Preprints

Distributing Persistent Homology via Spectral SequencesÁlvaro Torras Casas Abstract: We set up the theory for a distributive algorithm for computing persistent homology. For this purpose we develop linear algebra of persistence modules. We present bases of persistence modules, and give motivation as for the advantages of using them. Our focus is on developing efficient methods for the computation of homology of chains of persistence modules. Later we give a brief, self contained presentation of the MayerVietoris Spectral sequence. Then we study the Persistent MayerVietoris Spectral Sequence and present a solution to the extension problem. Finally we outline applications of our results for VietorisRips complexes, cubical complexes and \(\alpha\)complexes. 
Code

PerMaViss: Persistence Mayer Vietoris spectral sequenceÁlvaro Torras Casas This is an implementation of the Persistence Mayer Vietoris spectral sequence for computing persistent homology. For complete documentation, see permaviss.readthedocs.io. Visit the repositiory here PerMaViss. 
Talks
The Persistence MayerVietoris spectral sequence, University of Oxford, Topological Data Analysis seminar, 1st November.
Persistent Homology for Large Datasets, MS50 Numerical Methods to advance Mathematical biology research (part 2), EnuMath2019, Egmond aan Zee, The Netherlands, 30th September  4th October.
InputDistributive Persistent Homology, YTM 2019, EPFL, 22nd  26th July.
InputDistributive Persistent Homology, ECTR 2019, University of Sheffield, 6th of June 2019.
InputDistributive Persistent Homology, Guest talk at Topology Seminar, Universitat de Barcelona, 29th of May 2019.
InputDistributive Persistent Homology, 2019 Welsh Mathematical Colloquium, Gregynog Hall, 21st of May 2019.
InputDistributive Persistent Homology, GAPT seminar, Cardiff University, 21st of March 2019.
Distributing Persistent Homology using Spectral Sequences, Postgraduate Seminar, University of Leicester, 5th of December 2018.
Distributing Cohomology Computations via Sheaf Cohomology, 2018 Welsh Mathematical Colloquium, Gregynog Hall, 22nd of May 2018.
Teaching at Cardiff University
Autumn 2019, Tutor in Geometry.
Spring 2019, Tutor in Foundations II.
Spring 2019, Tutor in Finance I.
Autumn 2018, Tutor in Geometry.
Autumn 2017, Tutor in Linear Algebra.
Additionally, I am a regular tutor in Maths Support. This is a dropin service where students with mathematical questions can get help. This is provided by the Cardiff University School of Mathematics.
Grants
EPSRC studenship reference EP/N509449/1 number 1941653. Project: Persistent Sheaf Cohomology. Start 01/10/2017 end 31/03/2021.
Santander Master's Scholarship Award 20161017, University of Leicester. £5000 towards reducing student fees.