To be a postgraduate student here (as a Masters or Ph.D. student), you will need to be formally accepted by the University. Information about the enrollment procedure, academic and English language entry criteria, application forms etc.
I don't have funds available for student support, however you can look at the following link for information about UC's scholarships for postgraduate students.
Before I can support your application to the University as a postgraduate student intending to work with me, I need you to email me the following:
I. Your C.V. (résumé)
II. English Language Test score (IELTS, TOEFL, etc.) if English is not your first language, in which case you should meet the minimum requirements of the University. English requirements
III. Academic transcript(s), GPA (grade-point-average, please include the scale) and rank in your class/department, if available.
IV. Master's thesis or senior thesis, published or accepted papers (journal papers, papers in conference proceedings, technical reports, etc) or preprints, if any.
V. Funding plan (self, government, scholarships, etc).
VI. Your research interests, which should align with mine. Please have a look at my recent preprints on ArXiv and my not so recent preprints page. Also, a lot of my research uses some basic algebraic geometry, so it would help if you have prior exposure to that.
One or two letters of recommendation from your professors, sent directly to me, would be helpful. I might also request further information and perhaps a Skype interview. Please contact me, if you have any questions email@example.com.