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
Mon 9-11, Thu 1-2

Recent publications

Analytic continuation of differential operators and applications to Galois representations

We construct mod p differential operators on automorphic forms on unitary and symplectic groups, and describe their effect on the Galois representations attached to such forms.

E. Eischen, M. Flander, A. Ghitza, E. Mantovan, A. McAndrew

25 pages.

PDF

Some modular abelian surfaces

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

F. Calegari, S. Chidambaram, A. Ghitza

to appear in Mathematics of Computation, 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

ANTS XIII, Proceedings of the 13th Algorithmic Number Theory Symposium, Open Book Series 2, no. 1 (2019), pages 207-220.

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.

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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

2019 Semester 1

Lectures: Mon 8-9, Wed 12-1, Thu 12-1, Fri 2:15-3:15, all in Lyle Theatre (Redmond Barry building)

Consultation: Mon 9-11, Thu 1-2 in Peter Hall 166