# Current Academic Year Seminars

### BLOCK 8 - April/May 2016

**Friday, April 29th at Noon**

**TSC 122 Lecture Hall**

PIZZA PROVIDED

PIZZA PROVIDED

**Speaker:** Professor Emerita, Colorado College - Kathy Merrill**Title:** "Taming Messy numbers"

**Rated: **G (General Audience - No mathematics or computer science knowledge assumed.)

**Abstract:** Mathematical applications regularly require that we make simple rational approximations to messy numbers. For example, building the scale used in western music requires reconciling fifths and octaves, and thus making a simple approximation to the log (base 2) of 3. Developing a calendar based on both lunar and solar cycles requires a simple approximation to (365.242199)/(29.350588). Continued fractions provide the best way of approximating irrationals and messy fractions with simple fractions. This talk will describe the continued fraction algorithm both numerically and geometrically, and discuss applications that make use of it, such as those mentioned above. We will also explore continued fraction approximations for old friends like e, pi, the square root of 2, and the golden mean.

*

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### BLOCK 7 - March/April 2016

**Friday, April 1st**

**TSC 122 Lecture Hall**

Pizza Provided

SENIOR CAPSTONE PRESENTATIONS

Pizza Provided

SENIOR CAPSTONE PRESENTATIONS

Seniors present their capstone projects. Tentative Schedule of speakers:

12:00-12:20 - Yichun Shi - An Investigation of Bullying in Social Networks

12:25-12:45 - Venkatasai Ganesh Karapakula - Weird Variation in Bounded Stuff

12:50-1:10 - John Moody - High-Performance Persistent Graphs

1:15-1:35 - Nick Kramer - An Introduction to Logic Algebras

*

**Thursday, March 31st at 3pm**

**TSC 229**

**Robin Wilson, Emeritus Professor at Open University UK**

Speaker:

Speaker:

**Title:**"A century of graph theory"

**Rated: **PG-13 (A lot of undergraduate mathematics or computer science knowledge assumed.)

**Abstract: **This talk covers the period from around 1890, when graph theory was mainly a collection of isolated results, to the 1990s when it had become part of mainstream mathematics. Among many other topics it includes material on the four-colour problem, trees, graph structure, and graph algorithms. No particular knowledge of graph theory is assumed.

*

**Friday, March 25th at NOON**

**TSC 122 Lecture Hall**

PIZZA PROVIDED

PIZZA PROVIDED

**Speaker:** Robin Wilson, Emeritus Professor at Open University UK**Title:** "Stamping Through Mathematics"

**Rated: **G (No Mathematics knowledge assumed)

**Abstract:** In this talk, I shall cover the entire history of mathematics in one hour, illustrating the narrative with 300 postage stamps from around the world and illustrating a wide range of mathematics and mathematicians. Some of these stamps are highly bizarre and amusing. This talk is aimed at a general audience.

*

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### BLOCK 6 - February/March 2016

**Friday, March 4th at 2:30pm**

**TSC 229**

**Speaker:**Visiting Assistant Professor Molly Moran

**Title:**"Baumslag-Solitar Groups and their Boundaries"

**Rated: **PG-13 (A lot of undergraduate mathematics or computer science knowledge assumed.)

**Abstract:** In 1962, Gilbert Baumslag and Donald Solitar introduced a family of groups, BS(m,n), that are simple to describe and yet provide very interesting examples and counterexamples in group theory. We will discuss Baumslag-Solitar groups, not from an algebraic standpoint, but rather we will describe how we can think of these groups (and any finitely presented group) as geometric objects and discuss why these groups also provide interesting examples in this new setting. In particular we will discuss how to construct the boundary for Baumslag-Solitar groups, which provides many new examples of Z-structures.

Joint work with Craig Guilbault (University of Wisconsin-Milwaukee) and Carrie Tirel (University of Wisconsin-Fox Valley).

*

**Friday, February 26th at NOONFearlessFriday Student Level Talk**

**TSC 122 Lecture Hall**

**PIZZA PROVIDED**

**Title:**"Are you a topological pool shark?"

**Rated: **PG (Some undergraduate mathematics or computer science knowledge assumed.)

**Abstract:** The classic game of pool is played on a flat table. What other kinds of surfaces make sense to play on? What about a torus? Could YOU make a shot on a torus? This talk will be an interactive exploration of the topological properties of a surface that may (or may not!) make it desirable for pool.

