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Meetings

• Thursday, February 3, 2011 General Interest Meeting (with Pizza)
  
  
• Thursday, February 10 Free form meeting
  
  
• Wednesday, February 16 CoCo Seminar (Not a Math Club meeting), 8:30 am, BI-2221 (ITC Conference Room)
  Prof. Sabalka, "An Introduction to Persistent Homology"
  
  Abstract: In the past decade, mathematicians have developed useful computational tools for taking some theoretical concepts and using them as descriptors for real-world data sets. A major example of this is in the development of persistent homology. Persistent homology refers to a process of taking in a discrete data set like a point-cloud, and identifying medium- and large-scale topological features. Persistent homology has potential applications in any area where large amounts of data need to be aggregated and analyzed, including data encoding, computer imaging, and sensor networks, to name a few.
  
  In this talk, we will briefly discuss the notion of a topological space and topological properties. We will describe what the word homology means, and then describe persistent homology. We will end with some examples of persistent homology in action. No mathematical background in topology will be assumed.
  
  
• Thursday, February 17 Prof. Vavrichek, "Symmetries and Group Actions"
  
  Abstract: Groups are mathematical objects that satisfy a handful of axioms which are satisfied by number systems such as the integers. I will talk about the connection between groups and geometric spaces.
  
  
• Thursday, February 24 Free form
  
  
• Thursday, March 3 Prof. Kappe, "Cantor's Diagonalization Revisited: Constructing Transcendental Numbers"
  
  Abstract: An evolving awareness of the deep nature of the real numbers began over 2,500 years ago, when the Pythagoreans were startled by their discovery that numbers such as the square root of 2 were not rational. A recurring theme in their history is that the set of real numbers is richer and much more complex than is generally assumed. The demonstration by Cantor, that the reals cannot be enumerated, is a well-known landmark of these developments. Knowing that the rationals can be enumerated, it follows from Cantor's diagonalization that there exist irrational numbers. Similarly, knowing that the algebraic numbers can be enumerated, it follows that there exist transcendental numbers. But can one use Cantor's diagonalization for the construction of such numbers? The topic of this talk is the explicit construction of a transcendental number using Cantor's diagonalization.
  
  
• Thursday, March 10 Free form
  
  
• Thursday, March 17 Free form
  
  
• Thursday, March 24 No meeting because of Spring Break
  
  
• Thursday, March 31 Q&A with professors: course offerings for next semester
  
  
• Thursday, April 7 Marissa Belk (Cornell University), "Living in a Quotient Space"
  
  Abstract: A manifold is a space that locally "looks like" R^n. The surface of the earth, for example, is a 2-manifold. In times past, our civilization was unable to distinguish this surface from the side of a cube; sailors feared that they may sail off the edge of the earth. In this talk, we will discuss what life would be like in other 2-manifolds and venture into higher dimensions. We will then begin folding these manifolds along certain symmetries to get new (and often stranger) spaces called an Orbifolds. What do Orbifolds look like? And what is it like to live in an Orbifold?
  
  
• Thursday, April 14 Free form
  
  
• Thursday, April 21 No meeting because of Easter/Passover Break
  
  
• Thursday, April 28 Prof. Mazur, "On cutting polygons and coloring the plane"
  
  Abstract: The starting point for the talk will be the following question: is it possible to cut a rectangle into 2011 triangles of equal area? We will see that several very interesting and important ideas from various areas of mathematics are needed to answer this question.
  
  
• Thursday, May 5 Nathan Reff (BU), "Polytopes, Pick's Theorem and Ehrhart Theory" (with Pizza)
  
  Abstract: Suppose P is a convex polygon with integer coordinates. Pick's Theorem, in honor of Georg Pick, says that the area of P can be computed by counting lattice points on the interior and the boundary of P. We will discuss Pick's theorem as well as a generalization to higher dimensions via Ehrhart polynomials. If time permits, we will also discuss some applications.
  
  
• Thursday, May 12 Free form