# Current Academic Year Seminars

**BLOCK 8, 2015 - April/May**

Friday, April 24th at 2:30pm

TSC 229

**Speaker:** Andy Glen**Title: **Computational Probability: Algorithms and Applications

**Abstract:** The open source computational package A Probability Programming Language (APPL) represents an ongoing 20 year effort at combining symbolic algebra software with probabilistic results that, in the end, can be used to automate a number of theorems from probability theory. This talk will give a demonstration of the language, discuss some of the computational issues associated with the project and give some examples of application of the software. APPL is one of a kind probabilistic software (differentiated from statistical software) that primarily manipulates functions, not numbers. Applications can be found in all areas of probability and statistics to include stochastic processes, reliability engineering, probabilistic models, statistical models, financial mathematics, and so forth.

**Rated:** PG-13

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**BLOCK 7, 2015 - March/April**

**SENIOR CAPSTONE TALKSWednesday, Thursday and Friday April 8-10 TSC 122 Lecture Hall**

WEDNESDAY

1:00-1:25 Minqi Liu – A Three-species Model With Predator-prey, Competition,

And Mutualistic Interactions

Thesis Advisor: Andrea Bruder

1:30-1:55 Katy Martinez – Epidemiological Methods for Examining Bullying

Thesis Advisor: Andrea Bruder

2:00-2:25 Julia Napolitano – The Cantor set as a Fractal and its Applications in Art

Thesis Advisor: Marlow Anderson

2:30-2:55 BREAK

3:00-3:25 Gautam Webb –Generalization of the Heisenberg Algebra

Thesis Advisor: Michael Penn

3:30-3:55 Nicole Pey – From Markov Chains to Brownian Motion: Let's take a Random Walk

Thesis Advisor: Steven Janke

THURSDAY

1:00-1:25 Fanpei Liu – Introduction to Lebesgue Integral

Thesis Advisor: Fred Tinsley

1:30-1:55 Joe Howard – Using Hercules and the Hydra to Build Problem Solving Skills

Thesis Advisor: Michael Penn

2:00-2:25 Sam Spellman – Lobachevsky’s Spherical Trigonometry

Thesis Advisor: Marlow Anderson

2:30-2:55 BREAK

3:00-3:25 Maggie Bailey – Epidemics and Network Structures: A Stochastic Study

Thesis Advisor: David Brown

3:30-3:55 Chris Van Dusen - Methods to prevent over-fitting and solve ill posed problems in statistics: Ridge Regression and LASSO

Thesis Advisor: Fred Tinsley

FRIDAY

1:00-1:25 Emma Holmes – Realistic Driver Behavior Characteristics on Microscopic Traffic Flow

Modeling

Thesis Advisor: David Brown

1:30-1:55 Emily Stearns – Modeling Ocean Waves: Linear Wave Theory

Thesis Advisor: Amelia Taylor, Andrea Bruder, & Rodney James

2:00-2:25 Lou Brand – Neural Networks, Genetic Algorithms, and the Blood Brain Barrier

Thesis Advisor: Matthew Whitehead

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Friday April 3 at Noon

TSC 122 Lecture Hall*Pizza Provided!*

**Speaker:** Ben Ylvisaker

**Title: **Persistent Data Structures

**Abstract:** In the vast majority of the programming world, modifying a data structure results in the “destruction” of the previous version. With persistent data structures, it’s easy for a program to keep multiple versions of a structure simultaneously. In this talk we’ll cover why this is a useful idea and how it’s possible to implement with not-totally-ridiculous memory and time overhead.

**Rated:** PG

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**Friday March 27 at 2:30pm**

**TSC 229 **

**Speaker:** Rodney James

**Title: **Real Sandpile Groups

**Abstract:** Sandpile models were first introduced by physicists in the 1980’s as a way to study the dissipative dynamics of discrete systems on a lattice. In this model, grains of sand are placed on the vertices until a critical number of grains is present, at which point an avalanche occurs and the pile of sand topples over to its neighbors. Certain stable configurations of sand resulting from avalanches were later shown to form an abelian group. In this talk we will extend the sandpile model to real-valued quantities on each vertex, and show that there are stable configurations of these real-valued sandpiles that form a different abelian group.

