Algebra
& Discrete Mathematics Seminar
Spring 2010 Schedule
Location:
Minard 304A (Seminar Room)
Time: Tuesday, 10:00-10:50
a.m.
Organizer: Cătălin Ciupercă
9 February 2010
Sean Sather-Wagstaff,
NDSU: Extension and Torsion
Functors for Artinian Modules (III)
2 February 2010
Sean Sather-Wagstaff,
NDSU: Extension and Torsion
Functors for Artinian Modules (II)
Fall 2009 Schedule
Location:
Minard 304A (Seminar Room)
Time: Tuesday, 10:00-10:50
a.m.
Organizer: Cătălin Ciupercă
24 November 2009
Cătălin Ciupercă,
NDSU: Integral closure modulo
generic elements (III)
17 November 2009
Cătălin Ciupercă,
NDSU: Integral closure modulo
generic elements (II)
10 November 2009
Cătălin Ciupercă,
NDSU: Integral closure modulo
generic elements
27
October 2009
Bethany
Kubik, NDSU: Quasidualizing
Modules
and
their
relationship
to
Semidualizing Modules
Abstract: Let R be a local complete noetherian ring. A noetherian R-module C is semidualizing if Hom_R(C,C)is isomorphic to R and Ext_R^i(C,C)=0 for all i greater than or equal to 1. We introduce and study the artinian counterpart which we call a quasidualizing module. We explore the relationship between these two concepts through Matlis Duality.
20 October 2009
Sean Sather Wagstaff, NDSU: Semidualizing modules for rings of codimension 2 (part II)
13 October 2009
Sean Sather Wagstaff, NDSU: Semidualizing modules for rings of codimension 2
Abstract: Semidualizing modules are algebraic objects that are objects for the study of several aspects of commutative noetherian rings. However, the program of completely understanding the structure of the collection of such modules is still far from complete. We will provide a criterion for characterizing the semidualizing modules over Cohen-Macaulay rings of codimension 2, and we will prove that several classes of rings satisfy this criterion: generically Gorenstein rings (e.g., reduced rings), rings arising from fat point schemes, and rings that are obtained as quotients by monomial ideals. This is joint work with Susan Cooper.
6 October 2009
Azer Akhmedov, NDSU: On the girth of groups
Abstract: I'll introduce the notion of girth of a finitely generated group, and will mention examples of groups with finite as well as infinite girth. It is a classic theorem of J.Tits that every finitely generated linear group is either virtually solvable or contains non-abelian free subgroup. This result is called Tits Alternative. I'll introduce the so-called Girth Alternative, and compare it with Tits Alternative.
29 September 2009
Stacy Trentham, NDSU: MCD (maximal common divisor) Rings
Abstract: In this talk, we will be looking at MCD domains. In particular, we will examine some properties of polynomial extensions of MCD domains. We will end by generalizing the MCD property to include rings with zero divisors to see if polynomial extensions of these rings possess properties similar to their domain counterparts.
15
September
2009
Sean Sather-Wagstaff, NDSU:
Hilbert-Kunz multiplicities
8
September
2009
Cătălin Ciupercă,
NDSU: Structure theorems for certain integrally closed ideals
Algebra
& Discrete Mathematics Seminar
Spring 2009 Schedule
Location:
Minard 304A (Seminar
Room)
Time:
Thursday, 10:00-10:50
a.m.
Organizer:
Cătălin
Ciupercă
30
April 2009
Bethany
Kubik, NDSU:
Quasidualizing modules
23
April 2009
Sean
Sather-Wagstaff, NDSU:
Semidualizing
modules:
Some
background,
an
application, and some
structure (part III)
16
April 2009
Sean
Sather-Wagstaff, NDSU:
Semidualizing
modules:
Some
background,
an
application, and some
structure (part II)
9
April 2009
Sean
Sather-Wagstaff, NDSU:
Semidualizing
modules:
Some
background,
an
application, and some
structure
Abstract:
Semidualizing
modules
were "discovered" independently by Foxby,
Golod, Vasconcelos and Wakamatsu. I learned about them through some
work of Avramov and Fozby where semidualizing modules are used to
study local ring homomorphisms of finite G-dimension. I plan to give
three lectures on this subject. In the first lecture, I will present
some background information on these modules. In the second lecture,
I will discuss an application of semidualizing modules to a question
of Huneke on the rate of growth of the Bass numbers of a local ring.
