Current Academic Year Seminars
BLOCK 7, 2015 - March/April
Friday March 27 at 2:30pm
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.
BLOCK 5, 2015 - January/February
Friday February 6 at 2:30pm
Speaker: Kristen Walcott Justice (UCCS)
Title: Machine Learning in Software Test Prioritization Techniques
Friday February 6th at Noon
TSC 122 Tutt Lecture Hall
Speaker: Molly Moran
Title: Triangles: Using a Basic Shape to Understand Modern Goemetry
Thursday February 5th at Noon
Speaker: Molly Moran
Title: A Look at Group Boundaries and their Dimension
BLOCK 4, 2014 - December
Friday December 12 at Noon
TSC 122 Lecture Hall
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.
Friday, December 5 at 2:30 pm
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.
BLOCK 3, 2014 - October/November
Friday November 14 at 2:30pm
Speaker: Chris Sadowski of Ursinus College
Title: Representations of Affine Lie algebras and Integer Partitions
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
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.
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.
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.
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!
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)
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
Friday September 12th, Noon
TSC 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, 2:30pm
Speaker: Michael Penn
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