# Current Academic Year Seminars

**BLOCK 8, 2014 - April/May**

**Friday May 9, 2:30pm**

**Tutt Science 229**

**Speaker:** Stefan Erickson**Title:** Computer Security in the Post-Snowden Era

**Abstract**: The Snowden leaks about NSA spying have sparked a public debate about cybersecurity. There are many questions that people are struggling to answer. What is privacy? What is security? What is the right balance between individual privacy and national security? What will the effect of "big data" have on Internet commerce and security? The answer to these questions will inevitably have a huge impact on the future of society.

In this talk, we will explore many aspects of cybersecurity. We will explain how the Target Point-Of-Service breach occurred, what the Stuxnet worm is and why it was important, and how the recent "Heartbleed" bug worked. We will see what information the NSA has been gathering and how they exploited a weak random number generator to break a commonly used cryptosystem. We also hope to start a dialogue about the proper role of computer security. The talk is mostly rated G with occasional flashes of PG-13 material.

90% Rated G, 10% Rated PG13

**Friday May 2, Noon**

**Tutt Science 122 - Lecture Hall**

**Speaker:** Jim Powell, University of Utah (visiting professor)**Title:** Mathematics of the Life-Impaired: How Disease Theory Predicts the Zombie Apocalypse

Abstract:

Abstract:

From movies to pop music ("If I were a zombie, I'd never eat your brain...), it seems the undead are already taking over the world. The usually staid Centers for Disease Control launched a tongue-in-cheek "Preparedness 101: Zombie Apolcalypse" public campaign in 2011 to drive home the importance of emergency preparation. Even Utah State University has been infected as evidenced by USU Housing’s wildly popular, campus-wide“Humans vs. Zombies” (HvZ) war this past fall.

Anthropologist Krystal D'Costa suggests zombies capture our imagination because they represent modern society and technology gone awry and offer the perfect metaphor for an unstoppable pandemic. USU professor Jim Powell expands the zombie metaphor to illustrate the concepts and results of mathematical epidemiology. Using storylines from such movies as "Night of the Living Dead," "28 Days Later," "The Walking Dead" and "I am Legend," as well as data from the USU HvZ games, Dr. Powell will show how mathematicians model diseases. He'll talk about how scientists predict the course and impact of epidemics, discuss how "herd immunity" (vaccination levels for disease eradication) works and apply some of these modeling strategies to the understand and predict the spread of Chronic Wasting Disease (Zombie Deer) in southern Utah.

**Rated PG**

**Friday April 25, Noon**

**Tutt Science 122- Lecture Hall**

**Speaker:** Gene Abrams, University of Colorado at Colorado Springs**Title:** Fibonacci's Rabbits Visit the Mad Veterinarian**Abstract:** Since its origin (more than eight centuries ago) as a puzzle about the number of rabbits in a fantasmagorically expanding) colony, the Fibonacci Sequence 1,1,2,3,5,8,13,... has arguably become the most well-known of numerical lists, due in part to its simple recursion formula, as well as to the numerous connections it enjoys with many branches of mathematics and science.

Since their origins (less than two decades ago) as puzzles about the number of animals in a(fantasmagorically strange) veterinarian's oce, the (not so well-known) Mad Vet Scenarios have provided a source of thought-provoking entertainment to internet gamers and math enthusiasts alike. In this talk we'll show how Fibonacci's puzzle about rabbits is naturally connected to the puzzles found in the Mad Vet's oce. Along the way, we'll show how an investigation into Mad Vet Scenarios has led to the discovery of some heretofore unrecorded properties of the Fibonacci Sequence.

**Rated G. ** This talk is rated G, meaning that it is intended for the most General of audiences. No prior familiarity with Fibonacci's breeding rabbits, or with the Mad Veterinarian's transmogrication machines, or with any other type of fantasmagorical animal population dynamics, will be assumed.

Pizza wiill be served.

**BLOCK 7, 2014 - March/April**

**Wednesday April 9 AND Thursday April 10, 1:30-3:30****Tutt Science 122- Lecture Hall**

**Student Capstone Talks!!**

Light refreshements will be served.

