Structure preserving primal dual methods for gradient flows with
nonlinear mobility transport distances
Carrillo, J Wang, L Wei, C SIAM Journal of Numerical Analysis (29 Mar 2023)
Optimal stopping via distribution regression: a higher rank signature approach
Horvath, B Lemercier, M Liu, C Lyons, T Salvi, C (04 Apr 2023)
Group rings of three-manifold groups
Kielak, D Linton, M (21 Nov 2023)
Macrophage anti-inflammatory behaviour in a multiphase model of atherosclerotic plaque development
Ahmed, I Byrne, H Myerscough, M Bulletin of Mathematical Biology volume 85 issue 5 (29 Mar 2023)
Stability in the category of smooth mod-p representations of SL_2(Qp)
Ardakov, K Schneider, P Forum of Mathematics, Sigma (21 Mar 2024)
Tue, 25 Apr 2023
16:00
L6

Projected Green’s Function Methods Applied to Quasi-Periodic Systems and the Dry Ten Martini Problem

Dan Borgnia
(UC Berkeley)
Abstract

The resolvents of finite volume restricted Hamiltonians, G^(⍵), have long been used to describe the localization of quantum systems. More recently, projected Green's functions (pGfs) -- finite volume restrictions of the resolvent -- have been applied to translation invariant free fermion systems, and the pGf zero eigenvalues have been shown to determine topological edge modes in free-fermion systems with bulk-edge correspondence. In this talk, I will connect the pGfs to the G^(⍵) appearing in the transfer matrices of quasi-periodic systems and discuss what pGF zeros can tell us about the solutions to transfer matrix equations. Using these methods, we re-examine the critical almost-Matthieu operator and notice new guarantees on analytic regions of its resolvent for Liouville irrationals.
 

Minimal morphoelastic models of solid tumour spheroids: a tutorial
Walker, B Celora, G Goriely, A Moulton, D Byrne, H Bulletin of Mathematical Biology volume 85 issue 5 38 (29 Mar 2023)
Tue, 17 Oct 2023
15:00

Dehn functions of central products of nilpotent groups

Claudio Llosa Isenrich
(KIT)
Abstract

The Dehn function of a finitely presented group provides a quantitative measure for the difficulty of detecting if a word in its generators represents the trivial element of the group. By work of Gersten, Holt and Riley the Dehn function of a nilpotent group of class c is bounded above by nc+1. However, we are still far from determining the precise Dehn functions of all nilpotent groups. In this talk, I will explain recent results that allow us to determine the Dehn functions of large classes of nilpotent groups arising as central products. As a consequence, for every k>2, we obtain many pairs of finitely presented k-nilpotent groups with bilipschitz asymptotic cones, but with different Dehn functions. This shows that Dehn functions can distinguish between nilpotent groups with the same asymptotic cone, making them interesting in the context of the conjectural quasi-isometry classification of nilpotent groups.  This talk is based on joint works with García-Mejía, Pallier and Tessera.

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