Fri, 31 May 2024

12:00 - 13:15
L3

Multipartite Edge Modes and Tensor Networks

Ronak Soni
(Cambridge DAMTP)
Abstract
Holographic tensor networks model AdS/CFT, but so far they have been limited by involving only systems that are very different from gravity. Unfortunately, we cannot straightforwardly discretise gravity to incorporate it, because that would break diffeomorphism invariance. In this note, we explore a resolution. In low dimensions, gravity can be written as a topological gauge theory which can be discretised without breaking gauge-invariance. However, new problems arise. Foremost, we now need a qualitatively new kind of "area operator" which has no relation to the number of links along the cut and is instead topological. Secondly, the inclusion of matter becomes trickier. We successfully construct a tensor network both including matter and with this new type of area. Notably, while this area is still related to the entanglement in "edge mode" degrees of freedom, the edge modes are no longer bipartite entangled pairs. Instead they are highly multipartite. Along the way, we calculate the entropy of novel subalgebras in a particular topological gauge theory. We also show that the multipartite nature of the edge modes gives rise to non-commuting area operators, a property that other tensor networks do not exhibit. Based on arXiv:2404.03651.



 

Equidistribution of high traces of random matrices over finite fields and cancellation in character sums of high conductor
Gorodetsky, O Kovaleva, V Bulletin of the London Mathematical Society (07 May 2024)
Wishful thinking about consciousness
Grindrod, P IgMin Research volume 2 issue 5 302-308 (02 May 2024)
Two Ramsey problems in blowups of graphs
Girão, A Hancock, R European Journal of Combinatorics volume 120 103984 (01 Aug 2024)
Direct products of free groups in Aut(F_N)
Bridson, M Wade, R Geometric and Functional Analysis (05 Aug 2024)
Assessing aerodynamic influences on offshore foundation design for large wind farms
Wen, K Dehtyriov, D Byrne, B Journal of Physics Conference Series volume 2745 issue 1 (01 Apr 2024)
An Elekes–Rónyai Theorem for Sets With Few Products
Mudgal, A International Mathematics Research Notices rnae087 (06 May 2024)
Tue, 21 May 2024

14:00 - 15:00
C4

Fixation probability and suppressors of natural selection on higher-order networks

Naoki Masuda
(The State University of New York at Buffalo)
Abstract

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.
 

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