*

**Thursday, February 25th at 3pmResearch Talk**

**TSC 229**

**Title:**"Pretzel knots: Slices, Ribbons, and Mutations"

**Rated: **R (A lot of undergraduate mathematics or computer science knowledge assumed.)

**Abstract:** A long-standing open conjecture, the Slice-Ribbon Conjecture, posits the equivalence of two types of knots: slice knots and ribbon knots.* While many (most?) mathematicians seem to believe that the conjecture is false, all empirical evidence points to it being true. In 2011, Greene and Jabuka showed that the Slice-Ribbon Conjecture holds for the infinite family of odd 3-stranded pretzel knots. In their paper, they give a complete characterization of the slice/ribbon knots in that infinite family. The speaker will give an overview of her recent work regarding the Slice-Ribbon Conjecture for the class of odd 5-stranded pretzel knots. The two extra strands in this case add a level of complexity not seen in the 3-stranded case, specifically with regard to knot mutation. In fact, the main result states that if an odd 5-stranded pretzel knot is slice, then it is mutant to a ribbon knot.

*Slice knots, ribbon knots, pretzel knots, and knot mutation will all be defined in the talk.

*

**Friday, February 19th at NOON**

**TSC 122 Lecture Hall**

**PIZZA PROVIDED**

**Title:**"Graphs and Matrices and Zombies "

**Rated: **PG (Some undergraduate mathematics or computer science knowledge assumed.)

**Abstract:** A simple graph is an ordered pair G=(V,E) where V is a set of vertices and E is a set of edges, which are two-element subsets of V. The maximum nullity of G, denoted M(G), is the largest possible nullity over all real symmetric matrices whose ij-th entry (for i,j distinct) is nonzero whenever {i,j} is in E and is zero otherwise. Maximum nullity can be difficult to calculate on its own, but can be estimated using another graph parameter called the zero forcing number. The zero forcing number of G, denoted Z(G), is the size of a minimum zero forcing set in G and can be found by playing a color-changing infection game on the vertices of G. In this talk, I will introduce the concept of zero forcing and discuss its usefulness with regard to calculating the maximum nullity of a graph.

*

**Thursday, February 18th at 3pm**

**TSC 229**

**Title:**"A random version of the r-fork-free theorem"

**Rated: **R (A lot of undergraduate mathematics or computer science knowledge assumed.)

**Abstract:** Let P(n) denote the set of all subsets of [n] and let P(n,p) be the set obtained from P(n) by selecting elements independently at random with probability p. The r-fork partially-ordered set, or poset, is the family of distinct sets F, G_1,...,G_r such that F \subset G_i for all i. De Bonis and Katona showed that, for fixed r, any (r+1)-fork-free family in P(n) has size at most (1+o(1)){n\choose \lfloor n/2\rfloor}. In this talk, I will discuss a similar result for (r+1)-fork-free families in P(n,p). In particular, if pn\to\infty, then with high probability, the largest (r+1)-fork-free set in P(n,p) has size at most (1+o(1))p{n\choose \lfloor n/2\rfloor}. This result is influenced by the work of Balogh, Mycroft and Treglown, who proved a random version of Sperner's theorem using the hypergraph container method.

*

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### BLOCK 5 - January/February 2016

**Friday, February 5th at NOON**

**TSC 122 Lecture Hall**

PIZZA PROVIDED

PIZZA PROVIDED

**Title:** "The What and Why of Software Engineering"

**Rated: **PG (Some undergraduate mathematics or computer science knowledge assumed.)

**Abstract:** Software systems are growing in complexity as they grow in criticality. The stakes are high for software developers—software failures can have serious consequences—loss of money, loss of market, and even loss of human life. Software engineering processes are mechanisms for developing software systems with the goal of producing high quality software while managing time and budgetary concerns. This talk provides a high level introduction to software engineering by introducing the critical software engineering activities and describing the two main categories of software processes used to manage them.

*

**Thursday, February 4th at 3pm**

**TSC 229**

**Title:**"Using Text Mining Techniques to Extract Rationale from Unstructured Text"

**Rated: **PG13 (A lot of undergraduate mathematics or computer science knowledge assumed.)

**Abstract:** Design rationale has been an active area of research for over 30 years. The reasons for interest are clear—rationale captures the decisions, solutions, and intent during design. Still, rationale capture and use have not made the transition from research to practice. A critical issue is capture—rationale capture is viewed as expensive and tedious. Still, while rationale is not explicitly captured, that does not mean that rationale is not captured at all—decisions are documented in many ways throughout the development process. In this talk I will describe our investigation into techniques to identify and extract rationale from existing documentation. We have been experimenting with different text mining algorithms as well as comparing the results of using different features as the basis of classification, most recently using genetic algorithms to search for optimal feature combinations. Our results have accuracy similar to that achieved by humans attempting the same task.

