Fractional Euler characteristics and the idea of categorification |
Abstract: In many areas of mathematics one tries to understand complicated structures by combinatorial rules, often by assigning a combinatorial invariant to it. For instance Euler characteristics and Poincare polynomials are often used as invariants in algebra, topology and geometry. Polynomials are also used in representation theory to understand multiplicity formulas and decomposition numbers. In this talk I will illustrate this in a few examples and then explain the idea of categorification. This is in some sense the inverse of the above process and used to for instance to lift polynomial invariants of knots and manifolds to complicated structures with the ultimate goal to construct finer invariants. An interesting question hereby is whether one can realize rational numbers or fractions as Euler characteristics of something. |
Here are some directions to Northeastern University. Lake Hall and Nightingale Hall can be best accessed from the entrance on the corner of Greenleaf Street and Leon Street. The two halls are connected, with no well-defined boundary in between. In particular, 509 Lake Hall is on the same corridor as 544 Nightingale Hall. There is free parking available for people coming to the Colloquium at Northeastern's visitor parking (Rennaisance Garage). The entrance is from Columbus Avenue. If coming by car, you should park there and take the parking talon. After the lecture, you may pick up the payment coupon from Andrei Zelevinsky. |
Web page: Alexandru I. Suciu | Comments to: andrei@neu.edu | |
Posted:: September 22, 2012 | URL: http://www.math.neu.edu/bhmn/stroppel12.html |