## Jeremiah Hower, FIU: Arithmetic Surfaces and their Graphs

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Venue: | SIPA 100 |

Tuesday, April 17, 3.30 pm. SIPA 100

Jeremiah Hower, FIU

Title: Arithmetic Curves and their Graphs

Abstract: The complexity of a graph is an important invariant, captured by the Smith Normal From of the Laplacian Matrix. Smith Normal Forms are important in physics (sandpile models), combinatorics (chip-firing games), cryptography (discrete logarithm problem), and algebraic geometry (curve degenerations). We will discuss their connection to reducing a system of equations (with integer coefficients) modulo a prime. A new result relating the eigenvalues of a (generalized) Laplacian to the Smith Normal Form will be given.