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UNDERGRADUATE COLLOQUIUM


 The Mathematics Undergraduate Colloquium is held each Wednesday from 12:55 - 1:45 during the regular academic year in LCB 225. Each week a different speaker will present information on a specific subject area in mathematics. Anyone can come by to listen, socialize, get to know members of the department, and hear some interesting information on the many areas of mathematics.

Fall 2018 SCHEDULE

Peter Alfeld

Cool Mathematics

Abstract: I will in fact talk about some unsolved, or recently solved, problems in Mathematics. The main purpose of the meeting, however, will be to organize the Undergraduate Colloquium for those interested in taking it for credit (1 hour credit/no credit). For many participants this will be the first class in which they have to write a technical report. This is a complicated yet gratifying task. I will discuss some of the issues involved and also give a first introduction to the use of LaTeX.

The King Chicken Theorem

 Abstract:  Consider a flock of chickens. In any pair of chickens, one pecks the other. However, there might not necessarily be a chicken who pecks every other bird. Instead, we call a "king chicken" one that, for every other chicken in the flock, either pecks that chicken, or pecks a chicken who pecks it. By representing each chicken as a vertex and each pecking relationship with an edge, we can use graph theory to examine chicken politics. We will see every flock has a king, but this king is not necessarily unique, or even uncommon. 

Foraging in an Uncertain World

 Abstract:  Suppose you are an insect, foraging for sustenance across patches of plants. When your random search lands you on a plant, you must make some decisions. How long should you visit this specific plant? And when you leave, should you stay close or travel to a new patch that is less depleted? We will use the Marginal Value Theorem to find your optimal strategy in a world where you have total information. Then we will introduce uncertainty in the number and types of plants to see how this changes your strategy. We will also consider the plants' perspective, to see how their neighbors help or hurt them based on your foraging behavior.

The Porisms of Steiner and Poncelet


Abstract:  Draw two circles, one inside the other. Starting anywhere
between the two circles we can draw a chain of circles tangent to both. In
some cases the chain will close up on itself. Steiner's remarkable porism
states that whether the chain closes does not depend on where we start. We
will prove this during the talk, and discuss another such result due to
Poncelet if time permits.

 How Do Bacteria Talk? Understanding Bacterial Quorum Sensing by Mathematical Modeling

Abstract:  Quorum sensing is a bacterial communication mechanism that uses signal-receptor binding to regulate gene expression based on cell density, resulting in group behaviors such as biofilm formation and bioluminescence. In certain bacterial species such as Vibrio harveyi, several parallel quorum sensing signaling pathways drive a single phosphorylation-dephosphorylation cycle, which in turn regulates quorum sensing target genes. Through mathematical modeling, we investigate how signal integration is done at single cell levels and how bacteria use quorum sensing to measure its social and physical environment.

 

 

On the Labouchere Betting System

Abstract:  The Labouchere betting system was popularized in the late 19th century by British politician and journalist Henry Labouchere.  The system is easy to understand but surprisingly difficult to analyze.  In their 2001 book, One Thousand Exercises in Probability, Grimmett and Stirzaker posed the problem of proving that the maximum bet size in the Labouchere system applied to a fair game has infinite expectation, and they provided a solution.  Five years later it was discovered that their proof is incorrect, so the claim became a conjecture.  We will provide evidence suggesting that the conjecture is true, but the fact remains that it has defied resolution for 12 years.  That is, until July 2018 when it was finally settled by two graduate students at Stanford University.
 
Career Opportunities in the Tech Industry
 
Abstract:  In pursuit of your mathematics degree, you are developing valuable skills in communications, research and problem solving. These skills have broader utility in engineering, systems architecture, software development and data science. In this talk, I will discuss how you can leverage a degree in mathematics to pursue a career in the tech industry.
 
Fall Break

 

Fractal Patterns, Game Theory and Bali's Rice Terraces

Abstract:  Bali's famous rice terraces, when seen from above, look like colorful mosaics because some farmers plant synchronously, while others plant at different times.  The resulting fractal patterns are rare for human-made systems and lead to optimal harvests without global planning.  We'll describe a model of this system, introducing some notions from game theory, to help understand this peculiar example. 