...

**Friday March 28 at NOONTutt Science 122 - Lecture HallSpeaker:** Loren Cobb

**Title:**War, or Peace, or What? A Math Clinic Studies the 21st Century

**Abstract:**This talk will present the results of a semester-long mathematics clinic on predicting the fate of human society in the Twenty-First Century. This clinic, a required course for both undergraduates and graduate students in UC-Denver's Math Department, focused on what we can deduce about the coming century from the use of interlocking dynamic models of population growth, resource exhaustion (food, water, and fossil fuels), urbanization, economic growth, governance, education, and policy optimization. The results were surprisingly positive, although several very specific areas of severe conflict and human misery were identified.

**BLOCK 6, 2014 - February/March**

**Friday March 7 at NOONTutt Science 122 - Lecture HallSpeaker:** Marlow Anderson

**Title:**CYCLOID WARS: A case study in 17

^{th}century mathematics.

**Abstract:** The cycloid is a curve known as the “apple of discord”, because it produced so much controversy and debate among 17^{th} century mathematicians. We will examine this history, with particular attention paid to how these debates illustrate the evolving 17^{th} century answers to the following questions: What is geometry? What is a curve? What is a proof? Almost all of the great mathematicians of the century play a role, from Galileo and his students Torricelli and Cavalieri; to the French mathematicians in the Mersenne circle such as Roberval, Descartes and Fermat; to Leibniz, his mentor Huygens, and his students the Bernoulli brothers; and to Newton and his English predecessors Wren and Wallis.

**Rated PG **

**Friday February 28 at NOONTutt Science 122 - Lecture HallSpeaker:** David Brown

**Title:**The Power of Positive Feedback

**Abstract:** Many biological (and other) systems can be understood in terms of linked positive and negative feedback loops. Over the past 10 years, a common theme in much of my own research has been the role of positive feedback in driving interesting dynamics in biological systems. Here, positive feedback refers to self-reinforcing dynamical processes. I will show how feedback diagrams can be turned into mathematical models consisting of differential equations. I will then show how positive feedback can cause phenomena like bistability, rapid decision making, and spatial pattern formation. I will illustrate these ideas with examples from my research on predator-prey dynamics, chemical communication between bacteria, and the dynamics of tree line on Pikes Peak.

**Rated: PG/PG-13. ** Familiarity with differential equations is assumed, but the technical details will be kept to a minimum.

**BLOCK 5, 2014 - January/February**

**Friday, February 7 at Noon****Tutt Science 122 Lecture Hall**

**Speaker:**Ransanjalee Dissanayaka from Georgia State University

**Title: **Finite State Automata

**Abstract: **Automata Theory is an exciting, theoretical branch of computer science. Simply stated, automata theory is the study of abstract computing devices or "machines". Through automata, computer scientists are able to understand how machines compute functions and solve problems and more importantly, what it means for a function to be defined as computable or for a question to be described as decidable. Before there were computers in 1930's A Turing studied an abstract machine that model the power of real computers. Turing machine allow us to describe precisely what a computing machine could do and could not do. The simplest automata used for computation is a finite state automaton, also called a finite state machine. Finite automaton is a basic model of computational systems with ﬁnite memory. It is much more restrictive in its capabilities than a Turing machine. Finite state machines originally proposed to model brain functions, turned out to be extremely useful for variety of other purposes. They can be used to recognize a type of formal languages called regular languages and used for building certain types of software including lexical analyzers. This lecture will provide an introduction to theory of computation and finite state automata.

**Rating: **PG

**Friday, January 31 at Noon****Tutt Science 122 Lecture Hall**

**Speaker:**Ben Ylvisaker from Swarthmore College

**Title:** All Your Code Are Belong to Us

**Abstract:** Software today exists in a hostile environment. Vandals, thieves, hacktavists, and various government agencies are hard at work subverting computer systems of all sorts. Understand the common attack vectors and what can be done to defend against them is important for nearly everyone in modern society (to different depths, depending on one's role, of course). In this talk we will take a guided stroll through the Common Weakness Enumeration Top 25 software errors. We will cover the basics like stack overruns, script injections and public key cryptography or related topics, according to audience interest.

