## Title: Cayley’s formula for the number of labeled trees

Abstract: Cayley’s formula for the number of labeled trees is a famous result in Combinatorics and Graph Theory. In this talk, we will present two of the more interesting and elegant proofs for this result: one using a recursive formula, and one using double counting. These proofs were taken from "Proofs from THE BOOK" by M. Aigner and G. Ziegler.

## Title: Hilbert’s third problem: decomposing polyhedra

Abstract:

The great mathematician David Hilbert proposed 23 problems in 1900, and the third on Hilbert’s list of mathematical problems is related to the question: Given any two polyhedra of equal volume, is it always possible to cut the first into finitely many polyhedral pieces which can be reassembled to yield the second? The problem was solved by Hilbert’s student, Max Dehn, who proved that the answer in general is “no” by producing a counterexample.

In this talk, we will go over an elementary reworked proof of Dehn’s original proof, as given in “Proofs from THE BOOK” by M. Aigner and G. Ziegler.

## Title: Two times π^2/6

Abstract: There is a classical, famous and important result by Leonhard Euler from 1734, stating that the infinite sum of the reciprocals of the squares of natural numbers is equal to π^2/6. In this talk we will present two elementary but elegant and clever proofs of Euler’s result. These proofs involve double integrals and were taken from “Proofs from THE BOOK” by M. Aigner and G. Ziegler.

## Title: Conic Sections

Abstract:After an overview of Apollonius' life and his work on conic sections, this talk will demonstrate and prove a few of Apollonius’ theorems, using GeoGebra. Finally we will discuss Kepler’s work related to conic sections.

## Title: Modeling an Influenza Virus

Abstract: Every year before the influenza season begins, the United States focuses its efforts on vaccinating both the young and the elderly. This study uses data from the CDC, WHO, and CDPH and an SEIR model with a travel component to track the spread of the seasonal flu virus in California. The purpose of this study is to prove or disprove that the current immunization scheme is the most effective. The model will be used to find an effective vaccination scheme. The knowledge obtained will allow for earlier production of flu vaccines, a reduction of waste by preventing the over-vaccination of particular age groups, and help prevent spread of the influenza virus.

## Title: On the Inoculation of Networks, Big and Small

Abstract: As complex computer networks become more integral to our life, it is becoming more important to create effective and efficient defenses against cybercrime. An introductory foundation on the nature of computer networks and their representation as graphs will be outlined, and two methods will be presented for immunizing these computer networks. The first method will focus on small networks and use centrality measures to form an inoculation scheme. The second method will then transition to large-scale complex networks, and discuss inoculation schemes based on random processes that rely on the scale-free nature of large networks.

If you need a disability-related accommodation or wheelchair access information, please contact the Mathematics Department  at 559.278.2992 or e-mailmath.office@csufresno.edu. Requests should be made at least one week in advance of the event.