 The Hat Problem

Abstract: A group of prisoners is given an opportunity to play a game for their freedom. Each prisoner has a hat, either white or black (both equally likely), simultaneously placed on their heads. Absolutely no communication between prisoners is possible after this point.  Prisoners cannot see their own hat, but they can see the hats of the others.   The warden then rings a bell, and the prisoners must all simultaneously guess a color (white or black) or pass.  They all win their freedom when at least one prisoner guesses the color of their own hat without any incorrect guesses being made. If an incorrect guess is made (or if everyone passes), they are all marched back to prison.

The prisoners may work together to devise a strategy before the game begins. What is an optimal strategy for the prisoners to secure their freedom?  (Hint: if 45,000 prisoners fill Rice-Eccles stadium, there is a strategy that guarantees their freedom 99.996948242% percent of the time.)
Bombs away!
 
Abstract:  The city of Amsterdam is planning to redevelop a piece of land close to its harbor, but it is known that this piece of land has been bombarded several times by Allied forces in World War II. Historical research on old Allied military administration and reports by local police at the time, plus aerial photographs taken during the bombardment, have given a fairly precise picture of where there have been impact explosions during a bombardment, but also of how many bombs were actually dropped. About 10% of bombs dropped during WW II did not explode, and Amsterdam is no exception. Unexploded bombs form a risk, especially when the ground they are in is disturbed, for example by building activity. The city would really like to know what are the risks of finding an undetonated bomb in a specific area in or close to the bombardments. We developed a Bayesian model for the locations of the dropped bombs, and using the information on the explosions, we were able to determine a risk per square meter. Our approach uses a Metropolis Hastings algorithm to find the posterior probability measure of the location of the missing bombs, and in this talk we will try to explain these concepts.
 

The Behrens-Fisher Problem

Abstract:  "Which of the two populations is bigger on average?"  This is an often asked question in statistics.  An often provided answer is by way of a two sample t-test assuming the populations are approximately normally distributed, with about the same degree of variability. However, what if the populations have different degrees of variability?  It is not clear what the appropriate test should be!  This is the classic Behrens-Fisher problem. 

We will discuss some solutions to particular avatars of this general problem. 

Me, You and Math

Abstract:  How does learning mathematics in classrooms differ from the way mathematicians do mathematics (or does it)? Who does mathematics and why? What does the educational research say about the value of discussing mathematics? How can we create more inclusive classrooms and dispel the genius myth that lingers within the mathematics community? Does the structure of math classes impact student success? In this talk, we'll explore these questions and possibly challenge our own ideas about our individual roles within our mathematics community.

No talk, Thanksgiving Break. 

The Mathematics of Rainbows

 Abstract:  Are rainbows bridges to heaven? Or bows to shoot arrows of lightning? Is there really a pot of gold at the rainbow’s end?  “Where does the rainbow end, in your soul or on the horizon?”  (Pablo Neruda)

In this talk we will try to answer these questions (and many more) on the nature of rainbows by using many resources of mathematical physics.

Hotel Infinity 

Abstract:  You are the owner of Hotel Infinity. It has infinitely many rooms, and it's full. A new guest arrives and insists you give her a room. How do you accommodate her? The next day, a family with infinitely many members arrives, each of whom wants a private room. The next day infinitely many families, each with infinitely many members, arrive. Each family member insists on a private room. You can do it! Infinity is different.

Math 3000 (Receive Credit for Attending)

The Undergraduate Colloquium is open to anyone to attend; however, if students would like to receive credit, you may register for Math 3000.
This is a 1 credit hour CR/NC course. To receive credit:

  • You may not miss more than 2 of the colloquia
  • You will need to write a short paper on one of the topics presented during the semester. (Report Specifications)

Course Syllabus - Fall 2018

Past Colloquia


Course Coordinators 

Peter Alfeld  Lisa Penfold
Course Instructor                          Administrative Coordinator
pa@math.utah.edu ugrad_services@math.utah.edu
Last Updated: 11/26/18