Singapore University of Technology and Design, Information Systems Technology and Design

Position ID: 2464-POSTDOC1 [#15712]
Position Title: Math Research Fellow
Position Type: Postdoctoral
Position Location: Singapore, Singapore 487372, Singapore
Subject Areas: Algebraic/geometric/topological combinatorics, commutative algebra, discrete geometry, tropical geometry
Application Deadline: 2020/04/15help popup (posted 2020/02/20)
Position Description:    

SUTD was established in 2009 as a collaboration with MIT, and has recently in 2018 topped the list of emerging engineering schools in the world. At SUTD, there is a strong emphasis on interdisciplinary and collaborative research. Our unconventional naming of departments (or pillars) is a reflection of our philosophy that impactful research would naturally encompass multiple disciplines. SUTD is located in Singapore, a multiracial multicultural country, where English is the main language used in all schools and most workplaces, especially among people of different races.

We are seeking a highly motivated research fellow for research in algebraic/geometric/topological combinatorics, with a focus either on the combinatorics of simplicial complexes and polyhedral complexes from a rigidity-theoretic perspective; or on the face enumeration of simplicial manifolds from an algebraic perspective. The candidate is not required to have prior knowledge of rigidity theory, but must be willing to learn some rigidity theory.

For this project, we are interested in various algebraic, combinatorial, and topological aspects of several classes of simplicial complexes, so there are multiple possible research directions to pursue. A key starting point would be an explicit construction we already have, of an algebra structure on stress spaces of simplicial complexes. We would like to extend this "stress algebra" structure to polyhedral complexes, and better understand its connections to Stanley-Reisner rings, McMullen's polytope algebras, and tropical intersection rings. For this research direction, the candidate should ideally have experience in combinatorial commutative algebra, but is not required to have any prior knowledge of stresses and rigidity theory. Another direction is to understand the face enumeration of simplicial manifolds, from a rigidity-theoretic perspective. Similarly, prior knowledge of rigidity theory is not required, although the candidate is expected to have some experience working either with simplicial manifolds, or with f-vectors. Yet another direction is to better understand how the Betti numbers of simplicial manifolds influence face enumeration.

Duration of position: 3 years.
  • Required: PhD degree in mathematics.
  • The candidate should ideally have experience/interests in at least one of the following specific research areas:
    • Combinatorial and topological aspects of simplicial complexes
    • Combinatorial aspects of polytopes and polyhedral complexes
    • f-vector theory (inc. Stanley-Reisner rings of various classes of simplicial complexes)
    • Rigidity theory
    • Commutative algebra
    • Tropical geometry, intersection theory
Interested candidates should submit a cover letter, a current CV, as well as arrange for two reference letters. The candidate should ideally start as soon as possible, but the starting date is negotiable. Any queries can be sent directly to Ernest Chong (ernest_chong@sutd.edu.sg) with the email subject header "Math Research Fellow position".

Application Materials Required:
Submit the following items online at this website to complete your application:
Further Info:
www.sutd.edu.sg
 
8 Somapah Rd, #05-101
Building 1, Level 5
Singapore 487372

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