University of Virginia

Department of Mathematics

Kerchof Hall, 141 Cabell Drive

Charlottesville, VA 22904

*Email:* obus@virginia.edu

*Office Phone:* 434-924-4930

*Office:* Kerchof 208 (ON LEAVE 2016-17, Office: Warren Weaver Hall 613, Courant Institute)

*About Me:* I am an assistant professor in the Department of
Mathematics at the University of Virginia. For the academic year
2016-17, I am on leave at the Courant Institute. As you can see,
I am also an
artistic visionary in the field of web design.

Here is my CV.

** Publications **

2.

3. Vanishing cycles and wild monodromy

4. Fields of moduli of three-point G-covers with cyclic p-Sylow, I, Algebra Number Theory, 6, no. 5 (2012), 833--883

5. The (local) lifting problem for curves, Proceedings for Conferences in Kyoto "Galois-Teichmüller theory and Arithmetic Geometry" (2012), 359--412

6. Fields of moduli of three-point G-covers with cyclic p-Sylow, II, J. Théor. Nombres Bordeaux 25, no. 3 (2013), 579--633

7. Toward Abhyankar's inertia conjecture for PSL_2(\ell), Proceedings of the Luminy Meeting "Groupes de Galois géométriques et différentiels" (2013), 195--206

8. On Colmez's product formula for periods of CM-abelian varieties, Math. Ann. 356, no. 2 (2013), 401--418

9. Conductors of wild extensions of local fields, especially in mixed characteristic (0, 2), Proc. Amer. Math. Soc. 142 (2014), 1485--1495

10. (with Stefan Wewers) Cyclic extensions and the local lifting problem, Ann. of Math. 180, no. 1 (2014), 233--284

11. (with Stefan Wewers) Wild Ramification Kinks, Res. Math. Sci., 3:21 (2016), 27 pp.

12. The local lifting problem for A_4, Algebra Number Theory, 10, no. 8 (2016), 1683--1693.

13. Good reduction of three-point Galois covers, Algebraic Geometry, 4, no. 2 (2017), 247--262.

14. (with Colin Ingalls, Ekin Ozman, and Bianca Viray) Unramified Brauer Classes on cyclic covers of the projective plane (with an appendix by Hugh Thomas), Proceedings of the AIM Workshop, "Brauer groups and obstruction problems: Moduli and arithmetic," (2017), 115--153.

15. A generalization of the Oort conjecture (60 pp.), Comm. Math. Helv., to appear.

16. (with David Harbater, Rachel Pries, and Kate Stevenson) Abhyankar's conjectures in Galois theory: Current status and future questions (47 pp.), Bull. Amer. Math. Soc., to appear.

17. Lifting of curves with automorphisms (43 pp.), submitted.

18. (with John Doyle, Holly Krieger, Rachel Pries, Simon Rubinstein-Salzedo, and Lloyd West) Reduction of dynatomic curves (47 pp.), submitted.

19. (with Hilaf Hasson) The abc conjecture implies the weak diversity conjecture (6 pp.), submitted

Current Teaching

None

**Former Teaching **

Math 8620 (Algebraic Geometry), Virginia, Fall 2014

Math 7754 (Commutative Algebra), Virginia, Spring 2014

Liberia

I sit on the board of the I-HELP Liberia Project. I will be traveling to Liberia in Summer 2017 with a group representing the organization to help run a two-week STEM teacher training workshop.