Friday November 8, 2024

Sponsored by 

The Metropolitan New York Section of the Mathematical Association of America

and hosted at the CUNY Graduate Center.

Graph Theory Day is held at different locations in and around New York City. 
Our goal is to provide a learning and sharing experience on recent developments.
Please encourage your students to attend and present a poster.

Location: CUNY Graduate Center, 4th floor Science Room, 365 Fifth Avenue (at the corner of 34th Street and 5th Avenue) in Manhattan across from the Empire State Building.  The entrance is on 34th street and the Science Center is on the 4th floor.  

Registration:  There is no registration fee. However, please register online by Nov 5, 2024 by filling this Registration Form. 

Schedule (in Eastern Time ET)

11:00 am:  Check-In 

11:30 am:  Jinyoung Park (New York University)

12:30 am - 1:00 pm:  Lunch (8th floor cafeteria)

1:00 pm - 2:00 pm: Poster Session

2:00 pm - 3:00 pm:  Joshua Hiller (Adelphi University)

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Abstracts

Jinyoung Park (New York University)

Title: Threshold phenomena for random discrete structures

Abstract: In this expository talk, we will walk through some basics of the random graph theory, aiming to understand a high-level motivation for the Kahn--Kalai Conjecture (now the Park--Pham Theorem), which has been a central conjecture in the area of probabilistic combinatorics. Below is a more formal description of the work that we will discuss, but I will try to use concrete examples rather than the formal language, and will not assume much prior knowledge other than undergraduate-level combinatorics and probability.

More formal description: for a finite set X, a family F of subsets of X is said to be increasing if any set A that contains B in F is also in F. The p-biased product measure of F increases as p increases from 0 to 1, and often exhibits a drastic change around a specific value, which is called a "threshold." Thresholds of increasing families have been of great historical interest and a central focus of the study of random discrete structures, with estimation of thresholds for specific properties the subject of some of the most challenging work in the area. In 2006, Jeff Kahn and Gil Kalai conjectured that a natural (and often easy to calculate) lower bound q(F) (which we refer to as the “expectation-threshold”) for the threshold is in fact never far from its actual value. A positive answer to this conjecture enables one to narrow down the location of thresholds for any increasing properties in a tiny window. 

This talk is based on joint works with Keith Frankston, Jeff Kahn, Bhargav Narayanan, and Huy Pham. 

Joshua Hiller (Adelphi University)

Title: Hypergraph and a model of epidemiology

Abstract: The role of graph theory in modeling infectious epidemics has been a heavily studied application of graph theory since the initial outbreak of the COVID pandemic. However, the use of hypergraphs in the modeling of disease has received considerably less attention. In this talk we will show that the Armitage and Doll model of carcinogenesis (which is perhaps the best known and oldest mathematically rigorous, data-based model of cancer formation) can be interpreted as a stochastic coloring process on a simple hypergraph with one edge. With this in mind, we will then generalize the model to other hypergraphs and use them to propose possible answers to open questions in epidemiology and cancer therapy.

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Poster Session (1:00 - 2:00 pm)

There is a place to upload poster title and abstract on the registration form.  If you have any questions about the poster session, please email Dr. Sandra Kingan (skingan@brooklyn.cuny.edu).

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Local Organizing Committee: Sandra Kingan and Mingxian Zhong