3 papers
math-ph2025
Graded Contact Geometry and the AKSZ Formalism
Ivan Contreras, Nicolas Martinez-Alba, Rajan Amit Mehta
The AKSZ formalism is a construction of topological field theories where the target spaces are differential graded symplectic manifolds. In this paper, we describe an analogue of t…
math-ph2025
Supersymmetry Breaking in Graph Quantum Mechanics
Bek Herz, Ivan Contreras
In this paper, we develop the groundwork for a graph theoretic toy model of supersymmetric quantum mechanics. Using discrete Witten-Morse theory, we demonstrate that finite graphs…
math.SG2024
Symplectic Geometry, Poisson Geometry, and Beyond
Ivan Contreras, Diego Martinez, Nicolas Martinez +1
Symplectic and Poisson geometry emerged as a tool to understand the mathematical structure behind classical mechanics. However, due to its huge development over the past century, i…