Alex Ghitza

Senior Lecturer in Pure Mathematics

University of Melbourne

I am a senior lecturer 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 interested in computational aspects of number theory, algebraic geometry, representation theory, and other algebraic topics.

aghitza@alum.mit.edu
Peter Hall 166
School of Mathematics and Statistics, University of Melbourne, Parkville VIC 3010, Australia
Tue 11-12, Tue 3:15-4:15, Fri 1-2

Recent publications

Some modular abelian surfaces

We give explicit examples of modular abelian surfaces with trivial endomorphisms.

F. Calegari, S. Chidambaram, A. Ghitza

7 pages.

PDF

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

Geometric construction of the renormalised Atkin-Lehner operator modulo p

A. Ghitza

to appear in Transactions of the American Mathematical Society, 5 pages.

PDF

Differential operators on modular forms (mod p)

Survey of differential operators on mod p modular forms and effect on Galois representations

A. Ghitza

to appear in the proceedings of the workshop Analytic and Arithmetic Theory of Automorphic Forms, RIMS Kokyuroku, 13 pages.

PDF

Analytic evaluation of Hecke eigenvalues for Siegel modular forms of degree two

We compute Hecke eigenvalues of Siegel modular forms by numerical analytic methods.

O. Colman, A. Ghitza, N. Ryan

to appear in the proceedings of the 13th Algorithmic Number Theory Symposium ANTS-XIII (2018), 14 pages.

PDF Code

Computational Mathematics with SageMath

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

SIAM (2018), xiv+464 pages.

PDF

Number theory seminar

Intro to stacks: groupoids, continuous families

Alex Ghitza

Wed 15 Aug 2018 at 11am in Peter Hall 107

Current teaching

MAST10008 Accelerated Mathematics 1

2018 Semester 1

Lectures: Tue 9-11 in Rivett Theatre (Redmond Barry building), Wed 4:15-5:15 in Lyle Theatre (Redmond Barry building), Fri 12-1 in Rivett Theatre (Redmond Barry building)

Consultation: Tue 11-12, Tue 3:15-4:15, Fri 1-2 in Peter Hall 166

MAST30005 Algebra

2018 Semester 1

Lectures: Mon 12-1 in Old Geology 1, Wed 12-1 in Russell Love (Peter Hall building), Fri 10-11 in Old Geology 1

Consultation: pre-exam consultation: Fri 1 June 12-2, Fri 8 June 12-2, Wed 13 June 12-2, all in Peter Hall G38