Research

I am broadly interested in algebraic geometry. Most of my time is spent thinking about Cremona groups, Galois cohomology, Fano varieties, groups acting on varieties, and representation theory. At the moment, I am working on a large project to classify the symmetries of del Pezzo surfaces.

Publications and Preprints

1. J. M. Smith, Groups acting on cubic surfaces in characteristic zero, 2024. Submitted. arXiv:2401.15735

2. J. M. Smith, Automorphisms of quartic del Pezzo surfaces in characteristic zero , 2023. Submitted. arXiv:2308.07904

Invited Talks

1. Finite subgroups of the Cremona group, at the Algebraic Geometry Seminar at the University of Georgia (October 2023). (Slides)

2. Automorphisms of del Pezzo surfaces over number fields, at the AMS Special Session on Brauer Groups in Algebraic Geometry and Arithmetic III at the University of Cincinnati (April 2023). (Slides)

Contributed Talks

1. Methods to determine the symmetries of cubic surfaces, at the Graduate Colloquium Series at UofSC (February 2024). (Notes)

2. Automorphisms of del Pezzo surfaces in characteristic zero, at Algebraic Geometry Northeastern Series at the University of Pennsylvania (October 2023).

3. Automorphisms of del Pezzo surfaces over number fields, at Arithmetic Geometry and Algebraic Groups at the University of Virginia (May 2023). (Slides)

4. Automorphisms of del Pezzo surfaces over number fields, at the Georgia Algebraic Geometry Symposium at the University of Georgia (April 2023).

5. Automorphisms of del Pezzo surfaces, at the Binghamton University Graduate Combinatorics, Algebra, and Topology Conference at Binghamton University (November 2022).

6. Automorphisms of del Pezzo surfaces, at the Graduate Colloquium Series at UofSC (October 2022). (Notes)

Other Miscellaneous Talks

1. The field of moduli, at the Graduate Colloquium Series at UofSC (November 2023). (Notes)

2. Contractions, flips, and termination of the MMP, at the learning seminar on the Minimal Model Program at UofSC (November 2023). (Notes for the first session. Notes for the second session.)

3. A Riemann-Roch theorem for graphs, at the AGCANT student seminar at UofSC (September 2023).

4. An equivariant birational invariant, at the AGCA student seminar at UofSC (February 2023).

5. Invariant theory case studies, at the seminar on geometric invariant theory at UofSC (September 2022).

6. Diagonalizable groups, at the linear algebraic groups seminar at UofSC (July 2022).

7. Actions of algebraic groups on varieties, at the linear algebraic groups seminar at UofSC (May 2022).

8. Understanding forms with Galois cohomology, at the AGCA student seminar at UofSC (February 2022).

9. Introduction to Galois cohomology, at the AGCA student seminar at UofSC (November 2021).

10. Birational geometry of the projective plane, at the AGCA student seminar at UofSC (October 2021).

11. The character of a representation, at the representation theory seminar at UofSC (June 2021). (Slides for the first session)

12. An introduction to Weil divisors, at the AGNT seminar at UofSC (April 2021).