# Joe Rabinoff's Homepage

## Personal Information

I am an assistant professor in mathematics at the Georgia Institute of Technology. My research is in arithmetic and algebraic geometry, in particular in the interplay between non-Archimedean analytic spaces, tropical geometry, and classical algebraic geometry. I am supported by NSF DMS-1601842.

**Address**:

School of Mathematics

Georgia Institute of Technology

686 Cherry Street

Atlanta, GA 30332-0160

**Email**:

**Office**: Skiles 221

**Curriculum Vitæ**: CV

## Research and Publications

### Papers and Preprints

- Eric Katz, Joseph Rabinoff, and David Zureick-Brown,
*Diophantine and tropical geometry, and uniformity of rational points on curves*, 49 pages. Submitted. - Walter Gubler, Joseph Rabinoff, and Annette Werner,
*Tropical skeletons*, 42 pages. Submitted. - Eric Katz, Joseph Rabinoff, and David Zureick-Brown,
*Uniform bounds for the number of rational points on curves of small Mordell–Weil rank*, 40 pages. To appear in the Duke Mathematical Journal. - Walter Gubler, Joseph Rabinoff, and Annette Werner,
*Skeletons and Tropicalizations*, 46 pages. To appear in Advances in Mathematics. - Matthew Baker and Joseph Rabinoff,
*The skeleton of the Jacobian, the Jacobian of the skeleton, and lifting meromorphic functions from tropical to algebraic curves*, Int. Math. Res. Not. IMRN**16**(2015), 7436–7472, 36 pages. - Omid Amini, Matthew Baker, Erwan Brugallé, and Joseph Rabinoff,
*Lifting harmonic morphisms I: metrized complexes and Berkovich skeleta*, Res. Math. Sci.**2**(2015), Art. 7, 67 pages. - Omid Amini, Matthew Baker, Erwan Brugallé, and Joseph Rabinoff,
*Lifting harmonic morphisms II: tropical curves and metrized complexes*, Algebra Number Theory**9**(2015), no. 2, 267–315, 48 pages. - Mihran Papikian and Joseph Rabinoff,
*Optimal quotients of Jacobians with toric reduction and component groups*, 19 pages. To appear in the Canadian Journal of Mathematics. - Brian Osserman and Joseph Rabinoff,
*Lifting non-proper tropical intersections*, Tropical and Non-Archimedean Geometry, 15–44, Contemp. Math., 605, Amer. Math. Soc., Providence, RI, 2013, 29 pages. - Matthew Baker, Sam Payne, and Joseph Rabinoff,
*On the structure of non-archimedean analytic curves*, Tropical and Non-Archimedean Geometry, 93–121, Contemp. Math., 605, Amer. Math. Soc., Providence, RI, 2013, 28 pages. - Matthew Baker, Sam Payne, and Joseph Rabinoff,
*Nonarchimedean geometry, tropicalization, and metrics on curves*, 37 pages. To appear in Algebraic Geometry (Foundation Compositio Mathematica). - Joseph Rabinoff,
*Tropical analytic geometry, Newton polygons, and tropical intersections*, Adv. Math.**229**(2012), 3192–3255, 63 pages. - Joseph Rabinoff,
*Higher-level canonical subgroups for p-divisible groups*, J. Inst. Math. Jussieu**11**(2012),*no. 2*, 363–419, 56 pages. - Joseph Rabinoff,
*Hybrid grids and the Homing Robot*, Discrete Appl. Math**140**(2004),*no. 1–3*, 155–168, 13 pages. [From the Duluth REU.]

### Expository Articles

*The theory of Witt vectors*, a write-up of various "well-known" results about Witt vectors.*The Bruhat-Tits building of a p-adic Chevalley group and an application to representation theory*, my senior thesis at Harvard University.

## Teaching

### Current

- Math 4107, Abstract Algebra I, Spring 2016.

### Previous

- Math 6421, Algebraic Geometry I, Fall 2015.
- Math 4803/8803, Introduction to Algebraic Number Theory, Fall 2015.
- Math 4108, Abstract Algebra II, Spring 2015.
- Here are the lecture notes and homework for
*Unique Factorization and Fermat's Last Theorem*, a course I taught at the Canada/USA Mathcamp in the summer of 2012.

Please see my CV for a full list of my teaching experience.

## Non-math

### Horology

- My revised notes on H.R. Playtner's 1910 paper,
*An Analysis of the Lever Escapement*.