Speaker: Craig Huneke

Title: What is Commutative Algebra?

Abstract: This talk will describe some basic problems in commutative algebra, whose
solution requires a method called reduction to characteristic p. This method has
been codified in a theory called `tight closure'.  We will outline the main steps in
 reduction to char. p, and illustrate on some of the problems. These problems
include understanding rings of invariants of groups acting linearly on polynomial
rings, and questions concerning the behavior of polynomials which vanish to
prescribed multiplicities at points in the projective plane. Almost no advanced
knowledge beyond a course on rings, groups, and fields will be assumed.

.......................................................................................
Speaker: Hossein Andikfar

Title:  Decomposition numbers of finite groups of Lie type.

Decomposition numbers of of a finite group G (relative to some prime p) are
numerical invariants that relate the ordinary and p-mudular representations of
G. In this talk we give combinatorial results concerning some finite groups of
Lie type in characteristic 2 and suggest some possible ways for generalizing
these results in the frame work of simply connected semisimple finite groups of
Lie type via Deligne-Lusztig theory.

.......................................................................................
Speaker: Iana Anguelova

Title: Quantum vertex algebras and twisting by a bicharacter.

Abstract: I will explain how to use and develop the bicharacter
construction first proposed by  R. Borcherds in his paper 
'Quantum vertex algebras'. The bicharacter
construction uses the  Hopf algebra structure which underlines the
spaces of states for many  vertex algebras. We define
vertex operators  via a bicharacter  and study the
properties of the resulting vertex algebras. Then I will 
show how to identify the vertex operators defined via a bicharacter 
with the ones defined as generating series. Examples of such 
bicharacter construction are given by the quantum vertex operators 
related to symmetric polynomials.

....................................................................................
Speaker: Ananth Hariharan

Title: Approximating Artinian rings by Gorenstein rings

Abstract: The question we are interested in is the following: Given an
Artinian ring, how 'close' can we get to it by an Artinian Gorenstein
ring. In this talk I will briefly introduce Artinian Gorenstein rings and
make the notion of being 'close' precise. I will also discuss some past
results and an example.

...................................................................................
Speaker: Apoorva Khare

Title: Block decomposition for Category O over algebras of Crawley-Boevey
type

We explore how a simple question involving linear combinations of powers
of complex numbers, translates into a condition that ensures block
decomposition in Category O, over an algebra of Crawley-Boevey type.


....................................................................................
Speaker: Manoj Kummini

Title: Multiplicity Conjectures.

Abstract: We consider two conjectures due to Herz\"og-Huneke-Srinivasan and
Herz\"og-Srinivasan bounding the multiplicity of a homogeneous ideal $I$ in
a polynomial ring $R$. We describe a history of the problem and some known
results. Further, if $I$ is a square-free monomial ideal, we use
Stanley-Reisner theory to interpret the conjecture as a question on
simplicial complexes, giving some positive results for graphs.

.....................................................................................
Speaker: Sooraj Kuttykrishnan

Title: Polynomial automorphisms.

Let R be a domain and $ F \in \text{Aut}_R{R[X_1,...,X_n]}, n>1 $. A longstanding
open question asks whether $F$ is stably tame. i.e Does there exists $m \ge 0 $ and
new variables $X_{n+1},..., X_{n+m}$ such that the extended map $(F,X_{n+1},...,
X_{n+m})$ is tame?  When $n=2$ and R is a field the answer is yes with m=0 (This is
the well known Jung's Theorem). We will present some history of this problem and
some results in the affirmative when $n=2$.

.....................................................................................
Speaker:  Brian Pasko

Title:  The cohomology of a finite matrix subgroup.

Abstract:  I will present the mod-3 cohomology of the group of four by
four upper triangular matrices with entries from the field on three
elements modulo its center.  We will consider a split extension with
cyclic subgroup for which Siegel gives a method to construct the second
page of the associated Lyndon-Hochschild-Serre spectral sequence.

.....................................................................................
Speaker: Kenyon Platt

Title:  Nonempty blocks of Category \mathcal{O}_S

Abstract:  Category \mathcal{O}_S is a category of certain Lie algebra
modules, whose key objects are the generalized Verma modules (GVM's).
Category \mathcal{O}_S decomposes into a direct sum of special
subcategories called blocks of \mathcal{O}_S such that every module in
\mathcal{O}_S decomposes as a direct sum of modules with each summand
belonging to one of the blocks.  In this talk, I will discuss conditions
for a block to be nonempty.

.....................................................................................
Speaker:  Ibrahim Saleh

Title: Induced Representation of Quantum Groups

In this work, we introduce the definition of the Hopf
representations which is  a generalization of the Hopf module,
also we investigate the concept of quantum subgroups, and finally,
we construct induced Hopf module and induced Hopf representations.

.....................................................................................
Speaker: Prasad Senesi

TITLE:  Weyl Modules Associated to A_2^2

ABSTRACT:
We define maximal integrable and finite-dimensional loop highest weight
modules for the affine Lie algebra A_2^2.  A tensor product decomposition
rule is also given for these modules.  We then discuss the generalization
of these results to the remaining twisted affine algebras and conjecture a
general formule for the dimension of these modules.

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Will keep updated