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Fall 2017

The Graduate Student Seminar (GSS) is a series of short talks (30-60 minutes) which are given with the intended audience of FAU graduate and advanced undergraduate students. Talks should not suppose advanced prerequisite knowledge and provide a low pressure atmosphere for adjusting to the seminar style meetings which happen frequently on our campus.

Fall 2017 Organizers:
Andrew Thomack
Alex Milbrand (amilbrand2014@fau.edu)

Date Presenter Title and Abstract
9/8/17 Irma
9/15/17 Irma
9/22/17 Alexandra Milbrand LaTex: Writing Mathematics. Part 1 of a 3-part series sponsored by AMS FAU Student chapter
9/29/17 Maxime Murray Dynamical System: studying the future
10/6/17 Deferred to AWM AWM is hosting an event and all are encouraged to attend that instead.
10/13/17 Shane Keply, Shaun Miller, Zach Tyree Computation Softwares at FAU. Part 2 of a 3-part series sponsored by AMS FAU Student chapter
10/20/17 Sher Chhetri Compounding Statistical Distributions and Some Generalized Classes
10/27/17 Emrah Karagoz Multivariate Cryptography and An Intro to Algebraic Cryptanalysis
11/3/17 Dr. Stephen Locke, Dr. Koray Karabina, Dr. Erik Lundberg What is Graduate Research? Part 3 of a 3-part series sponsored by AMS FAU Student chapter
11/10/17 None Veteran's Day
11/17/17 Longfei Wei Game-Theoretic Methods and its Application for Cyber-Physical Security in Smart Grids
12/1/17 Sean Perry Primorials and the Phi Function

Abstracts

LaTex: Writing Mathematics

Alexandra Milbrand

Abstract: We will give an introduction to the mark-up language, LaTex, commonly used to write mathematics. We will overview basic concepts, how to install it and get a document started, and resources for further work. We will also showcase some of the many uses that are relevant to the graduate mathematician.

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Dynamical Systems: Studying the Future

Maxime Murray

Abstract: Dynamical systems are systems in which a function describes the time dependence of a point in a geometrical space. Their study applies to a diverse range of scientific applications like Biology, Physic or Medicine. In this talk I will introduce some of the elements that are gathering the interest of the researchers in this field; Equilibrium, Stable/Unstable Manifold, Bifurcation, Chaos, etc. Some results will be illustrated using the logistic equation and the Lorenz system

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Compounding Statistical Distributions and Some Generalized Classes

Sher Chhetri

Abstract: In the modern era of statistical distribution theory, many applied researchers propose several new models for analyzing real data sets. These models have been useful in the fields of finance, medical, engineering, biology, physics, computer science and others. In this presentation, we give a brief history of compounding distributions and discuss some of the widely used models to construct new statistical distributions and their generalizations. We will present applications of proposed models to cancer patients data and fire insurance claims data.

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Multivariate Cryptography and An Intro to Algebraic Cryptanalysis

Emrah Karagoz

Abstract: "Multivariate Cryptography" (MC) is a cryptographic system, or a set of primitives, based on multivariate polynomials over a finite field F. This term is mostly used in public key cryptography (PKC), however, it has many primitives in other areas of cryptography when it is seen in the algebraic aspect. These primitives are preferred as a trapdoor function since its security depends on solving systems of multivariate polynomial equations which is proven to be NP-hard or NP-complete (by reducing to 3SAT problem). In spite of its proven security, it has been very productive in terms of design and cryptanalysis and led to algebraic cryptanalysis because of vulnerabilities found in proposed algorithms. They become so popular in recent years because of post-quantum cryptography. They are considered to be good candidates because of their efficiency (since they also provides small key-sizes for desired security levels) and security (which depends on a NP-hard problem expected to be resistant to the quantum computers).

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Game-Theoretic Methods and its Application for Cyber-Physical Security in Smart Grids

Longfei Wei

Abstract: Smart grid is a critical infrastructure which is a large-scale and dynamic Cyber-Physical System (CPS) capable of advanced computing and communication, self-healing and autonomy. Along with an improved efficiency and reliability, cyber-physical security of the smart grid has become an important challenge. In order to design an optimized, secure and resilient smart grid, it will have to build on solid mathematical tools. Game Theory is one of the emerging class of models used to mitigate attacks on such complex systems. In order to protect the smart grid against cyber and physical attacks, a stochastic game-theoretic approach is proposed to analyze the optimal strategies that a power grid defender can adopt to protect the grid against potential attacks. First, an optimal load shedding technology is devised to quantify the physical impacts of coordinated attacks. Taking these quantified impacts as input parameters, the interactions between a malicious attacker and the defender are modeled using a resource allocation stochastic game. The game is shown to admit a Nash equilibrium and a novel learning algorithm is introduced to enable the two players to reach such equilibrium strategies while maximizing their respective minimum rewards in a sequence of stages. The convergence of the proposed algorithm to a Nash equilibrium point is proved and its properties are studied. Simulation results of the stochastic game model on the WSCC 9-bus system and the IEEE 118-bus system are contrasted with those of static games, and show that different defense resources owned lead to different defense strategies.

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Primorials and the Phi Function

Sean Perry

Abstract: We will be talking about the famous Euler phi function, which counts the numbers less than and relatively prime to a given integer. After a brief overview, we will take a look at some its salient features and specifically prove that the primorials form an "advancing lower bound" for this fabulous function.

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Archive of Abstracts

About the Speakers