Pure mathematics

Platonic solids, moduli spaces, and Calabi—Yau structures - Travis Schedler (Imperial College London)

Date: Tuesday 17 March 2020
Time: 2.00pm
Location: Michael Atiyah 119, University of Leicester
Abstract: I will recall how Platonic solids are classified via their symmetry groups. This leads to ADE Dynkin diagrams and in turn to Lie algebras and groups. The link is made by certain moduli spaces of 2-Calabi-Yau algebras. As I will explain, these are local models for the rich geometric spaces appearing in geometry and physics. I will use these to understand singularities of moduli spaces and classify new kinds of symmetries.

Positive Laurent polynomials, critical points, and mirror symmetry (joint work with Jamie Judd) - Konstanze Rietsch (King's College London)

Date: Tuesday 24 March 2020
Time: 2.00pm
Location: Michael Atiyah 119, University of Leicester
Abstract: In mirror symmetry a big role is played by Laurent polynomials. For example, consider the Laurent polynomial  W(x,y) = x+y+q 1/xy which arises as mirror dual to the complex projective plane X. This Laurent polynomial W is an example of the mirror superpotential of a toric symplectic manifold as constructed by Batyrev and Givental in the 1990s. This talk is about Laurent polynomials with coefficients in a field of (generalised) Puiseaux series in a variable q, such as this example W.  In joint work with Jamie Judd we show a positive Laurent polynomial has a unique positive critical point if and only if its Newton polytope has 0 in its interior. One application of this result, using mirror symmetry and work of Fukaya, Oh, Ohta, Ono, and Woodward, is to the construction of non-dispaceable Lagrangians in smoth toric manifolds (resp. orbifolds).