# 2013-2014 Mathematics Colloquia

## Schedule for Winter 2014

### Quantum Computing and Grover's Algorithm

#### Colloquium: Onye Ekenta (W&L '15)

Time: Tuesday, March 11th at 4:40 - 5:35pm

Place: duPont 104

Refreshments at 4:20pm.

Quantum computers are at the forefront of modern computer research. They have the potential to completely redefine what computers are capable of. If people become able to efficiently construct effective quantum computers the newfound computing technology would have vast implications in the fields of cryptography, artificial intelligence, physical simulations and likely many more areas which no one has yet conceived of. This talk will introduce he basics of how quantum computers work and what makes them so much more powerful than classical computers. It will explain in detail the process of one of the most famous quantum algorithms, Grover's algorithm, which is an algorithm that can find an element in a list that exploits the principles of quantum superposition and quantum entanglement to, in general, arrive at the solution faster than any classical computer could.

### Them Infamous Exploding Dots

#### Mathematics Symposium: Dr. James Tanton, St. Mark's School

Time: Tuesday, March 18th at 12:20 - 1:15pm

Place: Hillel Multipurpose Room

Refreshments provided

Believing that mathematics really is accessible to all, James Tanton (PhD, Mathematics, Princeton 1994) is committed to sharing the delight and the beauty of the subject. IN 2004 James founded the St. Marks Institute of Mathematics, an outreach program promoting joyful and effective mathematics education for both students and educators. James is now the Mathematician in Residence at the Mathematical Association of America in Washington D.C. He also conducts the professional development program for Math for America, D.C. He is the 200 recipient of the Beckenbach Book prize, the 2006 recipient of the Kidder Faculty Prize at St. Marks School, and a 2010 recipient of Ratheon Math Hero Award for excellence in school teaching.

### A Dozen Proofs that 1 = 2: A Misguided Review of Mathematics

#### University Lecture: Dr. James Tanton, St. Mark's School

Time: Tuesday, March 18th at 4:40 - 5:30pm

Place: Leyburn Northern Auditorium

Guidobaldo del Monte (1545-1647), a patron and friend of Galileo Galilei, believed he had witnessed the creation of something out of nothing when he established mathematically that zero equals one. He thereby thought that he had proved the existence of God! Although I daren't be so bold with my claims, I am willing to prove instead that one equals two. And, moreover, just to convince you that I am right I will do so multiple times over, drawing upon a wide spectrum of mathematical techniques: algebra and arithmetic, probability and mechanics, pure thought and physical action! Will you be able to find fault with any of my "proofs?"

### Open Problems in Knot Theory that everyone can try to solve

#### Colloquium: Sandy Ganzell, St. Mary's College of Maryland

Time: Wednesday, March 19th at 4:40 - 5:35pm

Place: duPont 104

Refreshments at 4:20pm.

The mathematical study of knots is over 200 years old. The subject has led to deep results in Topology and Geometry, as well as applications in Chemistry, Physics and Biology. Yet, despite considerable growth of the theory in recent years, there are fundamental questions that remain unsolved. Many of these problems are accessible even for beginners. Certainly, undergraduates have played an important role in the development of the field. In this talk we will discuss some of the history of Knot Theory and present several open problems that anyone can try to solve.

#### Folds and Cuts: Mathematics and Origami

##### Pi Mu Epsilon: Elizabeth Denne, W&L

Time: Tuesday, April 1st at 4:40 - 5:35 pm.

Place: Hillel Multipurpose room

Refreshments at 4:20pm

#### Finding Cycles in the kth power digraphs over integers modulo a prime and over Gaussian integers modulo a Gaussian prime

#### Honors Thesis Defense: Wenda Tu ('14)

Time: Wednesday, April 2nd at 3:35 - 4:30 pm.

Place: duPont 104

Refreshments/Reception at 3:15

Given Zp where p is an integer prime, let’s define Gp(k) to be the digraph whose set of vertices is Zp such that there is a directed edge from a vertex a to a vertex b if ak b mod p. First, we find our own way to decide if there is a cycle of length t in a given graph Gp(k) in Zp.Later, we extend our work from Zp to Z[i] /[p] for p Gaussian primes. We found similar ways to determine the cycles in Gp(k) in such Gaussian integer field.

