# Farbod Shokrieh - Research

MathSciNet profile
arXiv preprints

My work is partially supported by NSF CAREER DMS-2044564

## Publications:

• Jumps in the height of the Ceresa cycle. (with Robin de Jong)

• Tautological cycles on tropical Jacobians. (with Andreas Gross)

• Faltings height and Néron-Tate height of a theta divisor. (with Robin de Jong)

• Tropical moments of tropical Jacobians. (with Robin de Jong)

• Metric graphs, cross ratios, and Rayleigh's laws. (with Robin de Jong)
• Rocky Mountain Journal of Mathematics, Volume 52, Number 4, Pages 1403-1422, 2022.
• abstract | DOI | arXiv | bibtex

• Effective divisor classes on metric graphs. (with Andreas Gross and Lilla Tóthmérész)

• Cycles, cocycles, and duality on tropical manifolds. (with Andreas Gross)

• Limits of canonical forms on towers of Riemann surfaces. (with Hyungryul Baik and Chenxi Wu)
• Journal für die reine und angewandte Mathematik (Crelle's Journal), Volume 764, Pages 287-304, 2020.
• abstract | DOI | arXiv | bibtex

• Canonical measures on metric graphs and a Kazhdan's theorem. (with Chenxi Wu)

• Non-Archimedean and tropical theta functions. (with Tyler Foster, Joseph Rabinoff, and Alejandro Soto)

• Divisors on graphs, binomial and monomial ideals, and cellular resolutions. (with Fatemeh Mohammadi)

• Canonical representatives for divisor classes on tropical curves and the Matrix-Tree Theorem. (with Yang An, Matthew Baker, and Greg Kuperberg)

• Divisors on graphs, connected flags, and syzygies. (with Fatemeh Mohammadi)

• Chip-firing games, potential theory on graphs, and spanning trees. (with Matthew Baker)
• Journal of Combinatorial Theory, Series A, Volume 120, Issue 1, Pages 164-182, 2013.
• abstract | DOI | arXiv | bibtex

• Improved simulation of nondeterministic Turing machines. (with S. Kalyanasundaram, R. J. Lipton, K. W. Regan)

• The monodromy pairing and discrete logarithm on the Jacobian of finite graphs.

## Preprints:

• Torsor structures on spanning trees. (with Cameron Wright)

• A sheaf-theoretic approach to tropical homology. (with Andreas Gross)

## Miscellaneous:

• Oberwolfach report containing the extended abstract of some of my work with Robin de Jong (pages 564-566).

• ### Notes:

• Course notes on Abelian Varieties, scribed by various students in class. Here is another version scribed by Dan Collins.
I have not read or edited either of these notes. I would appreciate any comments or corrections.

• Course notes on Non-Archimedean Geometry, scribed by Daniel Miller.
I have not read or edited the notes. I would appreciate any comments or corrections.

• Short note on Basic von Neumann Algebra Theory. It was written mainly for my own benefit.

• ### Videos:

• Video of my talk on Heights and moments of abelian varieties at Zoom Algebraic Geometry (ZAG) Seminar in November 2021.

• Video of my collaborator's (Robin de Jong) talk on Asymptotic properties of the Ceresa cycle at Institut Mittag-Leffler in November 2021.

• Video of my talk on Graphs and arithmetic geometry at Bay Area Discrete Math Day in April 2021.

• Video of my talk on Matroids and their Jacobians at a BIRS/CMO Workshop in November 2015.

• Video of my talk on Riemann-Roch theory for graphs and tropical curves at a BIRS Workshop in March 2014.

 email: farbod@uw.edu office phone: (206) 543-1916 office: PDL C-443

 Disclaimer: This is not a publication of the UW, and UW has not edited or examined the content.