*

**Tuesday, February 2nd at NOON**

**TSC 122 Lecture Hall**

PIZZA PROVIDED

PIZZA PROVIDED

**Title:**"Sequence alignment: From brute force to BWA"

**Rated: **PG (Some mathematics or computer science knowledge assumed.)

**Abstract:** In this talk I will introduce the sequence alignment problem, particularly as it arises in genome sequencing, describe the dynamic programming algorithms that made sequence alignment tractable and conclude with the data structures and algorithms used in modern aligners, such as BWA, to efficiently align the billions of short reads produced by modern sequencing instruments.

*

**Monday, February 1st at 1pm**

**TSC 229**

**Title:**"From GPUs to genomes: Enabling large-scale biological data science"

**Rated: **PG - PG13 (Some to a lot of mathematics or computer science knowledge assumed.)

**Abstract:** Driven by new instrument technologies, the life sciences are experiencing an ongoing data explosion. That data is creating a corresponding need for new computational tools that can help scientists, clinicians and other domain experts extract meaningful insights and do so at scale. In this talk I will describe example applications from my past work in systems biology and my current work in medical genomics that demonstrate how innovations in high-performance computing and other related domains can be adapted to solve important data analysis challenges in the life sciences.

*

**Friday, January 29th at Noon**

**TSC 122 Lecture Hall**

PIZZA PROVIDED

PIZZA PROVIDED

**Title:**"Algorithms for Aggregating Inconsistent Information"

**Rated: **PG (Some mathematics or computer science knowledge assumed.)

**Abstract:** We have the ability to gather enormous amounts of data, and there are numerous challenges in organizing this data into usable information. One of the questions that arises is the question of how to combine inconsistent information from different sources: for example, how do rank movies based on user's ratings? How should we combine recommendations to a user based on different criteria into one ranking?

Can we get better search engines by combining the results of different algorithms? These problems are instances of the rank aggregation problem, which has a long history. In this talk, we will give an algorithm for this problem that efficiently finds a solution that is provably close to optimal. The key ideas in our analysis can also be used to give provably good algorithms for problems where we want to organize data into clusters, for example clustering documents based on similarity scores, and clustering genes based on microarray experiments.

*

**Thursday, January 28th at 3pm**

**TSC 229**

**Title:**"The Traveling Salesman Problem"

**Rated: **PG-13 (A lot of mathematics or computer science knowledge assumed.)

**Abstract:** The traveling salesman problem (TSP) is perhaps the most famous problem in combinatorial optimization: given a set of cities and the distances for traveling between each pair of cities, the goal of the problem is to find the shortest tour that visits each city once and returns to its starting point. Besides applications in routing, algorithms for the TSP have been used in areas as diverse as finding the most efficient way to drill circuit boards to mapping genomes.

Finding an optimal tour is known to be NP-hard; nevertheless, the past decades have seen great progress in solving real-world instances of the TSP. A starting point for solving TSP instances is a linear programming relaxation called the subtour LP. The subtour LP is known to give excellent lower bounds on TSP instances in practice, however, its theoretical worst-case behavior (the "integrality gap'') is not well understood. A famous conjecture states that the integrality gap of the subtour LP is at most 4/3. In this talk, we will discuss some recent new algorithms and results for certain cases of the TSP, that can be seen as steps towards resolving this conjecture.

*

**Friday, January 22nd at Noon**

**TSC 122 Lecture Hall**

PIZZA PROVIDED

PIZZA PROVIDED

**Title:**"Lines on polygon surfaces"

**Rated: **G (No mathematics or computer science knowledge assumed.)

**Abstract:**If you glue together opposite edges of a square, you get a torus (the surface of a donut). What happens if you travel forever in a straight line on the square torus surface? How can you keep track of where you've been? I'll discuss this question for the square torus, and for other surfaces made from polygons, and I'll explain the surprising connection to continued fractions. There will be lots of pictures, and a dance video.

*

**Thursday, January 21st at 3:00pm**

**TSC 229**

**Title:**"Veech surfaces and the Modules Miracle"

**Rated: **PG (A little undergraduate mathematics or computer science knowledge assumed.)

**Abstract: **A square has reflectional and rotational symmetries. The square torus surface has an additional symmetry, a shear. I will explain what this is good for, and I will show you that amazingly, many other surfaces also have these three symmetries.