### Polynomial Perplexity

#### Carrie Finch: W&L Math Department

Time: Tuesday, February 25th at 4:40pm

Place: duPont 104

Refreshments at 4:20 in duPont

Abstract: You're not alone; it's happened to all of us. When the moment presented itself, you balked. You stuttered. You stammered. And all you could come up with was x^2 + 2x + 3. That's the best you could do. And now, you're lying in bed, and just as you drift off to sleep, it comes to you: the perfect polynomial. If only you had thought of it at the right moment you would have been the life of the party! You would have put that bully in his place! You would have secured that promotion! Don't let this happen to you! In this talk, we'll discuss some tricks to help you quickly decide whether a polynomial is irreducible, and some other tricks to help you come up with an irreducible or reducible polynomial on a moment's notice. It will just be left to you to discern which one is called for in your particular social situation!

### Integer Sequences and Algebraic Identities

#### Cory Colbert: Ph.D. student at the University of Texas - Austin

Time: Wednesday, January 8th at 4:40pm

Place: duPont 104

Refreshments at 4:20 in duPont

Abstract: We begin by investigating the well-known Fibonacci sequence and observing that there are many surprising relationships between algebraic identities involving the golden ratio, and recurrence relations involving the Fibonacci sequence. We demonstrate that such relationships are no coincidence - many more nontrivial examples stem from a much broader class of recurrence relations.

### Schedule for Fall 2013

#### Mercer Consulting

##### Colin Bracis ('03), representative of Mercer

Come learn what it means to be an Actuary!

Time: Thursday, October 3 at 4:40pm

Place: duPont 104

Refreshments at 4:20pm in duPont

### Student Summer Research Presentations - Parent's Weekend

#### David "Mod Too" McKennon and Braedon Suminski

#### Colin Hagenbarth

#### Alyssa Hardnett

Time: Friday October 4 at 3:30

Place: duPont 104

Refreshments at 3:15 in duPont

### True or False?

#### Lenny Jones, Shippensburg University

Time: Thursday, October 17 at 4:40pm

Place: duPont 104

Refreshments at 4:20 in duPont

Abstract: Various statements will be presented and, with the help of the audience, we will attempt to determine whether each statement is true or false. Monetary rewards will be given for the best participants from the audience.

### Summer Research Opportunities

#### Carrie Finch, W&L Mathematics Professor

Time: Thursday, Nov. 7 at 4:40pm

Place: duPont 104

Abstract: Come and learn about summer research opportunities in math and the physical sciences.

### Come Meet Two Math Alumni

#### Liz Beazley and Susan Woodward

Time/Place: Friday, Nov. 8th, 2:30-4pm in Baker 207

Liz is a mathematics professor at Haverford College in Connecticut and Susan is an actuary.

All are invited to come and talk about graduate school in math or what it's like to be an actuary.

### Is every matrix the product of Toeplitz Matrices?

#### Bill Ross, University of Richmond

Time: Tuesday, November 12 at 4:40pm

Place: duPont 104

Refreshments at 4:20 in duPont

Abstract: Toeplitz matrices are square matrices which are constant along its diagonals. Recently, Ye and Lim showed that every matrix is the product of Toeplitz matrices. I will outline their proof. I addition, I will discuss work of one of my students who extended this result and showed that the set of all square matrices is the product of algebras of Toeplitz matrices. This talk will be very general and is definitely suited for both faculty and students.

### Is there a truth calculator for all of mathematics?

#### Sean Cox, Virginia Commonwealth University

Time: Wednesday, November 20 at 3:35pm

Place: duPont 104

Refreshments at 3:15 in duPont

Abstract: Can every conceivable mathematical statement, at least in principle, be either proved or disproved? Here "in principle" means that we ignore any constraints on time, resources, or ingenuity. This question was posed by David Hilbert around 1920. Hilbert also proposed a strategy, now known as Hilbert's Program, to obtain a "yes" answer to this question. In modern terms, he sought to prove the existence of a computer program which would take as an input any mathematical statement, and after some finite number of steps, tell us (correctly) whether the statement is true or false. Such a program actually exists in limited contexts; two famous examples are Presburger Arithmetic (basically number theory without multiplication) and the theory of the ordered field of real numbers. However, Kurt Goedel proved in the 1930s that the general form of Hilbert's Program is doomed: there exist simple mathematical statements about natural numbers which can neither be proved nor disproved. Moreover, this phenomenon persists even if we augment our mathematical arsenal by including new fundamental assumptions (axioms) about mathematical objects.