# Seminars & Colloquia Calendar

## Louis' Talk

#### Louis Gaudet - Rutgers University

Location: ** GSL - Joint Seminar with GCS**

Date & time: Wednesday, 04 April 2018 at 12:00PM - 1:00PM

Abstract: Given a (finite) graph G, there is a natural finite abelian group we can associate to G, called its Jacobian group. There are different sources of motivation for studying these groups. They are the “tropical” (i.e. piecewise-linear) analogs of classical algebro-geometric objects. They are used as models for certain physical systems—so-called “sandpile groups.” The statistics of Jacobian groups of random graphs are related to the Cohen-Lenstra heuristics, which describe statistics of ideal class groups of number fields. For instance, a fun fact: the Jacobian of a random graph is cyclic just about 79% of the time.Rather than discuss these connections in depth, we’ll explore a more basic question: which groups actually appear as the Jacobian of some graph? Along the way, we’ll observe and exploit connections of the Jacobian group to classical graph theoretic properties of interest: planarity, counts of spanning trees, etc. We’ll construct graphs whose Jacobians realize a large class of groups, and we’ll prove that there are infinite families of groups that cannot be realized as the Jacobian of any graph. The general question, however, is still open, and I will point out several possible research problems.

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Paul Feehan, Manousos Maridakis, Natasa Sesum Organizer's webpage

Lev Borisov, Emanuel Diaconescu, Angela Gibney, Nicolas Tarasca, and Chris Woodward Organizer's webpage

Jason Saied Seminar webpage

Brian Pinsky, Rashmika Goswami website

Corrine Yap Organizer's webpage

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Lisa Carbone, Yi-Zhi Huang, James Lepowsky, Siddhartha Sahi Organizer's webpage

Simon Thomas website

Kasper Larsen, Daniel Ocone and Kim Weston Organizer's page

Joel Lebowitz, Michael Kiessling

Yanyan Li, Haim Brezis

Brooke Ogrodnik website

Stephen D. Miller, John C. Miller, Alex V. Kontorovich, Alex Walker seminar website

Stephen D. Miller

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