Ismael Morales

Status

Postgraduate Student

https://sites.google.com/view/ismaelmorales/

Research groups

Address

Mathematical Institute
University of Oxford
Andrew Wiles Building
Radcliffe Observatory Quarter
Woodstock Road
Oxford
OX2 6GG

Major / recent publications

Prosolvable rigidity of surface groups (with Andrei Jaikin-Zapirain).
https://arxiv.org/abs/2312.12293
The Hanna Neumann Conjecture for graphs of free groups with cyclic edge groups (with Sam Fisher).
https://arxiv.org/abs/2311.12910
Profinite properties of residually free groups.
https://arxiv.org/abs/2306.13082
Virtual homology of limit groups and profinite rigidity of direct products (with Jonathan Fruchter).
https://arxiv.org/abs/2209.14925
On the profinite rigidity of free and surface groups. Math. Ann., 2024.
Parafree graphs of groups with cyclic edge groups (with Andrei Jaikin-Zapirain). J. Lond. Math. Soc., 2024.

Research interests

I study questions relating L^2 Betti numbers, residual properties of groups and profinite invariants. I am working under the supervision of Dawid Kielak and Richard Wade.

Prizes, awards, and scholarships

Oxford-Cocker Graduate Scholarship (since October 2021).

Teaching

M21 - Teaching assistant for B1.1 Logic.

H22 - TA for B1.2 Set Theory.

M22 - TA for two classes of C1.1 Model Theory.

H23 - Tutor for B1.1 Logic.

H23 - Tutor for C8.4 Probabilistic Combinatorics.

H23 - Tutor of the Williams College Oxford Programme for Non-commutative Algebra.

M23 - Tutor for two classes of B3.1 Galois Theory

H24 - Tutor for two classes of B3.4 Algebraic Number Theory