[ugrads] Fwd: Roosevelt Lectures in Mathematicas: Steve Cohen

Fred J. Hickernell hickernell at iit.edu
Wed Apr 29 13:12:22 CDT 2015



Best regards,
Fred J. Hickernell
hickernell at iit.edu

Begin forwarded message:

> From: Wilfredo Urbina Romero <wurbinaromero at roosevelt.edu>
> Date: April 29, 2015 at 9:51:09 AM CDT
> To: Ahmed Zayed <AZAYED at depaul.edu>, "crasinariu at colum.edu" <crasinariu at colum.edu>, "agiaqui at luc.edu" <agiaqui at luc.edu>, "L-Filus at neiu.edu" <L-Filus at neiu.edu>, "hickernell at iit.edu" <hickernell at iit.edu>, "shmuel at math.uchicago.edu" <shmuel at math.uchicago.edu>, "dept at math.uic.edu" <dept at math.uic.edu>, "R-Attele at csu.edu" <R-Attele at csu.edu>, "jfakhrid-deen at ccc.edu" <jfakhrid-deen at ccc.edu>, "saman2 at ccc.edu" <saman2 at ccc.edu>, "ddwhite at ccc.edu" <ddwhite at ccc.edu>, "chair at math.northwestern.edu" <chair at math.northwestern.edu>, "ihozo at iun.edu" <ihozo at iun.edu>, "mando at illinois.edu" <mando at illinois.edu>, "zshen at math.iupui.edu" <zshen at math.iupui.edu>, "mtimm at bradley.edu" <mtimm at bradley.edu>, "pgandrews at eiu.edu" <pgandrews at eiu.edu>, "harris at math.niu.edu" <harris at math.niu.edu>, "gbudzban at math.siu.edu" <gbudzban at math.siu.edu>, "gfseeli at ilstu.edu" <gfseeli at ilstu.edu>, "kzumbrun at indiana.edu" <kzumbrun at indiana.edu>
> Subject: Roosevelt Lectures in Mathematicas: Steve Cohen
> 
> 
> Dear chairman of the math department,
> 
> The second Roosevelt Lecture in Math will be given be Prof. Steven Cohen,
> from Roosevelt University
> 
> on Thursday and Friday May 7 & 8, 2015
> Place:
> Roosevelt University
> Wabash building Room 1017
> 420 S Michigan Ave Chicago
> 
> Info and registration at
> http://www.roosevelt.edu/MathLectures.
> 
> Title: Almost everything you want to know about Representation Theory*
> *But were afraid to ask.
> 
> Abstract: Representation Theory is about viewing elements of any group as
> invertible linear transformations of a vector space. This provides a
> universal setting for all groups and possibly a way to organize the
> classification of finite simple groups. This talk will give an
> introduction to the subject, look at some examples where the theory works
> well, and consider some challenging aspects of the exceptional cases.
> 
> 
> There is going to be three lectures: the first one will be on
> Thursday 05/07 2:30-3:30 pm, the second one on Friday 05/08 morning 9:30 -11:30 am and the
> third one will be on Friday 08/08 afternoon 2:00-4:00 pm
> 
> Abstract of the Lectures:
> 
> - In the first lecture, I will provide an introduction to groups and group actions on a set. Groups are simple algebraic structures with a single operation. Two important examples are groups of permutations of n objects and groups of invertible linear transformations of an n-dimensional vector space, V. This latter example is denoted GLn(V) and leads naturally into the definition of a finite group representation as a mapping of the group into GLn(V). The default for V is that it is a vector space with scalars coming from the complex numbers, but representations can be defined using any field. In this way, each group element is identified with a matrix with entries from the field.  Some basic examples are explored and results established about irreducible representations including Schur's lemma and the basics of group characters. Finally, I will introduce Lie Algebras. These are vector spaces that come equipped with a non-associative multiplication operation on the set of vectors. Examples and basic properties will be demonstrated. This lecture will be accessible to most students who have had linear algebra and especially accessible to those that have had Abstract Algebra.
> 
> -In the second lecture we will focus on major established results for these three settings: the classification of finite simple groups, the representation theory and classification of Lie Algebras, and the classification of the irreducible representations of finite groups. Lie Algebras can be decomposed into a toral subalgebra and a set of 1-dimensional subalgebras known as a system of roots. Group representations are classified using Character theory. Characters are class functions from the group to the field underlying the vector space and distinct group representations have distinct characters.
> 
> - In the third lecture, we will look at the connections between all three areas including the construction of Lie Groups from Lie Algebras from an algebraic and topological perspective. Some applications will be presented.  Finally the more difficult problems will be considered. Some fields have finite characteristic, that is there exists an integer n>0 such for all elements k in the field K, nk=0. In fact, n must be prime and the complications occur when n divides the cardinality of the group, G. In that case, V is no longer a vector space but the more general structure of a module. Modular representation theory.
> 
> 
> 
> Perhaps some members of your department may be interested in this
> conference so I would be very grateful if you can transmit this
> information to your department.
> 
> 
> 
> Thanks in advance. Best regards,
> 
> 
> 
> Wilfredo Urbina-Romero.
> Department of Mathematics and Actuarial Sciences
> Roosevelt University
> 


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