Andrew Scott Obus

Education

Ph.D., Mathematics, University of Pennsylvania Philadelphia PA

AB, Mathematics, Harvard College Cambridge MA

Books

Obus, A. (2009). Ramification of primes in fields of moduli of three-point covers. (p. 139). ProQuest LLC, Ann Arbor, MI.

Journal Articles

(2023). Conductor-discriminant inequality for hyperelliptic curves in odd residue characteristic. Interational Math. Res. Notices, 13 pp..

Dang, H., Das, S., Karagiannis, K., Obus, A., & Thatte, V. (2022). Local Oort groups and the isolated differential data criterion. JOURNAL DE THEORIE DES NOMBRES DE BORDEAUX, 34(1). 251-269.

(2022). Explicit minimal embedded resolutions of divisors on models of the projective line. Res. Number Theory, 8(2). Paper No. 27, 27.

(2021). Stabilization indices of potentially Mumford curves. 33 pp..

(2021). Superelliptic curves with many automorphisms and CM Jacobians. Math. Comp., 90(332). 2951--2975.

(2020). Explicit resolution of weak wild quotient singularities on arithmetic surfaces. J. Algebraic Geom., 29(4). 691--728.

(2019). Reduction of dynatomic curves. Ergodic Theory Dynam. Systems, 39(10). 2717--2768.

(2018). The $abc$ conjecture implies the weak diversity conjecture. Albanian J. Math., 12(1). 8--14.

(2018). Abhyankar's conjectures in Galois theory: current status and future directions. Bull. Amer. Math. Soc. (N.S.), 55(2). 239--287.

(2017). A generalization of the Oort conjecture. Comment. Math. Helv., 92(3). 551--620.

(2017). Good reduction of three-point Galois covers. Algebr. Geom., 4(2). 247--262.

(2016). The local lifting problem for $A_4$. Algebra Number Theory, 10(8). 1683--1693.

(2016). Wild ramification kinks. Res. Math. Sci., 3. Paper No. 21, 27.

(2014). Conductors of wild extensions of local fields, especially in mixed characteristic $(0,2)$. Proc. Amer. Math. Soc., 142(5). 1485--1495.

(2014). Cyclic extensions and the local lifting problem. Ann. of Math. (2), 180(1). 233--284.

(2013). On Colmez's product formula for periods of CM-abelian varieties. Math. Ann., 356(2). 401--418.

(2013). Fields of moduli of three-point $G$-covers with cyclic $p$-Sylow, II. J. Th'eor. Nombres Bordeaux, 25(3). 579--633.

(2012). Vanishing cycles and wild monodromy. Int. Math. Res. Not. IMRN, (2). 299--338.

(2012). Fields of moduli of three-point $G$-covers with cyclic $p$-Sylow, I. Algebra Number Theory, 6(5). 833--883.

(2010). Wild tame-by-cyclic extensions. J. Pure Appl. Algebra, 214(5). 565--573.

Book Chapters

(2019). Lifting of curves with automorphisms. Open Problems in Arithmetic Algebraic Geometry (pp. 9--59). Int. Press, Somerville, MA.

(2017). Unramified Brauer classes on cyclic covers of the projective plane. Progr. Math. (pp. 115--153). Birkh"auser/Springer, Cham.

(2013). Toward Abhyankar's inertia conjecture for $PSL_2(l)$. S'emin. Congr. (pp. 195--206). Soc. Math. France, Paris.

(2012). The (local) lifting problem for curves. Adv. Stud. Pure Math. (pp. 359--412). Math. Soc. Japan, Tokyo.

Media Contributions

(2020). Notices of the American Mathematical Society.

Presentations

Obus, A. S. (2024, June 20). Mac Lane valuations and Le Borgne's improvement of Ax's theorem.. Recent trends in algebra, geometry, and arithmetic. Vlora, Albania (on Zoom): Research Institute of Science and Technology.

Obus, A. S. (2024, October 20). Mac Lane Valuations and Applications to Conductor-Discriminant Inequalities. Columbia Automorphic Forms and Arithmetic Geometry Seminar. : Columbia University.

Obus, A. S. (2024, November 20). Fun With Mac Lane Valuations. Algebra Seminar. : Wesleyan University.

Obus, A. (2021, January 31). Superelliptic curves with many automorphisms and CM Jacobians. Joint Meetings of the AMS/MAA. Online: American Mathematical Society.

Obus, A. (2021, January 31). Conductor-discriminant inequalities for superelliptic curves. AMS/MAA Joint Meetings. Online: American Mathematical Society.

Obus, A. (2021, November 30). Mac Lane valuations and an application to weak wild quotient singularities. VIASM Algebraic Geometry Seminar. Online: Vietnam Institute for Advanced Studies in Mathematics (VIASM).

Obus, A. (2021, February 28). Fun with Mac Lane valuations. Heilbronn Number Theory Seminar. Online: University of Bristol.

Obus, A. (2020, February 28). Conductor-Discriminant Inequalities for Hyperelliptic Curves. Algebra and Number Theory Seminar. Hanover, NH: Dartmouth College.

Obus, A. (2020, March 31). Superelliptic Curves: Many Automorphisms vs. Complex Multiplication. AMS Southeastern Sectional Meeting (Cancelled). Charlottesville, VA: American Mathematical Society.

Obus, A. (2020, February 28). Characteristic 0 vs. Characteristic p: Galois covers of curves. CUNY Graduate Center Colloquium. CUNY Graduate Center: CUNY Graduate Center.

