Discrete period matrices and related topics
Christian Mercat

TL;DR
This paper explores discrete analogs of classical Riemann surface concepts, demonstrating convergence of discrete period matrices to their continuous counterparts through critical map sequences.
Contribution
It introduces discrete period matrices and proves their convergence to continuous matrices using critical map sequences.
Findings
Discrete period matrices are well-defined and relate to classical matrices.
Convergence of discrete to continuous period matrices is established.
New discrete analogs of Riemann's bilinear relations are developed.
Abstract
We continue our investigation of Discrete Riemann Surfaces with the discussion of the discrete analogs of period matrices, Riemann's bilinear relations, exponential of constant argument, series and electrical moves. We show that given a refining sequence of critical maps, the discrete period matrix converges to the continuous one.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsMathematical Dynamics and Fractals · Geometric and Algebraic Topology · Quasicrystal Structures and Properties
