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Open and Accessible Problems in Knot Theory

*Thursday, August 1, 1:00 p.m. – 5:00 p.m., Marriott, Ballroom A *

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. The final time slot in the session will consist of a discussion/reception where faculty and undergraduates can further discuss open problems with the speakers.

**Organizers:**

Lew Ludwig, Denison University

Laura Taalman, James Madison University

**Turning Knots into Flowers**

*1:00 p.m. – 1:20 p.m.*

Colin Adams, Williams College

**Knot Mosaics**

*1:30 p.m. – 1:50 p.m.*

Lew Ludwig, Denison University

**The Forbidden Number of a Knot**

*2:00 p.m. – 2:20 p.m.*

Sandy Ganzell, St. Mary’s College of Maryland

**Folded Ribbon Knots in the Plane**

*2:30 p.m. – 2:50 p.m.*

Elizabeth Denne, Washington & Lee University

**Graphs that are Intrinsically Linked with an Unused Vertex**

*3:00 p.m. – 3:20p.m.*

Joel Foisy, SUNY Potsdam

**Sequences, Spiral Knots, and the Elephant in the Room**

3:30 p.m. – 3:50 p.m.

Laura Taalman, James Madison University

**Problems in Virtual Knot Theory**

4:00 p.m. – 4:20 p.m.

Louis Kauffman, University of Illinois at Chicago

**Question & Answer Session**

4:30 p.m. – 5:00 p.m.

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Developments in Commutative Algebra

*Thursday, August 1, 2:00 p.m. – 5:50 p.m., Marriott, Ballroom B*

Commutative algebra may be thought of as studying solutions of many equations in many unknowns when, typically, the solution is not unique. The set of solutions could then be viewed geometrically, but one can instead encode all the relevant information about the equations in algebraic objects called commutative rings. Study of the resulting ring structure can then give information about the geometric object, or can be pursued in its own right. In this Invited

Paper Session, current research results in commutative algebra will be presented in a way that will be inviting to a non-expert audience.

**Organizers:**

Susan Loepp, Williams College

Janet Striuli, Fairfield University

**Zero-Divisor Graphs of Certain Semigroups Associated to Commutative Rings**

*2:00 p.m. – 2:20 p.m.*

Neil Epstein, George Mason University

**An Introduction to Path Ideals**

*2:30 p.m. – 2:50 p.m.*

Leah Gold, Cleveland State University

**Associated Primes of the Third Power of Cover Ideals**

*3:00 p.m. – 3:20 p.m.*

Cameron Bishop, Fairfield University

**Totally Reflexive Modules**

*3:30 p.m. – 3:50 p.m.*

Janet Striuli, Fairfield University

**Hilbert Series, H-Vectors, and the Fibonacci Sequence**

*4:00 p.m. – 4:20 p.m.*

Branden Stone, Bard College

**Going to Great Lengths…**

*4:30 p.m. – 4:50 p.m.*

Hans Schoutens, New York City College of Technology

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Complex Geometry Research and Accessible Problems

*Friday, August 2, 2:00 – 4:50 p.m., Marriott, Ballroom A*

Complex geometry continues to be an area of fruitful research at all levels, from undergraduates to professional researchers. Areas as diverse as algebraic geometry and complex dynamics make use of the structure that complex analysis provides. In this session the speakers will highlight areas of current research related to complex geometry and point out opportunities for research involving undergraduates.

**Organizers:**

Lynette Boos, Providence College

Su-Jeong Kang, Providence College

**Locating and Counting the Zeros of the Polynomials \(p(z) = z^n + z^k-1\)**

*2:00 p.m. – 2:20 p.m.*

Michael Brilleslyper, US Air force Academy

**Minimal Surface and Harmonic Mappings**

*2:30 p.m. – 2:50 p.m.*

Jane McDougall, the Colorado College

**Composition Operators and the Geometry of the Unit Disk**

*3:00 p.m. – 3:20 p.m.*

Christopher Hammond, Connecticut College

**Complex Variables and Gravitational Lensing by a Spiral Galaxy**

*3:30 p.m. – 3:50 p.m.*

Erik Lundberg, Purdue University

**Connecting Real and Imaginary Parts of Complex Quadratic Functions to Julia Sets**

*4:00 p.m. – 4:20 p.m.*

Julia Barnes, Western Carolina University

**Complex Analysis and Soap Films**

*4:30 p.m. – 4:50 p.m.*

Michael Dorff, Brigham Young University

##
AMS-MAA Special Session: Coding Theory and ...

*Friday, August 2, 2:00 – 4:50 p.m., Marriott, Ballroom B*

Whenever information is transmitted or stored, errors are bound to occur. It is the goal of coding theory to devise efficient methods of adding redundancy to the information so that these errors can be detected and corrected. By its very nature, coding theory lies at the intersection of mathematics, computer science, and electrical engineering. Many different areas of mathematics have found applications in coding theory, including linear algebra, combinatorial designs, number theory, group theory, algebraic geometry, and graph theory, just to name a few. Each talk in this session will highlight a connection between coding theory and some area of mathematics, either by discussing how that branch of mathematics was used to obtain a recent coding theoretic result or by discussing how coding theory can be incorporated into an undergraduate-level course in that branch of mathematics.

