## Academic Year 2017 - 2018

### Spring 2018

### Fall 2017

No Talk - First Week of Classes

**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.

**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.

**Pseudo-random numbers: {mostly} a line {of code} at a time**

*Abstract:* Random numbers have an amazing range of application in both theory and practice.
Approximately-random numbers generated on a computer are called pseudo-random. This
talk discusses how one generates and tests such numbers, and shows how this study
is related to important mathematics and statistics - the Central-Limit Theorem and
the Χ2 measure - that have broad applications in many fields. Come and find out what
the Birthday Paradox, Diehard batteries, gorillas, Euclid, French soldiers, a Persian
mathematician, Prussian cavalry, and Queen Mary have to do with random numbers.

**The Angel Problem and other Games of No Chance**

*Abstract:* I'll discuss John Conway's "Angel Problem," a simple sounding game for two players (the angel and the devil). The game was introduced in
1982, and the problem of finding a winning strategy remained unsolved until 2005.
We'll talk about several variants of the game, and how these can be solved. Finally,
we'll discuss one or two other games that fall under the umbrella of combinatorial
game theory.

Casey Johnson (Math Department Alumnus)

**Student Opportunities at Department of Defense (with a little bit of math)**

*Abstract*: We discuss at a high level a variety of security-related positions within the U.S.
Government that may

be of interest to mathematicians. This will include professional opportunities, as
well as internships

available to undergraduates. As time permits, we will turn our attention to several
related algebra

problems and show how they can be combined to construct a primitive computer.

**Complex and Tropical Nullstellensatze**

*Abstract*: If a system of linear equations has no common solution, then by eliminating variables,
one can obtain 1 = 0 as a linear combination of the given equations. Hilbert’s *Nullstellensatz *or “zero set theorem” says that the same thing happens with polynomial equations provided
that one allows for complex solutions (and polynomial combinations). In the world
of tropical numbers we consider polynomial *relations *and then there is a result of the same nature. We’ll talk about this and also about
why the Nullstellensatz is the foundation of Algebraic Geometry.

**Big Data Employer Panel**

## Location - LCB Loft (4th floor)

*Abstract: *Want to know what it's really like to work in a job realting to math, data, and statistics?
Do you have questions about what it takes to land a position in "the real world" or
what classes you should focus on now for your future career success? Hear from former
students and get your questions answered! Food and networking to follow the panel.

**The scallop theorem**

*Abstract:*Bacteria and other small swimming organisms can't coast. Once they stop moving their flagella, they come to a complete stop instantaneously. They live in a world where inertia doesn't matter. We, on the other hand, live and swim in an inertia dominated world. The scalloptheorem is a beautiful and simple geometric argument explaining why if inertia does not matter, you can't swim with a single hinge or via reciprocal motion. While the scallop theorem tells us what does not work, it does not explain the rich swimming behavior observed in nature. To answer this question, applied mathematicians use a combination of model, analysis and simulation starting from the famous Navier-Stokes equations.

**Past Colloquia**

(links to Fall 1999 - Spring 2017)