Obus, A. (2020, January 31). Mac Lane Valuations and an Application to Resolution of Wild Quotient Singularities. Number Theory Seminar. Athens, GA: University of Georgia.

Obus, A. (2019, April 30). Dynatomic curves: the good, the bad, and the irreducible. Colloquium. Dalhousie University, Halifax, Nova Scotia: Dalhousie University.

Obus, A. (2019, April 30). The Life and Mathematics of Évariste Galois. Feliks Gross Award Ceremony. CUNY Graduate Center: CUNY Academy.

Obus, A. (2019, February 28). Fun with Mac Lane valuations. Emory University Algebra Seminar. Atlanta, GA: Emory University.

Obus, A. (2019, February 28). Fun with Mac Lane valuations. Georgia Institute of Technology Algebra Seminar. Atlanta, GA: Georgia Institute of Technology.

Obus, A. (2019, April 30). Conductor-discriminant inequalities for hyperelliptic curves. AMS Spring Sectional Meeting. Hartford, CT: American Mathematical Society.

Obus, A. (2019, April 30). Mac Lane valuations, conductors, and discriminants. Algebra Seminar. Charlottesville, VA: University of Virginia.

Obus, A. (2019, May 31). Fun with Mac Lane Valuations. Algebraic Geometry Seminar. Stony Brook, NY: Stony Brook University.

Obus, A. (2019, June 30). "Abhyankar's conjectures". AMS Math Research Community "Explicit Algebraic Geometry in Characteristic p". Whispering Pines, RI: American Mathematical Society.

Obus, A. (2019, November 30). Conductor-Discriminant Inequalities for Hyperelliptic Curves. Galois Seminar. Philadelphia, PA: University of Pennsylvania.

Obus, A. (2018, April 30). Reduction of dynatomic curves: The good, the bad, and the irreducible. IDA/CCS Colloquium. Bowie, MD: Institute fo Defense Analyses, Center for Computing Sciences.

Obus, A. (2018, September 30). Explicit resolution of weak wild quotient singularities. Algebra Seminar. University of Virginia: Unviersity of Virginia.

Obus, A. (2018, March 31). Reduction of dynatomic curves: The good, the bad, and the irreducible. Ohio State University Number Theory Seminar. Columbus, OH: Ohio State University.

Obus, A. (2018, February 28). Reduction of dynatomic curves: The good, the bad, and the irreducible. Baruch College Special Colloquium. New York, NY: Baruch College (CUNY).

Obus, A. (2018, February 28). Reduction of dynatomic curves: The good, the bad, and the irreducible. Queens College Special Colloquium. Queens, NY: Queens College (CUNY).

Obus, A. (2018, January 31). Abhyankar's conjectures on Galois covers of the affine line; or, if you can't prove that something doesn't exist, does it exist?. Bryn Mawr College Special Colloquium. Bryn Mawr, PA: Bryn Mawr College.

Obus, A. (2018, March 31). Explicit resolution of weak wild quotient singularities. AMS Central Sectional Meeting. Columbus, OH: AMS.

Obus, A. (2018, November 30). Explicit resolution of weak wild quotient singularities. Binghamton University Algebra Seminar. Binghamton, NY: Binghamton University.

Obus, A. (2018, October 31). Conductor-Discriminant inequalities for hyperelliptic curves. AMS Central Sectional Meeting. Ann Arbor, MI: AMS.

Obus, A. (2017, May 31). Hurwitz Trees and Lifting. Simons Symposium on Tropical and Non-Archimedean Geometry. Elmau, Germany: Simons Foundation.

Obus, A. (2017, July 31). Reduction of Dynatomic Curves. Conference on the Algebraic and Analytic Theory of Quadratic Forms. University of Georgia: University of Geoergia.

Obus, A. (2016, September 30). An introduction to frobenioids. Kummer Classes and Anabelian Geometry. University of Vermont: University of Vermont.

Obus, A. (2015, December 31). The local lifting problem for A_4. Conference on Algebraic Geometry. Bangalore, India: ISI-Bangalore.

Obus, A. (2014, June 30). The local lifting problem. AMS/IMU Joint Meetings. Tel Aviv, Israel: AMS/IMU.

Obus, A. (2014, October 31). Cyclic extensions and the local lifting problem. Valuation theory and its applications. Oberwolfach, Germany: Oberwolfach Mathematical Institute.

Obus, A. (2013, June 30). Lifting of cyclic extensions. Arithmetic of Fields. Oberwolfach, Germany: Oberwolfach Mathematical Institute.

Obus, A. (2012, June 30). Cyclic extensions and the local lifting problem. Galois Covers and Deformations. Bordeaux, France: University of Bordeaux.

Obus, A. (2012, June 30). Cyclic extensions and the local lifting problem. Dutch Intercity Number Theory Seminar. University of Utrecht: University of Utrecht.

Obus, A. (2012, February 28). Cyclic extensions and the local lifting problem. Winter School on Galois Theory. Luxembourg: University of Luxembourg.

Obus, A. (2010, March 31). Fields of moduli of three-point covers. Differential and Geometric Galois Theory. Luminy, France: Centre International de Recherche en Mathématiques.

Obus, A. (2010, October 31). Toward the Oort conjecture. Galois Theory and Arithmetic Geometry. Kyoto, Japan: University of Kyoto/RIMS.

Obus, A. (2009, February 28). Fields of moduli of three-point covers. Arithmetic of Fields. Oberwolfach, Germany: Oberwolfach Mathematical Institute.

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