C4

The Hilbert scheme of d-points on a smooth surface is a well-studied object that still enjoys relatively large interest. We generalize Aldo Conca's Canonical Hilbert-Burch matrices and obtain explicit families of d-points. We show that such descriptions give us Białynicki-Birula cells of the Hilbert scheme for any choice of one-dimensional torus, thus describing the punctual component. This can be potentially applied to the study of singularities of the nested Hilbert scheme of points.

Gotzmann's regularity and persistence theorems provide tools which allow us to find explicit equations for the Hilbert scheme Hilb_P(P^n). A natural next step is to generalise these results to the multigraded Hilbert scheme Hilb_P(X) of a smooth projective toric variety X. In 2003 Maclagan and Smith generalise Gotzmann's regularity theorem to this case. We present new persistence type results for the product of two projective spaces, and time permitting discuss how these may be applied to a more general smooth projective toric variety.

In this talk I will explain how a dictionary between the Bondi-Sachs and the Newman-Penrose formalism can be used to organize the subleading data appearing in the metric for asymptotically-flat spacetimes. In particular, this can be used to show that the higher Bondi aspects can be traded for higher spin charges, and that the latter form a w_infinity algebra.

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.