# Invited Paper Sessions

## Knot Theory

Part A: Thursday, August 4, 8:30 a.m. - 9:50 a.m., Fairfield
Part B: Thursday, August 4, 2:00 p.m. - 4:20 p.m., Fairfield

With the increase in undergraduate research there is also an increased need for open and accessible problems for students to tackle. Knot theory is particularly fertile ground for such problems. Each speaker in this session will introduce a topic, pose three open questions that are accessible to undergraduate research, and place the questions in context of the topic.

Organizers:
Lew Ludwig, Denison University

### Part A

Thursday, August 4, 8:30 a.m. - 9:50 a.m., Fairfield

#### Turning Knots into Flowers: Petal Number and Related Problems

8:30 a.m. - 8:50 a.m.

#### Knot Mathematical Fiddlestix: An Introduction to Lattice Knots

9:00 a.m. - 9:20 a.m.
Jennifer McLoud-Mann, University of Washington, Bothell

#### Problems Related to Spanning Surfaces of Knots

9:30 a.m. - 9:50 a.m.
Cynthia Curtis, College of New Jersey

### Part B

Thursday, August 4, 2:00 p.m. - 4:20 p.m., Fairfield

#### Rope Magic and Topology

2:00 p.m. - 2:20 p.m.
Louis Kauffman, University of Illinois, Chicago

#### Khovanov Homology Mod 2 Detects Adequate Homogeneous States (NEW)

2:30 p.m. - 2:50 p.m.
Thomas Kindred, The University of Iowa

#### Accessible Problems for Undergraduates in Knot Coloring(CANCELED)

2:30 p.m. - 2:50 p.m.
Candice Price, Sam Houston State University

#### Computer Algorithms for Counting Knot Mosaics

3:00 p.m. - 3:20 p.m.
Lew Ludwig, Denison University

#### Gamifying Knot Theory

3:30 p.m. - 3:50 p.m.
Jennifer Townsend, Bellevue College

#### Unknotting Knots

4:00 p.m. - 4:20 p.m.
Allison Henrich, Seattle University

## The Mathematics of Games

Thursday, August 4, 2:00 p.m. - 3:50 p.m., Harrison

Games, how to win them and how to design them, often lead to mathematical questions. Generally intractable games, such as poker, have ‘toy’ variants that yield to explicit mathematical analysis, while some simple ‘solved’ games such as tic-tac-toe become very challenging when moves are auctioned to the highest bidder. The talks in this session discuss the design considerations of games and the determination of optimal play in both games of chance and no-chance.

Organizer:
Michael Catalano-Johnson, Susquehanna International Group

#### Recent Advances in Game Design

2:00 p.m. - 2:20 p.m.
David Pettey, Susquehanna International Group

#### Solving Poker-Like Games

2:30 p.m. - 2:50 p.m.
Bill Chen, Susquehanna International Group

#### Richman Games

3:00 p.m. - 3:20 p.m.
Daniel Loeb, Susquehanna International Group

#### Misère Russian Roulette (with Multiple Revolvers)

3:30 p.m. - 3:50 p.m.
Michael Catalano-Johnson, Susquehanna International Group

## Mathematics and Magic

Friday, August 5, 1:00 p.m. - 3:55 p.m., Fairfield

Speakers will demonstrate and explain magic tricks based on interesting mathematical principles.

Organizer:
Arthur Benjamin, Harvey Mudd College

#### Tricks You Can Count On

1:00 p.m. - 1:15 p.m.
Irl BivensDavidson College

#### Shuffling Cards and Binary Numbers

1:20 p.m. - 1:35 p.m.
Steve ButlerIowa State University

#### More Card Effects from the Perfect Shuffle

1:40 p.m. - 1:55 p.m.
Doug Ensley, Shippensburg University

#### Dunninger Meets DeBruijn

2:00 p.m. - 2:15 p.m.
Ron Graham, University of California, San Diego

#### Telepathy or Tele-mathy-y?

2:20 p.m. - 2:35 p.m.
John Harris, Furman University

#### Tricks with SET $^®$

2:40 p.m. - 2:55 p.m.
Liz McMahon and Hannah Gordon, Lafayette College

#### Fitch Cheney's 5 Card Trick for Values of 5 Less Than 5

3:00 p.m. - 3:15 p.m.
Colm Mulcahy, Spelman College

#### This is Knot a Trick!

3:20 p.m. - 3:35 p.m.
Allison Henrich, Seattle University

#### Stretching Your Mind with Topological Mime

3:40 p.m. - 3:55 p.m
Tim and Tanya Chartier, Davidson College

## Mathematics and the Life Sciences at MBI

Friday, August 5, 1:00 p.m. - 4:10 p.m., Harrison

In this session we demonstrate how the mathematical sciences help address important and interesting questions in neuroscience, virology, cancer immunology, cellular communication, and sleep cycle dynamics.

