I am an associate professor in Pure Mathematics at the University of Melbourne, in Australia. My research is in arithmetic algebraic geometry, an area at the intersection of number theory and algebraic geometry. I am also keenly interested in computational aspects of both number theory and algebraic geometry.
I am part of the Number Theory Group, and of Number Theory Down Under.
Anna Medvedovsky and I taught a short course on Galois representations and modular forms at the Introduction to SAGA research school at Luminy in early 2023.
Chenyan Wu and I organised the 2020 Number Theory Down Under meeting.
email -- arXiv -- orcid -- github -- bitbucket -- google scholar
Consultation: 15-20 minutes after each lecture, at the lecture theatre; Thursdays 10:30-11:30 and Fridays 11:30-12:30 in my office (Peter Hall 166).
Mailing address: Alex Ghitza, School of Mathematics and Statistics, The University of Melbourne, Parkville VIC 3010, Australia
Recent publications (more here)
- S. Anni, A. Ghitza, A. Medvedovsky, Deep congruences + the Brauer-Nesbitt Theorem, 23 pages.
- A. Ghitza, T. Yamauchi, Automorphy of mod 2 Galois representations associated to certain genus 2 curves over totally real fields, 17 pages.
- A. Ghitza, Effective computation of Kurihara numbers, Appendix to 'Indivisibility of Kato's Euler systems and Kurihara numbers' by Chan-Ho Kim, in Proceedings of the workshop Algebraic Number Theory and Related Topics 2018, RIMS Kokyuroku Bessatsu B86 (2021), 63-86.
- E. Eischen, M. Flander, A. Ghitza, E. Mantovan, A. McAndrew, Differential operators mod p: analytic continuation and consequences, Algebra and Number Theory 15, no. 6 (2021), 1469-1504
- F. Calegari, S. Chidambaram, A. Ghitza, Some modular abelian surfaces, Math. Comp. 89 (2020), 387-394.
- A. Ghitza, The Atkin-Lehner automorphism mod p geometrically, Appendix to 'Newforms mod p in squarefree level, with applications to Monsky's Hecke-stable filtration' by S. V. Deo and A. Medvedovsky, Trans. Amer. Math. Soc. Ser. B 6 (2019), 245-273.
- A. Ghitza, Differential operators on modular forms (mod p), Proceedings of the workshop Analytic and Arithmetic Theory of Automorphic Forms, RIMS Kokyuroku No. 2100 (2019), 52-64.
- O. Colman, A. Ghitza, N. Ryan, Analytic evaluation of Hecke eigenvalues for Siegel modular forms of degree two, ANTS XIII, Proceedings of the 13th Algorithmic Number Theory Symposium, Open Book Series 2, no. 1 (2019), 207-220.
- P. Zimmermann, A. Casamayou, N. Cohen, G. Connan, T. Dumont, L. Fousse, F. Maltey, M. Meulien, M. Mezzarobba, C. Pernet, N. M. Thiéry, E. Bray, J. Cremona, M. Forets, A. Ghitza, H. Thomas, Computational Mathematics with SageMath, SIAM (2018), xiv+464 pages.