Participant Talks

A limited number of participants will have the opportunity to give twenty-minute talks presenting their research. If you would like to give a talk, please contact us with a title and an abstract. All participants, including those giving talks, should still consider contributing posters.

Victoria Hoskins, Stratifications by Harder-Narasimhan types

We firstly review a stratification of a complex projective scheme with a reductive group action and ample linearisation such that the GIT semistable subscheme is the open stratum. We then discuss how to construct quotients of the group action on the unstable strata and provide a categorical quotient of each unstable stratum. We end by studying a stratification of a quot scheme parametrising sheaves over a projective scheme which has an action by a special linear group. We relate this stratification with a stratification by Harder-Narasimhan type and describe the associated categorical quotient.

Franciska Petényi, The number of zeroes of irreducible characters of the symmetric group

A well known result of Burnside states that every nonlinear irreducible character of a finite group vanishes on some element of the group. The aim of this work is to construct estimates on irreducible characters of the symmetric group. I use the results of Gallagher, Chillag and Wilde to construct some further estimates and to show infinitely many examples, on which one of the estimates is better then the other.

Thomas Preu, An example of Brauer-Manin obstruction on a diagonal quartic surface

We will briefly review the method of Brauer-Manin obstruction and introduce the algebraic and transcendental parts of the Brauer group of a variety. We motivate an example - the surface given by the equation 0=x4+3y4-4z4-9w4 by surveying the frontiers of what is known in this field and give a concrete number theoretic result in this context. If time permits we will sketch how to prove the properties we stated for our example in the last part.

Muhammad Imran Qureshi, Constructing polarised varieties in weighted flag varieties

Vahid Yazdanpanah, Inverse limit of GIT quotients of Grassmannians by a torus