Abstract: Using mathematics to gain new insights into the biological sciences requires the use of existing techniques and also the development of new mathematics. The interplay between math and life sciences is a key component of the mission of the Mathematical Biosciences Institute (MBI). This session samples research related to several of MBI's recent and upcoming thematic programs: molecular biosciences, cancer and the immune system, network dynamics, mathematical neuro-science, and the analysis of complex data.

In this session, we discuss how the mathematical sciences are utilized to make contributions to biological and biomedical questions. Theory and concepts from algebra, geometry, dynamical systems, numerical analysis, probability theory, and other areas will be presented. The math will be used to uncover symmetries in neural activity, quantify signaling dynamics inside cancerous immune cells, consider the impact of oscillations on coupled cells, investigate circadian rhythms and energy regulation, and increase the understanding of viruses and how to overcome their resistant nature.

Organizer:
Reginald L. McGee, Mathematical Biosciences Institute

#### Why We Sleep: Math Sheds New Light on Personal Energy Conservation

1:00 p.m. - 1:30 p.m
Janet Best, The Ohio State University

#### Dynamical Systems and Emergent Properties of Cell Networks

1:40 p.m. - 2:10 p.m.
Richard L. Buckalew, Mathematical Biosciences Institute

#### Singled Out: Using Single-Cell Data to Identify Signaling Trends in Leukemia

2:20 p.m. - 2:50 p.m.
Reginald L. McGee, Mathematical Biosciences Institute

#### An Insight to Viral Assembly through Normal Model Analysis

3:00 p.m. - 3:30 p.m.

#### Binocular Rivalry and Symmetry Breaking

3:40 p.m. - 4:10 p.m.
Marty Golubitsky, Mathematical Biosciences Institute

## Numbers, Geometries, and Games: A Centenarian of Mathematics

Saturday, August 6, 1:00 p.m. - 3:10 p.m., Fairfield

Born nearly at the same time as the MAA, Richard Guy has had a tremendous impact on mathematics through his (continuing) work in number theory, geometry, and game theory. This session brings together friends an colleagues to talk about these mathematical areas, to celebrate Richard's achievements, and to mark his transition to his second century.

Organizers:
Steve Butler, Iowa State University
Barbara Faires, Westminster College

#### Sums of Unit Fractions

1:00 p.m. - 1:20 p.m.
Ron Graham, University of California San Diego

#### Products of Farey Fractions

1:30 p.m. - 1:50 p.m.
Jeffrey Lagarias, University of Michigan

#### Some Tiling Problems

2:00 p.m. - 2:20 p.m.
Steve Butler, Iowa State University

#### Fibonacci Plays Billiards, Again

2:30 p.m. - 2:50 p.m.
Elwyn Berlekamp, University of California Berkeley

#### Remarks

3:00 p.m. - 3:10 p.m.
Richard Guy, University of Calgary

## Undergraduate Research Projects in the Mathematical Sciences

Saturday, August 6, 1:00 p.m. - 3:20 p.m., Harrison

The undergraduate mathematics curriculum continues to evolve from expository classes to students working on original research projects. This curriculum change has created a need in the mathematical community for more REU programs and for faculty to develop accessible research projects for students at their respective institutions. For new faculty, developing such projects may be challenging, as their particular expertise might require extensive background and is hence not suitable for an undergraduate audience. Fortunately, faculty programs, such as The Center for Undergraduate Research in Mathematics (CURM) Mini-Grants, Preparation for Industrial Careers in Mathematical Sciences (PIC Math) Preparing Undergraduates Through Mentoring toward PhD’s (PUMP), Project NExT (New Experiences in Teaching), and Research Experience for Undergraduate Faculty (REUF), have an impressive track record of helping faculty develop and promote accessible research projects at the undergraduate level.

In this session, past CURM, PIC Math, PUMP, Project NExT, and REUF faculty participants present the mathematical results of their student’s original mathematical research and share tools they learned and used to develop these projects. In addition, speakers will provide early-career faculty with information related the respective faculty programs and open problems that are accessible to undergraduate students. Mathematical topics are broad and include number theory, graph theory, applications of PDEs, and industrial mathematics.

Organizers:
Pamela E. Harris, Williams College
Alicia Prieto Langarica, Youngstown State University

#### Counting Dessins

1:00 p.m. - 1:20 p.m.
Naiomi Cameron, Lewis & Clark University

#### PIC Math: A Course for Undergraduate Students to Do Research on Actual Problems from Industry

1:30 p.m. - 1:50 p.m.
Michael Dorff, Brigham Young University

#### Constructing Solutions to Truncated Moment Problems and Applications to PDE; a PUMP Undergraduate Research Group

2:00 p.m. - 2:20 p.m.
Cynthia Flores, California State University, Channel Islands