*

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### BLOCK 4, 2015 - November/December

**Friday, December 11th at 2:30pm**

**TSC 229**

Speaker:Andy Glen

Speaker:

**Title:**"Goodness of Fit: Memoryless No Hitters"

**Rated: **PG-13 (A lot of undergraduate mathematics or computer science assumed.)

**Abstract: **This talk will be a primer on Goodness of Fit statistical testing with applications to “No Hitters” in major league baseball. The empirical distribution function will be introduced and used as means to understand various goodness of fit methods to include: Chi-square techniques, Kolmogorov-Smirnov techniques and most importantly Anderson – Darling techniques. A review of the exponential distribution and the memoryless property will follow. Finally we will show that time between no hitters in baseball is adequately fit by the exponential distribution, thus giving us a very intuitive example of the memoryless property, a rare enough occurrence in real world data. Other rare events also have this property.

*

**Friday, December 4th at NOON**

**TSC 122 Kresge Lecture Hall**

**Pizza is Provided and there will be a recruitment session for the CU Boulder graduate CS program immediately after the talk.**

**Speaker:** Dr. Sriram Sankaranarayanan, CU Boulder, Computer Science

**"Towards a Verified Artificial Pancreas"**

Title:

Title:

**Rated: **PG (A little undergraduate mathematics or computer science assumed.)

**Abstract: **We describe our ongoing research on the mathematical modeling and analysis of artificial pancreas controllers. The artificial pancreas project is developing a series of increasingly sophisticated, software controlled devices that will automatically control insulin infusions to patients with type-1 diabetes in order to manage their blood glucose levels. On one hand, the device promises to greatly ease the process of managing blood glucose levels for people with type-1 diabetes. However, the device can potentially malfunction due to a combination of software design bugs and adversarial usage conditions. Such malfunctions may expose the patients to dire consequences that include coma or even death. How do we convince ourselves that artificial pancreas devices are free of such malfunctions? This problem of verifying computer systems is one of the grand challenges of computer science as a whole, and is well known to be undecidable in its full generality. We describe the process of mathematically modeling the artificial pancreas closed loop to simulate real-life situations directly inside a computer. Next, we describe a simulation-based approach to automatically explore the behaviors of these models to isolate interesting, potentially life threatening behaviors. While this approach does not completely automate the verification process, it provides useful results when applied to some artificial pancreas control algorithms. We conclude by emphasizing the need for rigorous mathematical modeling combined with computational analysis of these models to combat the potential risks posed by increased automation in areas such as robotics, transportation and medicine.

*

**Friday, November 20th at 2:30pm**

**TSC 229**

**Michael Penn**

Speaker:

Speaker:

**"The Universality of the Virasoro Algebra in Mathematics and Physics"**

Title:

Title:

**Rated: **PG-13

**Abstract: **The study of representation theory is, in essence, the reduction of the study of abstract algebraic structures to linear algebra — the study of vector spaces and linear transformations. The Virasoro algebra finds its way into the representation theory of all suitably interesting Lie algebras. During this talk, we will explore the Virasoro algebra by its definition, its appearance in the representations of other Lie algebras, and its applications to the seeming disparate subjects of number theory and physics.

This talk will provide all of the necessary definitions and consider several in depth examples, a strong knowledge of linear algebra is all that is required for full understanding.

*

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### BLOCK 3, 2015 - October/November

**Friday, November 6th, at 2:30pm****TSC 229****Speaker**: Steven Janke**Title**: "The Central Limit Theorem: More of the Story"

**Abstract**: Undergraduate probability courses present a version of the Central Limit Theorem published in 1810. Basically, it claims (under certain constraints) that the sum of several random variables converges to the normal distribution (bell-shaped curve). For statistics, one result of the theorem is that the sample mean is approximately normal. Yet, the common version of the theorem is really only the beginning of a series of results that start to explain why, for example, experimental errors are nearly normally distributed. This talk will trace these results, along with the development of the relevant analysis, and highlight the more recent connections with entropy and the second law of thermodynamics.

**Rated**: PG13 with R sections (A lot of undergraduate with some graduate mathematics or computer science assumed.)

*

**Friday, October 30th, at 2:30pm****TSC 122 Kresge Lecture Hall****Speaker**: Jeff Treviño, Assistant Professor of Music and Technology at CC**Title**: "One Through Eight...Except Five: Problems and Potentials of Computationally Represented and Processed Music Notation"

**Abstract**: For over four decades, music researchers have attempted to computationally model common practice Western music notation and a canonic repertoire of symbolic manipulations thereof. I'll introduce some of the basic representational and processing challenges of this field (with an emphasis on rhythmic notation), review some of my research team's novel solutions, and finally demonstrate some of the artistic applications of Python programming in our team's creative work as composers.

