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

*About Me:* I am an assistant professor in the Department of
Mathematics at the University of Virginia. 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, Comm. Math. Helv., 92, no. 3 (2017), 551--620.

16. (with David Harbater, Rachel Pries, and Kate Stevenson) Abhyankar's conjectures in Galois theory: Current status and future questions, Bull. Amer. Math. Soc., 55, no. 2 (2018), 239--287.

17. (with John Doyle, Holly Krieger, Rachel Pries, Simon Rubinstein-Salzedo, and Lloyd West) Reduction of dynatomic curves (47 pp.), Ergodic Theory Dynam. Systems, to appear.

18. Lifting of curves with automorphisms (43 pp.), Questions in Arithmetic Algebraic Geometry (F. Oort, ed.), to appear.

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

20. (with Stefan Wewers) Explicit resolution of weak wild quotient singularities of arithmetic surfaces (30 pp.), preprint.

Current Teaching (Fall 2018)

**Former Teaching **

Math 3351 (Linear Algebra), Virginia, Spring 2018

Math 1320 (Calculus II), Virginia, Summer 2016

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 and am involved in writing the LIberian Math Olympics contests. I traveled to Liberia in the Summers of 2011, 2013, and 2017 with groups representing the organization to help run two-week STEM teacher training workshops.