.  Tropical Independence I:  Shapes of Divisors and a Proof of the Gieseker-Petri Theorem
with S. Payne, Algebra and Number Theory, 8 (2014)
a video of me speaking about this result can be found here.

11.  A Simplicial Approach to Effective Divisors in \bar{M}_{0,n}
with B. Doran and N. Giansiracusa, International Mathematics Research Notices, 2 (2017).

10.  Veronese Quotient Models of \bar{M}_[0,n} and Conformal Blocks
with A. Gibney, H. Moon, and D. Swinarski, Michigan Mathematical Journal, 62 (2013)

9.  Towards a Tropical Proof of the Gieseker-Petri Theorem
with V. Baratham, C. Mata, D. Nguyen, and S. Parekh, Collectanea Mathematica 65 (2014), 17-27.

8.  Log Canonical Models and Variation of GIT for Genus Four Canonical Curves
with S. Casalaina-Martin and R. Laza, Journal of Algebraic Geometry 23 (2014), 727-764

7.  GIT Compactifications of M_{0,n} and Flips
with N. Giansiracusa and H. Moon, Advances in Mathematics 248 (2013), 242-278.

6.  Stability of Second Hilbert Points of Canonical Curves
with M. Fedorchuk, International Mathematics Research Notices (2012)

5.  The Geometry of the Ball Quotient Model of the Moduli Space of Genus Four Curves
with S. Casalaina-Martin and R. Laza, Compact Moduli Spaces and Vector Bundles, Contemp. Math. 564 (2012)

4.  Rational Fibrations of \bar{M}_{5,1} and \bar{M}_{6,1}
Journal of Pure and Applied Algebra 216 (2012), 633-642.

3.  Birational Contractions of \bar{M}_{3,1} and \bar{M}_{4,1}
Transactions of the American Math Society 365 (2013), 2863-2879.

2.  Completions of UFDs with Semi-Local Formal FIbers
Communications in Algebra, 34, 347-360 (2006)

1.  Controlling Formal Fibers of Principal Prime Ideals
with A. Dundon, S. Loepp, J. Provine and J. Rodu
, Rocky Mountain Journal of Mathematics, 37, 1871-1891 (2007)

Expository Papers

4.  Chip Firing and Algebraic Curves
Notices of the AMS, 1875-1881 December (2021)

3.  Recent Developments in Brill-Noether Theory
with S. Payne, to appear.

2.  What to Expect at a Large Public Research University
with C. Manon, Notices of the AMS, 813-814 June/July (2020)

1.  Degeneration of Linear Series From the Tropical Point of View and Applications
with M. Baker, Proceedings of the Simons Symposium on Nonarchimedean Geometry.