Mathematical sciences

Mathematical sciences


Host Department
Department of Mathematics



Research Topic B

Abstract of the proposed UNIPhD research project


The Deligne-Mumford compactified moduli space categorizes stable algebraic curves with marked points, crucial in algebraic geometry for intersection theory. Its cohomology ring, too intricate to explore entirely, leads us to focus on the more manageable tautological ring. This subring derives from natural geometric elements within the moduli space, generated by psi and kappa classes. The aim is to uncover all tautological relations among these generators.

Our project centers on conjectured tautological relations, potentially verifying the strong DR/DZ equivalence conjecture. This conjecture posits a deep connection between different integrable hierarchies within cohomological field theories (CohFTs). While verified for simpler CohFTs and specific Gromov-Witten theory cases, we seek to provide more evidence and potentially prove this equivalence. Furthermore, expanding the investigation to include generalizations, such as homotopy CohFTs, quantum and super hierarchies associated with a CohFT, opens up an exciting path for further development.



Short bio

I was born in Malaysia and am currently a Ph.D. student in mathematics, specializing in arithmetic and complex algebraic geometry. Previously, I pursued my master’s degree in mathematical physics in France, working on cohomological field theory and Givental’s theory under the guidance of Prof Guido Carlet. My academic journey began with a bachelor’s degree in physics in Malaysia, where my focus was on the differential geometric structures of general relativity and cosmology.
My interest has always revolved around the mathematical foundations that underpin modern theoretical physics. Currently, my research goal is to better comprehend the enigmatic relationship between enumerative geometry and integrable systems. It is an exciting topic to study as it offers powerful mathematical results as well as important implications for string theory and quantum gauge theory. Beyond intellectual interests, I enjoy group treks and playing sports, meeting people from diverse cultures, and attending retreats during my spare time.

Topic assigned to
Ishan Singh


Project documents