**Rated:** PG-13

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**BLOCK 5, 2015 - January/February**

**Friday February 6 at 2:30pmTSC 229 **

**Speaker:** Kristen Walcott Justice (UCCS)

**Title:** Machine Learning in Software Test Prioritization Techniques

**Abstract:** TBA.

**Rated:** PG-13

***Friday February 6th at NoonTSC 122 Tutt Lecture Hall **

*Pizza provided!*

**Speaker: **Molly Moran

**Title:** Triangles: Using a Basic Shape to Understand Modern Goemetry

**Abstract:** TBA

**Rated:** G

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**Thursday February 5th at Noon**

**TSC 229**

**Speaker: **Molly Moran

**Title:** A Look at Group Boundaries and their Dimension

**Abstract:** TBA

**Rated:** R

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**BLOCK 4, 2014 - December**

**Friday December 12 at Noon****TSC 122 Lecture Hall***Pizza provided!*

**Speaker: **Marlow Anderson

**Title:** Recent Progress on the Twin Prime Conjecture

**Abstract:** The Twin Prime Conjecture asserts that there are infinitely many pairs of primes separated by 2, like 3 & 5, 5 & 7, 11 & 13, and so on. In almost two centuries, there has been no real progress in proving this. However, in May of 2013, Zitang Zhang thrilled the mathematical world by announcing a proof that there are infinitely many pairs of primes separated by no more than 70,000,000. This is quite a bit bigger than 2, but it was the first such finite bound ever proved. In an exciting summer, a collaborative on-line team worked hard to reduce the bound, and we know now that there are infinitely many prime pairs separated by no more than 246. In this talk, I will describe the historical and mathematical background to this problem, and describe a bit about the recent developments.

**Rated:** PG

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**Friday, December 5 at 2:30 pm ****TSC 229**

**Speaker:** C. Edward Chow, Department of Computer Science University of Colorado at Colorado Springs**Title:** Intrusion Tolerance and Cloud

**Abstract:** In this talk I will review the assumptions, ideas, and techniques developed for intrusion tolerance, which can be used to tolerate Distributed Denial of Service (DDoS) attacks, with the side effect of providing multiple alternate routes that improve performance and reliability. We will then discuss new ideas for utilizing cheap cloud resource for enhancing DDoS defense and building Secure Systems. With this new intrusion tolerance paradigm in mind, we have developed enhanced secure Domain Name System (DNS) for querying new evolving IP address mapping and multipath indirect routing using a set of proxy servers. The multiple paths established in this secure overlay network provide better bandwidth, higher reliability, and enhanced security.

**Rated PG-13**

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**BLOCK 3, 2014 - October/November**

**Friday November 14 at 2:30pmTSC 229 Speaker: **Chris Sadowski of Ursinus College

**Representations of Affine Lie algebras and Integer Partitions**

Title:

Title:

**Abstract:**The Rogers-Ramunujan partition identities have many deep ties to the representation theory of affine Lie algebras. In this talk, we introduce these identities and recall some facts about them. Then, following the work of Feigin, Stoyanovsky, Calinescu, Capparelli, Lepowsky, and Milas, we discuss how these identities arise in the study of “prinicpalsubspaces” of the standard modules for the affine Lie algebra sl(2)^ and we also discuss generalizations to higher rank cases. It turns out that generators-and-relations results for these principal subspaces are crucial to this work. We describe new generators-and-relations results about the principal subspaces of the standard sl(3)^-modules and we give a conjecture for the corresponding presentations of the principal subspaces of the standard sl(n)^-modules for general n. We also provide new results for the principal subspaces of certain standard sl(n)^-modules, generalizing earlier work by Calinescu

Rated: PG-13

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Friday November 7, Noon

Rated: PG-13

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Friday November 7, Noon

**TSC 122 Lecture Hall**

**Speaker:** Steven Janke

**Title: **Shadows in Computer Graphics

**Abstract**: Constructing simple shadows for computer graphics scenes is a relatively straightforward geometry problem, but to make the procedure efficient and to deal with more complex cases, it helps to call on projective geometry. This talk will introduce some projective geometry ideas and show how shadows and perspective drawing are related. By using special coordinates (homogeneous), we can make it easier to draw more complex shadows on the computer screen.

**Rated:** PG

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**Friday Oct. 31, 2:30 pm**

**Tutt Science Center 229**

**Speaker:** Molly Moran, University of Wisconsin-Milwaukee, CC Class of 2009

**Title:** How to Measure Distance between Two Points at Infinity: Metrics on the Visual Boundary of CAT(0) Spaces

**Abstract**: Two types of metric spaces that are widely studied in Geometric Group Theory are CAT(0) spaces and δ-hyperbolic spaces. Both spaces can be defined in terms of thinness of triangles. Somewhat surprisingly, the rather simple definitions turn out to capture the large-scale behavior of these spaces, in particular their curvature. In this talk we will define these spaces, discuss their boundaries at infinity, and how we could measure distances between points in the boundary.

