Invented on May 18th, 2007 (by Oleg Ivrii and Zavosh Amir-Khosravi) a "rigorous" defintion of CoolStuff is against our philosophy, so I will only give some guidelines what qualifies stuff to be cool:
- The process of CoolStuff is to learn mathematics by application. Here at CoolStuff, we believe that to understand a subject is to see it used in action.
- By its nature, it is elementary, simple, elegant and intuitive. Sometimes, it could even be accessible to highschool students if it did not use a simple fact from topology or abstract algebra. Nevertheless, CoolStuff benefits from its highly intelligent audience.
- CoolStuff does not belong to a single subject, it draws from all of mathematics. By its nature, it cannot be found in a university classroom, which tries to partition all of mathematics into "subjects".
- CoolStuff should be able to stand by itself as a final result, with no applications in mind (even though, applications make it even more cool).
- When it is a well-known theory, the focus is on showing examples rather than dunking theorems one by one.
Of course, classical university education has its merits too :-).
CoolStuff is now organized by Yuri Burda. Contact (in person, or by email) if you are interested in giving a talk.
Previous CoolStuff Seminars can be found at the following link: http://www.math.toronto.edu/oleg/css/coolstuff.html
An introduction to combinatorial species
University of Toronto
11:10 (Thursday, Jan. 28, 2010
BA6180, Bahen Center, 40 St. George Street
A generic problem in enumerative combinatorics is posed as follows: in how many ways can a set of size n be equipped with some specified type of structure? For example, one could define a particular class of graphs, and ask how many of these there are on a given vertex set. The resulting sequence of integers can be algebraically packaged in the form of a generating series.
Joyal's theory of species provides an elegant framework for formalizing the notion of "type of structure on a finite set", in such a way that combinatorial operations on species correspond naturally to algebraic operations on generating series. This can be exploited, in combination with some algebraic tools like the Lagrange Implicit Function Theorem, to solve various enumerative problems in a slick way. I will give an introduction to the theory of species and demonstrate a few of these applications to enumeration.
Dates in this series
- · Thursday, Jan. 07, 2010:
Quasiconformal Distortion (Oleg Ivrii)
- · Thursday, Jan. 28, 2010:
An introduction to combinatorial species (Brad Hannigan-Daley)
- · Thursday, Feb. 04, 2010:
Flipping functions: bundlish things and their classifying gadgets (Omar Antolín Camarena)
- · Thursday, Feb. 25, 2010:
The ADHM Construction of Instantons (Jonathan Fisher)
- · Thursday, Mar. 25, 2010:
Ruler and Compass Constructions for Cheapskates (Omar Antolín Camarena)
- · Thursday, Jan. 20, 2011:
Blaschke Worlds (Oleg Ivrii)
- · Thursday, Apr. 28, 2011:
Blaschke Worlds (Oleg Ivrii)