**Rating:**

20% G

60% PG

20% PG13

**Friday, January 24 at Noon****Tutt Science 122 Lecture Hall**

**Speaker**: Jim Boerkoel from Harvey Mudd College**Title:** Helping Human-robot Teams Stay Coordinated

**Abstract**: An emerging trend in robotics is the development of inherently safe, mobile robots that are designed to assist humans across a wide variety of tasks. Humans are good at intuitively perceiving and quickly adapting to the intentions and conventions of their human teammates with little or no explicit communications. Robots, on the other hand, face the challenge of optimizing and adapting their schedules to, what to them appears to be, their inherently unreliable, non-communicative, and irrational human teammates. A primary goal of my work is to equip robots with methods to quickly and robustly develop plans that (1) adapt to established conventions to successfully negotiate human-oriented environments and (2) augment the workﬂow of human workers to increase overall productivity, safety, and quality. In this talk I discuss a new, distributed robotic scheduling approach that builds on classical shortest-path algorithms to enable a robot to coordinate its activities with its human teammates while providing them flexibility and autonomy.

**Rated PG**: A little undergraduate mathematics assumed.

**BLOCK 4, 2013 - December**

**BLOCK 4, 2013 - December**

**Friday, December 13 at 2:30 pmTutt Science 229**

**Speaker:** Jonathan Portiz **Title:** Computation in Nearby Universes**Rated**: mostly PG with brief interludes of PG13/R (A little to a lot of undergraduate mathematics or computer science assumed.)**Abstract:**

When first introduced, the Turing Machine (TM) seemed an entirely non-physical formalization of computation, but insights from thermodynamics and quantum mechanics showed this was not entirely true. The good news was the discovery of algorithms for quantum TMs which were much faster than the best classical ones -- even breaking important modern cryptographic algorithms. I will describe some of these physical influences on computation, including a brief introduction to quantum computation (which could be useful since all signs point to the imminent arrival of actual quantum computers). I will then propose a way to vary the "structure group" underlying the physics of TMs, in essence to do computation on other universes. A surprising mathematical connection is the relationship of probabilistic computation with some beautiful classical linear algebra.

BLOCK 3, 2013 - November

**ber****BLOCK 3, 2013 - Novem**

**Friday, November 15 at 2:30 pmTutt Science 229**

**Speaker:** Charles Morgenstern, CC alum, and graduate student at the Colorado School of Mines.

**Title:** Acoustic Wave Scattering with FEM-BEM **Rated**: PG-13 (A lot of undergraduate mathematics or computer science assumed.)**Abstract:**

This talk is a brief investigation into numeric methods for approximating time harmonic acoustic wave scattering in two-dimensions by bounded inhomogeneities and impenetrable objects. First boundary element methods (BEM) and finite element methods (FEM) are considered alone, and then a new method which couples these two is presented. Using the coupled method global solutions can be computed for problems too complex for a boundary element method alone. Parallel and serial computing performance as well as convergence for the method will be discussed. This is a joint project with Prof. Mahadevan Ganesh at the Colorado School of Mines and is supported by the National Science Foundation.

***

**Friday, November 8 at 12 pmTutt Science, Kresge Lecture Hall (TSC 122)**

**Speaker:** Matthew Whitehead

**Title:** Can Robots Build Robots that Build Robots? **Rated**: G**Abstract:**

Imagine a large warehouse filled with spare electronic and mechanical parts. Is it possible to build a robot that goes into the warehouse and builds an exact copy of itself? If so, then those copies could build more and more robots until the building materials were exhausted.

This talk will explore the computational requirements of machine self-replication using cellular automata. After seeing several examples of simple self replicators, we will then consider replicating Turing-complete machines: machines that can compute any computable function.