**Rated:** PG-13

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**BLOCK 2, 2014 - October**

**Friday Oct. 17, 3:00pm**

**Tutt Science Center 229**

**Speaker:** Kathy Merrill**Title:** Wavelet sets for Determinant ±2 Matrices**Abstract**: A wavelet set is a set that tiles ℝn under both translation by the integer lattice and dilation by a matrix. I recently discovered a proof that all determinant ±2 matrices have wavelet sets that are simple in the sense of being finite unions of convex sets. This talk will describe what is special about determinant 2, and then present the main ideas of this proof.

**Rated:** PG-13

*****

**Friday October 10th, Noon**

**Tutt Science 122 - Kresge Lecture Hall**

*Pizza will be served!*

**Speaker:** CC alumna Sarah Wolff**Title:** A Random Walk through Algebra **Abstract:** How many shuffles does it take to completely randomize a deck of cards? This simple question, answered by Persi Diaconis in 1986, opens up an entire world of mathematics: the theory of randomness. In this talk, we will develop and analyze the random walk created by shuffling a deck of cards and then apply what we’ve learned to other interesting settings. The theory of randomness has applications not only in card shuffling but also economics, genetics, computer science, psychology, and much more!

**Rated: **G

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Friday October 3rd, 2:30pm**Tutt Science 229**

**Speaker:** Fred Tinsley

**Title:** Group embeddings, recursiveness (logic, argh!), and topology

**Abstract:** In the early 1960’s Graham Higman characterized those finitely generated groups that embed in finitely presented groups.[i] This amazing theorem pinpointed those finitely generated groups whose relation set is *recursively enumerable* as precisely those groups that embed in some finitely presented group. Such groups are called *recursively presented*. In obtaining this result, Higman “firmly established that the connection between the logical notion of recursiveness and questions about finitely presented groups is not accidental but very deep”.[ii] Of course, these concepts also are important in theoretical computer science. But to a topologist such as me, finitely presented groups are quite desirable as they are naturally the fundamental groups of high-dimensional, closed manifolds (surfaces) while at the same time are potentially better understood using computational methods (computers). We will investigate whether the necessarily universal techniques used by Higman (and others since) can be helpful in obtaining embeddings of specific recursively presented groups that are important to a project in which I am currently involved.

[i] Higman, G: “Subgroups of finitely presented groups”, Proc Royal Soc London Ser A 262, 455-475 (1961)

[ii] Lyndon, R, Schupp, P: Combinatorial Group Theory, Springer-Verlag, Berlin Heidelberg New York (1977), p 214.

**Rated: **PG13 (though X in some places)

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**BLOCK 1, 2014 - September**

**Friday September 19th, 3pm**

**Tutt Science Second Floor Skilling Commons**

This week, on Sept. 19, we will have a special edition of Fearless Friday. Some of our students who did research projects this past summer (either here or elsewhere) will be presenting their work in a small poster session. There will be approximately 7 posters, on topics from pure and applied math and computer science . There is a special time and location: 3:00 – 4:00 pm, in the 2nd floor open area ("Skilling Commons") of Tutt Science. Light refreshments will be served.

- Lou Brand: Genetic algorithms, neural networks, and the blood-brain barrier
- Emma Holmes: Modeling microscopic and macroscopic traffic flow utilizing the particle filter and the ensemble Kalman filter
- Melissa Jay: Speech intelligibility index model: A key aspect to a child's development of speech and language
- Nick Kramer: Multi-valued logics and their algebras
- Minqi Liu: A three-species model with predator-prey, competition, and mutualistic interactions
- Katy Martinez: How to prevent bullying: A mathematical approach
- Denali Molitor: Self-organized criticality for optimal random search

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**Friday September 12th, NoonTSC 122 and Math Dept Lounge**Ice cream social and Dept Research Overviews

Come join the Mathematics and Computer Science department with the annual welcome back event, where every professor will be giving a brief overview of their research. Topics covered will range from applying abstract algebra to evolutionary biology to topology and designing robust cellular automata. This is a chance for returning students to reconnect with faculty and peers, and new students to introduce themselves and discover what’s happening. It’s also a chance for majors to consider research alongside their professors.

**Rated:**G - PG13

***Friday September 5th, 2:30pmTSC 229Speaker: **Michael Penn

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