**Organizers: **

Katherine Morrison, University of Northern Colorado

Judy L. Walker, University of Nebraska – Lincoln

**Using Coding Theory for Quantum Cryptography **

*2:00 p.m. – 2:20 p.m.*

Susan Loepp, Williams College

**Coding Theory, Designs, and Finite Geometries **

*2:30 p.m. – 2:50 p.m.*

David Clark, University of Minnesota

**Coding Theory and Elementary Number Theory**

*3:00 p.m. – 3:20 p.m. *

Justin Peachey, Davidson College

**Coding Theory and Neuroscience**

*3:30 p.m. – 3:50 p.m.*

Nora Youngs, University of Nebraska - Lincoln

**Coding Theory and Graph Search Algorithms **

*4:00 p.m. – 4:20 p.m.*

Elizabeth Weaver, Indiana University Southeast

**Coding Theory and Instrumentation**

*4:30 p.m. – 4:50 p.m.*

Jonathan Hall, Michigan State University

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Recent Developments in Mathematical Finance

*Saturday, August 3, 1:00 – 4:45 p.m., Marriott, Ballroom B*

This invited paper session will address recent challenges and solutions in Mathematical Finance. In particular, presentation themes will cover the theories of optimal investment, options pricing, risk management and price impact for large investors. The mathematical methods used herein are primarily from the field of Stochastic Analysis, but also branch out to include results from general Probability Theory, Partial Differential Equations, Convex and Harmonic Analysis, as well as Game Theory.

While the chief objective of the session is to provide results from the forefront of research into Mathematical Finance, a significant secondary goal is to make the talks accessible to a broader audience. Special attention will be paid to undergraduate and graduate students, as well as those researchers with a basic working knowledge of Probability and Stochastic Processes. Indeed, this session hopes to convince those who attend it that there are many interesting and challenging open problems in Mathematical Finance, both from a Mathematical and “Real World” perspective.

**Organizers:**

Tomoyuki Ichiba, University of California Santa Barbara

Scott Robertson, Carnegie Mellon University

**Static Fund Separation of Long Term Investments**

*1:00 p.m. – 1:30 p.m.*

Scott Robertson, Carnegie Mellon University

**Occupation Times, Drawdowns, and Drawups for One-Dimensional Regular Diffusions**

*1:45 p.m. – 2:15 p.m.*

Hongzhong Zhang, Columbia University

**Volatility – A Key Concept in Mathematical Finance**

*2:30 p.m. – 3:00 p.m.*

Stephan Sturm, Worcester Polytechnic Institute

**Portfolios Under Rank-Based Equity Market Models**

*3:15 p.m. – 3:45 p.m.*

Tomoyuki Ichiba, UCSB

**Trends and Trades**

*4:00 p.m. – 4:30 p.m.*

Olympia Hadjiliadis, CUNY Brooklyn

##
Climate and Geophysical Modeling

*Saturday, August 3, 2:00 – 3:50 p.m., Marriott, Ballroom A*

Mathematical models of the atmosphere, oceans, and other geophysical systems and are a key part of understanding Earth system dynamics and the effects of climate change. The Earth system is immensely complex and mathematical and computational techniques are vital to analyzing and studying the dynamics. In honor of the 2013 Mathematics of Planet Earth initiative, this session will highlight role of mathematics in modeling, predicting, and explaining behavior in areas such as hydrodynamics, atmospheric and oceanic circulation, sea ice, and biogeochemical processes. It will focus research involving computational models of geophysical systems and the integration of data into these models.

**Organizer:**

Matthew J. Hoffman, Rochester Institute of Technology

**Improving Climate Models Using Non-Global Data Assimilation and Parameter Estimation**

*2:00 p.m. – 2:20 p.m.*

Lewis Mitchell, University of Vermont

**A Hybrid Ensemble Kalman Filter / Variational Method for Data Assimilation of the Ocean**

*2:30 p.m. – 2:50 p.m.*

Steven Penny, University of Maryland

**Numerical Modeling of Vegetation-Climate Feedbacks: An Example over Western Africa**

*3:00 p.m. – 3:20 p.m.*

Clement Alo, Montclair State University

**Quasi-Periodic Fluctuations in Climate Due to Sea Ice**

*3:30 p.m. – 3:50 p.m.*

Raj Saha, Bowdoin College