We study the half-space KPZ equation with a Neumann boundary condition, starting from stationary Brownian initial data. We derive a variance identity that links the fluctuations of the height function to the transversal fluctuations of a half-space polymer model. We then establish optimal fluctuation exponents for the height function in both the subcritical and critical regimes, along with corresponding estimates for the polymer endpoint. Based on a joint work with Yu Gu.

We formulate a new version of the local Langlands correspondence for discrete L-parameters which involves (Weyl orbits of) packets of representations of all twisted Levi subgroups of a connected reductive group G through which the parameter factors and prove that this version of the correspondence follows if one assumes the pre-existing local Langlands conjectures. Twisted Levi subgroups are crucial objects in the study of supercuspidal representations; this work is a step towards deepening the relationship between the representation theory of p-adic groups and the Langlands correspondence. This is joint work with David Schwein (Bonn).

The Chekanov-Eliashberg dga is a powerful invariant for Legendrian links. Using augmentations of this dga, one can truncate its differential to produce linearized contact homology. About two decades ago, Sabloff established a duality in this setting, closely linked to the Poincaré duality of Lagrangian fillings. This truncation has since been generalized into a unital A-infinity category, Aug_+. In this talk, I will present new results that extend Sabloff duality from the level of cochain complexes to A-infinity bimodules over Aug_+. The key tool in this extension is Ng's LSFT algebra, which enlarges the Chekanov-Eliashberg dga. If time permits, I will also discuss how the LSFT algebra encodes additional homotopy coherent data, providing further insights into Sabloff duality.