Colloquium Lecture Series

Colloquium Lecture Series

Colloquium Lecture Series

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Guest Colloquium Lecture Series

Dr. Kathryn Leonard

Speaker: Dr. Kathryn Leonard, Occidental College, California, USA
Date/Time: April 15, 2019  |  4pm-5pm
Venue: Room 129, School of Business and Public Administration (SPBA), University of Guam

Abstract

Shape understanding––looking at a shape and intuitively understanding which parts are, e.g., body, arms, legs, toes, and ears––is almost effortless for humans. Training a computer to understand shapes in a similar way presents substantial challenges. This talk will discuss human shape perception and the challenges of automation. We will describe a promising mathematical shape model, the Blum medial axis. Using the Blum medial axis, we will propose a method for automatically decomposing a shape into a hierarchy of parts and determining the similarity between those parts. We will end by comparing our automated results to human perception data gathered from a massive user study. Time permitting, we will present recent work using neural networks to learn skeletal models.

Speaker's Biography

Dr. Kathryn Leonard's research interests are in geometric modeling with applications to computer vision and computer graphics. Her work has been recognized with a CAREER award from NSF, the Henry L. Alder Award for Excellence in Teaching from the MAA, and a Service Award from the AWM. She became a math major in her junior year of college, after her petition to waive the university's math GE requirement was rejected. Currently, she is Professor and Chair of the newly-formed Computer Science Department at Occidental College. She also directs the NSF-funded Center for Undergraduate Research in Mathematics and leads the AWM research networks Women in Shape and Women in the Data Science and Mathematics. She has held positions at CSU Channel Islands, where she helped build a university, Caltech, MSRI, and Pomona College. She still gets no respect from her cats.

On Friday, March 15, 2019, at 4:00 –5:20 p.m. in WB 3, the UoG Mathematics Faculty will hold a Colloquium Session to the 2019 University of Guam – Shibaura Institute of Technology Conference and Workshop in Mathematics

We are proudly presenting one of our speakers at the 2019 UoG – SIT Conference and Workshop to be held on March 22-23, 2019

Randomly Perturbed Ergodic Averages by Dr. JaeYong Choi.

Dr. Balakrishnan

Speaker: Dr. Jennifer Balakrishnan at Boston University
Date/Time: Dec 14 & 15, both 10am-12pm
Venue: 107AB Computer Center, University of Guam

Abstract

Elliptic curves over the rational numbers are curves that can be described by an equation y2 = x3 + ax + b, where a and b are rational numbers. Despite such a simple description, there are many open questions about these curves (some involving prize money of a million dollars!) I'll describe some open questions and present computational tools to investigate them during this hands-on workshop. Let's see what we discover!

Speaker's Biography

Jennifer Balakrishnan is a number theorist working on explicit methods for curves. Her research is motivated by various aspects of the classical and p-adic Birch and Swinnerton-Dyer conjectures, as well as the problem of algorithmically finding rational points on curves. She is currently the Clare Boothe Luce Assistant Professor of Mathematics at Boston University and is the recipient of a Sloan Research Fellowship. Previously, she was a Titchmarsh Research Fellow at the Mathematical Institute of the University of Oxford, a Junior Research Fellow of Balliol College, Oxford, and an NSF Postdoctoral Fellow at Harvard. Balakrishnan graduated from Harvest Christian Academy (2002) and received an AB and AM from Harvard University (2006) and a PhD in Mathematics from MIT (2011).

On Friday, November 16, 2018, at 4:00 –5:20 p.m. in WB 3, Dr. Raymond Paulino will hold a lecture titled:

Groups, Rings, and Things: Minimal Reductions

"Abstract Algebra is a branch of Mathematics that started out from solving equations in the 1800s, and now has many applications. I first introduce the star of Abstract Algebra known as a Group and give a brief sample of Group examples. Then I move to realm of Commutative Algebra. I will introduce the notion of a Ring and, in particular, Ideals, Noetherian Rings and Cohen-Macaulay Rings. Finally, I will discuss some of my results on Minimal Reductions of Edge Ideals."

The Challenges in Mathematics Colloquium Lecture Series is organized by the Division of Mathematical Sciences of the Colleges of Natural and Applied Sciences of the University of Guam. Our location is at the Division of Mathematical Sciences in Warehouse B, next to the Health-Science Building. Our intention is to introduce a wider audience of those who are interested in mathematical challenges into state-of-the-art mathematical theories, puzzles and open problems. We invite students, colleagues working in any area of science and everybody who wants to learn more about mathematics in an accessible setting.

Everybody is welcome!

For more information: see below flyer or contact Dr. Zoltan Szekely at zszekely@triton.uog.edu


Student Colloquium Lecture Series

Friday, October 11 

A MAGIC TRICK USING REED-SOLOMON CODES


Presenters: Angelika Argao1, Abigail Pobre1, and Alex Leon Guerrero2
Location: Room SC-200, Science Building
Time: 4:30 p.m.

