Math Club
All talks

Thursday, April 14, 2011, 01:00PM, NAC 6113
Ethan Akin (CCNY), Dynamic Fractals a la FurstenbergThere are two ideas associated with fractals. According to one a fractal is a set with fractional dimension. The one I will be considering is that a fractal is a set which exhibits selfsimilarity. As you blow up the scale near a point the scaledup figures repeatedly look like the original. Furstenberg introduced a natural dynamic notion of what it means for a closed subset of a square to be a fractal at one of its points. This is the concept I will describe, replacing the square by the sequence space on a finite number of symbols.
Remark: This will follow the Undergraduate Awards Ceremony held in NAC 8/133B at noon.

Tuesday, May 12, 2009, 12:30PM, NAC 4113
Ranja Reda (Vienna University of Technology), Rotational Invariant Importance SamplingA new importance sampling technique to increase the efficiency of rare event simulation. By using a multidimensional rotational invariant auxiliary density, this method can be applied to estimate risk measures for credit risk portfolios where the method of importance sampling via mean shifting is not applicable. This is especially the case in inhomogeneous portfolios, i.e. portfolios with multiple areas of high losses. Furthermore, rotational invariant importance sampling allows calculating contributions to risk measures of different customer clusters in credit porfolios quicker and more precisely.
Our new model, rotational invariant importance sampling has already been implemented in Bank Austria's system. Their main credit portfolio with about 2000 clients is already measured through our new simulation technique. As you can imagine there was lot of work to be done as far as the calibration of the model, finding the optimal parameters for the new importance sampling density, etc.

Thursday, April 30, 2009, 12:30PM, NAC 6/114
Rochelle (Shelley) Ring (CCNY), Becoming a High School Mathematics ProfessorCome join us on April 30 in NAC 6/114 12:301:30 to learn about an exciting career opportunity! If you are looking for a rewarding, satisfying and secure profession, come learn about how you can become a high school mathematics teacher and begin working at a wonderful job right after college. Light refreshments will be provided at the meeting.

Tuesday, April 28, 2009, 12:30PM, NAC 4113
Rene Ardila (CCNY), Matrix Number Theory: Factorization in Integral Matrix SemigroupsFactorization theory is a prominent field of mathematics; however, most previous research in this area lies in the commutative case. Noncommutative factorization theory is a relatively new topic of interest. This talk examines the factorization properties of noncommutative atomic semigroups of matrices, including results on the minimum and maximum length of atomic factorizations, the elasticity and the delta set of the semigroups.
This talk is suitable for those who have had linear algebra.

Tuesday, March 10, 2009, 12:30PM, NAC 4113
Michael Levin (Department of Philosophy), Category Theory as a Structuralist Foundation for MathematicsIt is often said that mathematics studies "structure," an idea that has been picked up by a number of philosophers. This idea has certain advantages over thinking of mathematics as a body of inferences from uninterpreted postulates, and also the platonistic idea that, e.g., number theory is about Numbers. Category theory might be thought of as "structuralism in action." I will illustrate this idea with a discussion of the "number objects" in arbitrary categories. Time permitting, I will say a little about the category axioms themselves.
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