Secants and Birational Geometry of Toric Varieties
Loughborough UniversityLoughborough, United Kingdom
Course overview
Algebraic geometry studies geometric objects, called algebraic varieties, that are the solution sets of systems of polynomial equations. Algebraic varieties can be thought of as subsets embedded in projective space; the interplay between the intrinsic properties of a variety and the properties of its embedding forms a major theme in classical algebraic geometry. However, many interesting algebraic varieties come with natural embeddings into other ambient spaces, such as toric varieties, and there has been a recent growth of interest in understanding the properties of these embeddings as well.
The aim of this project is to improve our understanding of these issues by studying constructions such as secant varieties in the context of toric embeddings. The results will be applied to study the birational geometry of blowups of toric varieties, giving a clearer picture of the class of Fano-type varieties in higher dimensions. The successful applicant will join the Geometry and Mathematical Physics Research Group, which currently includes 12 permanent academic staff along with several research associates and PhD students.
The group has a vibrant research culture, with activities including weekly research seminars, weekly meetings between students and supervisors, and excellent links with groups in neighbouring institutions. 94% of Loughborough’s research impact is rated world-leading or internationally excellent. REF 2021
Key highlights
- Research on secant varieties within toric embeddings
- Applies results to birational geometry of blowups of toric varieties
- Aims to clarify Fano-type varieties in higher dimensions
- Join a research group of 12 permanent academic staff
- Weekly research seminars and weekly student–supervisor meetings
- Strong links with geometry groups at neighbouring institutions
Entry requirements
- Degree: 2:1 — to include Mathematics
Scholarships
Alumni Bursary
10% of tuition fees which will be credited to the student’s tuition fee account.
Up to 10% of feesAlumni Discount
UK students: £1,500 tuition fee discount for one academic year. International students: £3,000 tuition fee discount for one academic year.
Care Leaver's Scholarship
Excellence Scholarships
UK students: £3,000 off tuition fees; International students: £6,000 off tuition fees which will be credited to the student’s tuition fee account.
International Sports Student Postgraduate Bursary
Our International Sports Student Postgraduate Bursary offers a £12,000 tuition fee discount (set against the tuition fees of your chosen postgraduate taught programme ONLY).
Up to £12,000London 10th Anniversary Award
£5,000 off tuition fees.
Up to £5,000Loughborough Business School Scholarship
£1,500 (UK students) and £3,000 (international students) off tuition fees which will be credited to the student’s tuition fee account.
MBA Progress with Purpose Scholarship
50% of tuition fees which will be credited to the student’s tuition fee account.
Up to 50% of feesQatari Ghanim Al-Muftah Excellence Scholarship
Careers this course leads to
- Postdoctoral researcher in algebraic geometry
- University lecturer in mathematics
- Research mathematician
- Data scientist
- Quantitative analyst
- Cryptographer
Cost of study
UK/Home: £5,238 | International: £23,100
Admission
Applications are made through AHZ at no cost. Share your transcripts, English test scores and personal statement, and your AHZ Counsellor will review your profile, submit your application to Loughborough University, and guide you through interview, offer, CAS and visa — right up to enrolment.
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