**Rated**: PG

*

**Friday, October 23rd, at NOON****TSC 122 Kresge Lecture Hall****Pizza Provided **

**Speaker**: Amy Hepner '09

**Title**: "The Analytics of Social Progress."

**Abstract**: Come explore how the ideas of data science are being used to inform social progress efforts. Examples include: Predicting police officers at an increased risk of having an adverse interaction with the public; identifying students in danger of not graduating on time; improving environmental advocacy programs; identifying causes of home abandonment.

Mathematical concepts will be explained in everyday language. Career opportunities presented throughout.

**Rated**: G

*

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### BLOCK 2, 2015 - September/October

**Friday, October 9th at NOON**

TSC 122 Kresge Lecture Hall**Pizza Provided Speaker:** Sarah Fletcher Mercaldo, Vanderbilt University

**Title:**"Best Practices for Constructing and Applying Clinical Prediction Models in the Presence of Non-Ignorable Missing Data"

**Rated: **PG-13

**Abstract: **Clinical prediction models use clinical and demographic information to predict the probability that a patient has a certain disease or clinical status. When patient data is missing, care must be taken in both constructing and applying the prediction model. In this presentation, I will introduce different types of missing data often observed in clinical and electronic medical record data. While certain kinds of missing data can be imputed successfully with simple or fancy imputation schemes, the most complicated case when the data are missing NOT at random presents substantial problems for researchers. Here I present several strategies for imputing data that are missing NOT at random and I evaluate and compare the performance of these strategies.

For demonstration, I will use the TREAT risk prediction model, which was developed from a cohort of 492 participants with known or suspected lung cancer evaluated for lung surgery. In this cohort 264 patients had complete data, and 228 patients were missing at least one predictor. When a physician is applying the TREAT model at the bedside to a patient, he may not know or have access to all the information the model requires, and thus how that data is imputed becomes critical to the application of the model. Prediction models such as the TREAT model are being used more frequently to inform clinical decisions. However, published prediction models cannot be applied when a patients clinical data is missing. Proper handling of missing data is key to developing a robust and accurate prediction model

*

**Friday, October 2nd at NOONTSC 122 - Kresge Lecture HallPizza will be provided!**

**Speaker:** Benjamin Ylvisaker**Title:** "Google, The NSA and The Supreme Leader are Listening!"

**Rated:** PG

**Abstract:** There is an enormous amount of private data sent and stored insecurely over the Internet. Powerful governmental, corporate and/or criminal organizations are actively collecting and exploiting this data. This talk will introduce a broad range of concepts in

information security and privacy. In particular we will discuss new ideas related to storing data securely in public cloud storage services.

All majors must write up four talks in order to graduate. Talk write ups should be submitted through Canvas. If you wish to be added to the Canvas page, please contact one of the paraprofs.

*

**Friday, September 4th at 2:30pm in TSC 229****Speaker:** Darren Funk-Neubauer**Title:** "Bidiagonal Pairs and Bidiagonal Triples." **Rated:** PG-13 with R rated sections**Abstract:** Roughly speaking, a bidiagonal pair is a pair of diagonalizable linear transformations on a finite-dimensional vector space, each of which acts in a bidiagonal fashion on the eigenspaces of the other. A classification of bidiagonal pairs will be presented. Then I will describe how to construct all bidiagonal pairs using representations of the Lie algebra sl_{2} and the quantum group *U*_{q} (sl_{2}) . Next, I will explain how to extend the definition of bidiagonal pair to a triple of linear transformations, thus defining a bidiagonal triple. I will discuss in what sense a given bidiagonal pair determines a bidiagonal triple. Lastly, I will describe the classification of bidiagonal triples.

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**BLOCK 1, 2015 - August/September**

Departmental Research Overview and Ice Cream Social

Friday, September 4th at NOON

TSC 122 - Tutt Science Lecture Hall

**Rated** G

This general-audience talk will showcase the various research interests of the Department of Mathematics and Computer Science at Colorado College. Each faculty member will provide a brief description of their scholarly pursuits. *Pizza will be provided!*

Faculty speakers will include

• Marlow Anderson - Wild Automorphisms of the Complex Plane, History of Mathematics

• David Brown - Mathematical Biology

• Andrea Bruder - Differential Equations

• Rodney James - Tropical Geometry

• Steven Janke – Computational Complexity

• Molly Moran - Geometric Group Theory

• Stefan Erickson - Computational Number Theory and Cryptography.

Immediately after the talk, we will be hosting an ice cream social for all students in the department lounge on the second floor of Tutt Science

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