Algebra and its Applications (Fall 2006)

Welcome to the Algebra and its Applications seminar home page!

The seminar is organized by Ettore Aldrovandi. Please send an email to contact me.

The meeting time and place is the standard one: Thursdays, at 2:00 p.m. in 104 LOV


Aug. 31 Organizational Meeting
Sept. 7 Behrang Noohi (FSU) Introduction to Topological Stacks I
Sept 14 Introduction to Topological Stacks II
Sept 21 Introduction to Topological Stacks III
Sept 28 Special Q&A meeting I
Oct 5 Special Q&A meeting II
Oct 12 Behrang Noohi (FSU) Introduction to Topological Stacks IV
Oct 19 Behrang Noohi (FSU) Fundamental groups of topological stacks
(Introduction to Topological Stacks V)
Nov 2 Behrang Noohi (FSU) Algebraic topology of topological stacks
(Introduction to Topological Stacks VI)
Nov 9 Giles Levy (FSU) Transformations of recurrence equations
Nov 16 Giles Levy (FSU) Transformations of recurrence equations, II
Nov 23 Thanksgiving
Nov 30 Ruben De Beerst (FSU) Finding Bessel solutions of differential equations using generalized exponents
Dec 5, 1:00 pm, 200 LOV
Note special time, date, and place
Emin Tatar (FSU) (Introduction to) Differential Graded Categories
Dec 7 Emin Tatar (FSU) (Introduction to) Differential Graded Categories, II


Behrang Noohi: Introduction to Topological Stacks

In this expository talk we define topological stacks and explain briefly how classical homotopy theory can be extended to the setting of topological stacks. We motivate this by showing that each of the following classes of objects gives rise naturally to a class of topological stacks: 1) graphs of groups, or more generally, complexes of groups, 2) orbifolds, 3) algebraic stacks over C, 4) topological spaces with a group action, 5) differential groupoids, 6) foliated manifolds. In particular, we show how certain general results about topological stacks specialize to certain, well-known or new, results in each of these theories.

Giles Levy: Transformations of recurrence equations

In order to gain more information from certain irreducible recurrence equations, an algorithm that expresses these as functions of better understood recurrence equations will be presented.

Ruben De Beerst: Finding Bessel solutions of differential equations using generalized exponents

In this talk we will consider the differential equation x2 y''(x) + x y'(x) - (x2 + v2) y(x) = 0 which solutions are the modified Bessel functions. After applying the operations "change of variables" (map x to a rational function f(x)), "exp-product" (multiply by a solution of a first order differential equation) and "gauge transformation" (map a solution y to r0 y+ r1 y' where r0 and r1 are rational) we will get a differential equation of second order, which solutions can be expressed with Bessel functions. There are algorithms considering two of the three operations, but the algorithm that will be presented in this talk can also find Bessel solutions if all three operations were applied. In this new approach we will use the notion of generalized exponents to get information that is invariant under all three operations and we will show, how we can find the function f(x) and the number v. Once we have done this we can use other algorithms to find the other transformations.

Emin Tatar: (Introduction to) Differential Graded Categories

In this talk we define differential graded categories (dg-categories) and their derived categories, and show that the latter have triangulated and algebraic category structures. We also talk briefly about how derived categories are used to explain the algebraic triangulated categories.

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