***

**Friday, November 1, 2:30pm****Tutt Science 229Speaker: **Dr. Gerald de Souz, PhD from The University of Albany, Albany - New York

**: From Fourier Analysis to Wavelet Analysis**

Title

Title

**Rated: PG-13Abstract**: In this talk, we discuss the origin of Fourier and wavelet analyses and explain the connections between them. In fact, in this presentation we will discuss the following:

How much information is needed to** reconstruct **a situation (signal)? And how we accomplish it? If a situation (signal) is represented by a function f(x). How can we decompose this function f(x) into “simpler” functions and from these “simpler functions” recovery all necessary information about f(x)? – **Building block functions**.

Assume we have too much information about a given situation (signal). How can we throw away some of these information and still have a complete necessary information about the situation (signal)? **Compression**

This is an informative talk and it is suitable for a general audience including students. My friend and late Paul Halmos often advised colloquium speakers “to make the first 15 minutes of their talks accessible to the entire audience. Do you know how difficult that is?” *Notices of the AMS*, February 2009.

I will try to follow his advice.

“Mathematics contains ideas that can be, and deserve to be, communicated to the wider public – even if what is communicated is at the level of appreciation rather than practical knowledge.” – Barbara Burke Hubbard, *The World According to Wavelets*, 1996.

**A bit about our speaker**: Geraldo Soares de souza, PhD from The University of Albany, Albany - New York in the area of Harmonic Analysis. He is currently a full Professor of Mathematics at Auburn University in Auburn, Alabama. He has had several Master and PhD students and publications in his area of expertise. For over 25 years, he has led a series of conferences in Harmonic Analysis and Related Areas at Auburn University sponsored by NSF. He and his colleagues have led several international projects in Africa, South America, Central America, etc. Recently, he and some colleagues have been awarded nearly 500 thousand dollars from NSF and other agencies to create a more robust infrastructure to support mathematics education in Africa.

**BLOCK 2, 2013 - Oc**tober

Denali Molitor, Hanson Smith and Ravi Donepudi (three of our current students) will give a PG rated talk on their research.

**Time: ** 2pm (Note this is not a usual time for us!)

**Location:** Kresge Lecture Hall, Tutt Science 122 Reception to Follow. **Titles: ** Fractal Analysis, Equal Circle Packing on Flat Tori, Rational Numbers and Function Fields: Similarities and Differences

*The real world is full of rough surfaces, which poses the challenge of how to represent and study these surfaces mathematically. Fractal analysis, although it still poses unrealistic structural restrictions on these rough surfaces, provides a first step toward this goal. By defining Laplacians on fractals, we can also then study how some functions behave on these rougher spaces. This presentation will focus on how space-filling Peano curves can be used to define Laplacians on certain classes of fractals by defining a way to continuously trace through subsequent graph approximations of the fractals.*

**Fractal Analysis (Denali Molitor):****The study of maximally dense packings of disjoint equal circles in di fferent types of containers is a problem in Discrete Geometry that has developed over the past forty years. The optimal densities and arrangements are known for packings of small numbers of equal circles in hard boundary containers, including squares, equilateral triangles and circles. In this presentation, I will explore packings of small numbers of equal circles in a boundaryless container called a flat torus. We will introduce the basic concepts (including the notion of a flat torus, an optimal packing and the graph of a packing), demonstrate many maximally dense arrangements for four equal circles, and outline a proof of their optimality. This research was conducted as part of the 2013 REU program at Grand Valley State University.**

*Equal Circle Packing on Flat Tori (Hanson Smith):***Function fields are interesting analogs of the familiar rational numbers. Although these two objects appear very different at a first glance, they have many properties in common. Many problems that are difficult to solve in the rational numbers become very simple in this new setting. Among the most famous of these is the Riemann Hypothesis, which we will prove in this setting. I also present work I did over the summer relating to extensions of these function fields. There should be something for everyone at this talk. Please pass the word along to anyone who might be interested!**

*Rational Numbers and Function Fields: Similarities and Differences (Ravi Donepudi)*:

**Rating:** PG

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