Abstract:

Error detecting and error correcting codes comprise one of the key areas in coding theory and can be applied to various real-life situations. Reed-Solomon codes, in particular, play a vital role in ensuring that data received via storage devices, such as CDs and DVDs, and mobile and satellite communication, is error-free. On a smaller scale, the application of these codes can be demonstrated using magic tricks. With some help from some cards, a cube, and a little bit of magic, we can guess your correct color and number! We explore how this magic trick is constructed through the use the Galois field of 8 elements and Reed-Solomon codes to generate the correct answer.


A GAME-THEORETICAL APPROACH IN MODELING A POTENTIAL SARS OUTBREAK WITH MULTIPLE CONTROL STRATEGIES


Presenters: Regina-Mae Dominguez1
, Aurienne Cruz1, and Brian Lee2
Location: Room SC-200, Science Building
Time: 5:00 p.m.

Abstract

Severe Acute Respiratory Syndrome (SARS) is a viral respiratory disease that is caused by the coronavirus SARS-CoV. SARS is a nosocomial disease that is transferred through the air, making it highly contagious. We construct a game-theoretic model of SARS in which individuals choose whether to participate in either vaccination based on proposed vaccine data or education with quarantine against SARS in order to maximize their own benefits. We find that SARS is eliminated when the relative cost of education and vaccination with respect to their infection costs are zero, respectively. However, the optimal Nash Equilibria of education and vaccination are close to their herd immunity within 5% when the relative cost of education is allowed up to a 10% increase while the relative cost of vaccination is allowed up to a 0.6% increase.

1 Student from University of Guam
2 Student from St. John's School 

 

Friday, October 18

MAKING MAGIC WITH CODING THEORY


Presenters:
Gino Reyes1 
and Angela Zhang2
Location: Room SC-200, Science Building
Time: 4:30 p.m.

Abstract

Although coding theory is most known for its applications in technology, it can also be applied to create a magic trick. A popular example involves the use of binary numbers and Hamming Code, where a performer can guess the number an audience member secretly chooses. For our trick, we will also use Hamming Code. The main difference is that we will be implementing ternary. Instead of using binary like the previous trick, which allows an audience member to choose one of sixteen different numbers, using ternary will allow the audience member to choose one of twenty-seven numbers. In addition, we will also be presenting a second magic trick that utilizes Reed-Solomon Code instead. Furthermore, we have created models that will allow both magic tricks to run smoothly without any need to perform calculations.


VACCINATION AND EDUCATION TO COMBAT YELLOW FEVER: A GAME THEORETICAL APPROACH


Presenters: Jovic Cassi1
, Jaelene Manibusan1, Heera Kodiyamplakkal3, and Brian Joseph3

Location: Room SC-200, Science Building
Time: 5:00 p.m.

Abstract

Yellow fever is a vector-borne disease found in parts of South America and Africa, and had recent outbreaks occurring early 2019 in Brazil. It is transmitted by the mosquito Aedes aegypti. Strategies used to combat the disease include the use of a vaccine or educating the population to control the mosquito population and prevent mosquito bites. In this paper, we present a game-theoretical model to compare both vaccination and education strategies in which individuals may choose to protect against yellow fever and maximize their own benefits, effectively balancing the cost of protection and the risk of contracting yellow fever. We find critical thresholds for the costs of vaccination and education, above which no one will use the vaccine or get education. Also, we find relative cost ranges of vaccination and education with respect to the cost of infection to determine whether a single strategy is dominant over the other, or a mixed strategy involving both is viable.

1 Student from University of Guam
2 Student from Harvest Christian Academy
3 Student from St. John's School 

 

Friday, October 25

AN EXPOSITION ON MONSKY'S THEOREM


Presenters: William Sablan1
REU at University of Chicago
Location: Room SC-200, Science Building
Time: 4:30 
p.m.

Abstract

Since the 1970s, the problem of dividing a polygon into triangles of equal area has been a surprisingly difficult yet rich field of study. This paper gives an exposition of some of the combinatorial and number theoretic ideas used in this field. Specifically, this paper will examine how these methods are used to prove Monsky's theorem which states only an even number of triangles of equal area can divide a square.


INTO THE REVERIE: ANALYZING THE DREAM MARKET


Presenters: Dwight Sablan1
REU at Indiana University-Purdue University Indianapolis (IUPUI)
Location: Room SC-200, Science Building
Time: 5:00pm

Abstract

The Dark Web is an area of the internet that exists on an encrypted network where anonymity of users is preserved through the use of the Tor-Browser. This feature makes it a popular ground for users to engage in illicit activities, most notably, involvement in the online drug market. In this study, we analyze data collected from 2018-2019 on several cryptomarkets to understand contemporary darkness market at its pinnacle. We take a closer look at the goods and services being sold, behaviors in the buyer-seller network, and the economy of Dark Web marketing. Techniques in statistical analysis and data mining will be used via tools that enhance data augmentation, visualization, and comprehension (i.e. Beautiful Soup, Python, MySQL, Plotly, and Jupyter). By investigating illicit activities on these markets, we aim to provide the necessary comprehensive analysis to further promote law enforcement intervention and established policies in the cryptocurrency ecosystem.

1 Student from University of Guam