Time: 16:30-18:00

Location: Mondi 3 / Central Building

Speaker 1: Assylbek Olzhabayev (Maas group)

Title: Superconcentration for minimal surfaces in random environment

Abstract: We study the variance of the energy of minimal surfaces in random environment in dimensions up to 4. We consider two different models, introduced by Dembin, Elboim, Hadas, and Peled, and by Agresti, Clozeau, and Fischer. We prove an upper bound on the variance of the form

Var[min E] ≲ Lᵈ⁻¹ / (log L)ᶿ 

for some θ > 0, which is a logarithmic improvement over the classical theory (such as spectral gap inequality). Our proof is inspired by the proof of sublinear variance in first-passage percolation by Benjamini, Kalai, and Schramm, which we adapt to higher dimensions. This adaptation relies on a quantiative homogenisation result that was obtained by Agresti et. al.

Speaker 2: Nhok Tkhai Shon Ngo (Hausel Group)

Title: On the character theory of some infinite-dimensional groups

Abstract: For a group G, the characters of G (positive-definite class functions normalized at the identity) often encode a lot of information about its representation theory. For compact groups, for example, indecomposable characters are in one-to-one correspondence with irreducible unitary representations. For infinite-dimensional groups the situation is more subtle, but a complete description of characters is known in several important cases, including the infinite symmetric and infinite unitary groups, thanks to the work of Thoma, Voiculescu, Vershik, Kerov and others. In this talk we discuss a new family of examples: inductive limits of groups taken along "block-diagonal" embeddings, a construction inspired by uniformly hyperfinite (UHF) C^*-algebras.