C4

Population structure substantially affects evolutionary dynamics. Networks that promote the spreading of fitter mutants are called amplifiers of selection, and those that suppress the spreading of fitter mutants are called suppressors of selection. It has been discovered that most networks are amplifiers under the so-called birth-death updating combined with uniform initialization, which is a common condition. We discuss constant-selection evolutionary dynamics with binary node states (which is equivalent to the biased voter model with two opinions in statistical physics research community) on higher-order networks, i.e., hypergraphs, temporal networks, and multilayer networks. In contrast to the case of conventional networks, we show that a vast majority of these higher-order networks are suppressors of selection, which we show by random-walk and Martingale analyses as well as by numerical simulations. Our results suggest that the modeling framework for structured populations in addition to the specific network structure is an important determinant of evolutionary dynamics.
 

Junior Strings is a seminar series where DPhil students present topics of common interest that do not necessarily overlap with their own research area. This is primarily aimed at PhD students and post-docs but everyone is welcome.

Junior Strings is a seminar series where DPhil students present topics of common interest that do not necessarily overlap with their own research area. This is primarily aimed at PhD students and post-docs but everyone is welcome.

Junior Strings is a seminar series where DPhil students present topics of common interest that do not necessarily overlap with their own research area. This is primarily aimed at PhD students and post-docs but everyone is welcome.

The talk introduces an analytical framework for examining socio-spatial segregation across various spatial scales. This framework considers regional connectivity and population distribution, using an information theoretic approach to measure changes in socio-spatial segregation patterns across scales. It identifies scales where both high segregation and low connectivity occur, offering a topological and spatial perspective on segregation. Illustrated through a case study in Ecuador, the method is demonstrated to identify disconnected and segregated regions at different scales, providing valuable insights for planning and policy interventions.

Symplectic duality predicts that affine symplectic singularities come in pairs that are in a sense dual to each other. The Hikita conjecture relates the cohomology of the symplectic resolution on one side to the functions on the fixed points on the dual side.  

In a recent work with Ivan Losev and Lucas Mason-Brown, we suggested an important example of symplectic dual pairs. Namely, a Slodowy slice to a nilpotent orbit should be dual to an affinization of a certain cover of a special orbit for the Langlands dual group. In that paper, we explain that the appearance of the special unipotent central character can be seen as a manifestation of a slight generalization of the Hikita conjecture for this pair.

However, a further study shows that several things can (and do!) go wrong with the conjecture. In this talk, I will explain a modified version of the statement, recent progress towards the proof, and how special unipotent characters appear in the picture. It is based on a work in progress with Do Kien Hoang and Vasily Krylov.