Event
Ph.D. Research Proposal: Geyang Wang
Wednesday, September 2, 2026
5:00 p.m.
AVW 1146
Souad Nejjar
301 405 8135
snejjar@umd.edu
ANNOUNCEMENT: Ph.D. Research Proposal Exam
Name: Geyang Wang
Committee:
Prof. Alexander Barg (Chair/Advisor)
Prof. Prakash Narayan
Prof. Armand Makowski
Date/time: Wednesday, September 2 at 5:00 PM
Location: AVW 1146
Title: Locally Recoverable Storage on Infinite Graphs: A Statistical-Mechanical Approach
Abstract: Codes with locality allow a failed storage node to be repaired by reading only a few nearby nodes. Carried over to an infinite graph, this gives a recoverable system: bits sit on the vertices, and the value at each vertex is determined by its neighbors according to a local rule. How much information can such a system store, and what does a typical admissible configuration look like at large scale?
This proposal treats recoverable systems on two-dimensional lattices as interaction models of statistical mechanics. Under the recovery rule considered here, the admissible configurations are the maximal independent sets of the underlying graph, and the object of study is the Gibbs measures on these sets, indexed by an activity parameter or temperature parameter. Such a measure need not be unique — a unique measure means the system has a single typical appearance, whereas several coexisting measures mean it can settle into distinct large-scale phases.
Completed work on the square and triangular lattices establishes capacity bounds, uniqueness at high temperature, and phase-coexistence at both high and low activity. The proposed work extends the analysis to general periodic planar graphs and to mixtures of several particle shapes, and to related information-theoretic problems.