In the third lecture, I will discuss some recent progress on the
question of whether a given local ring has exactly 2^n semidualizing
modules for some integer n.
12
March 2009
Travis
Trentham, NDSU: A
generalization of Krull dimension (part III)
5
March 2009
Travis Trentham, NDSU: A
generalization of Krull dimension (part II)
26
February 2009
Travis Trentham, NDSU: A
generalization of Krull dimension
Abstract: In this talk we
will look at a generalization of our present notion of Krull
dimension. It will be shown that this definition is well-defined in
the sense that every ring admits a unique Krull dimension. Further,
it wil be shown how Krull dimension is preserved in all ring
extensions that are INC and GU. We will also be looking at some
interesting pathologies that have presented themselves. If time
allows, we will compare the Krull dimensions of R and R[x], where R
is a ring having infinite Krull dimension.
22
January 2009
Azer Akhmedov, NDSU: Groups without
big tiles and tiles in symmetric spaces with arbitrarily big Heesch
number
Abstract: I will discuss the following property of a
discrete group G:
(P) Given any finite subset K of G, there
exists a finite subset F of G such that F contains K and and F tiles
G.
The main question is, do all groups have this property? The
answer is negative; I will discuss some ingredients of the
construction and related to that, we will see how it helps to
construct tiles with arbitrarily big Heesch number in symmetric
spaces of rank one simple Lie groups. Interestingly, the idea works
in all symmetric spaces (including hyperbolic spaces of dimension
greater than two) except for the hyperbolic plane.
Fall
2008 Schedule
Location:
Minard 304A
(Seminar Room)
Time:
Tuesday,
11:00-11:50
a.m.
Organizer:
Cătălin
Ciupercă
2
September 2008
Josh Lambert, NDSU: The
Biplanar Crossing Number of C_k x C_l x C_{2m} x P_n
Abstract
9
September 2008
Azer Akhmedov, NDSU:
Perturbations of Wreath Products and Quasi-Isometric Rigidity
I
Abstract: Groups are often endowed with a
left-invariant metric which allows them to be viewed as metric spaces
along with the more traditional view of groups as isometries of
metric spaces. Starting with the works of Cayley and Dehn, this
approach to studying groups has proven to be very fruitful.
In the early 80's, M.Gromov initiated a broad program of
classifying groups up to quasi-isometry. Based on his deep
insight, he conjectured that "algebraic properties of groups are
geometric", i.e. groups with quasi-isometric Cayley graphs
should share the same (or similar) algebraic properties. This
phenomenon is called a quasi-isometric rigidity.
Some sporadic counterexamples to this conjecture were known. By
introducing the notion of perturbation of wreath products of groups,I
show that many-many algebraic properties fail to be invariants of
quasi-isometry. In fact, one can initiate a counter-program to say
that if a property does not satisfy certain finiteness condition then
most likely it is not preserved under quasi-isometry.
For my constructions, I introduce a new class of groups which I call
traveling salesman groups. These groups are interesting independently
and have proven to be useful in other areas as well, e.g. in the
theory of amenable groups.
The first talk is for a
very general audience. In the second talk I will mainly discuss
traveling salesman groups.
16
September 2008
Azer Akhmedov, NDSU:
Perturbations of Wreath Products and Quasi-Isometric
Rigidity
II
30 September
2008
Catalin Ciuperca, NDSU: Numerical
criteria for integral dependence
7
October 2008
Catalin Ciuperca, NDSU:
Numerical criteria for integral dependence II
14
October 2008
Sean Sather-Wagstaff, NDSU:
Gorenstein presentations and semidualizing modules
Abstract: A
famous result of Foxby, Reiten and Sharp says that a Cohen-Macaulay
local ring admits a dualizing module if and only if it is a
homomorphic image of a Gorenstein ring. We augment this result by
showing that such a ring admits a nontrivial semidualizing module if
and only if it admits a Gorenstein presentation Q/I such that the
ideal I has a nontrivial decomposition. This is joint work with David
Jorgensen and Graham Leuschke.
21
October 2008
Sean Sather-Wagstaff, NDSU:
Gorenstein presentations and semidualizing modules II
28
October 2008
Hamid
Rahmati, University of Nebraska-Lincoln
Title: Contracting
endomorphisms and Gorenstein modules
Abstract:
A finite module M over a noetherian local ring (R,
m, k) is said to be Gorenstein if Ext_R^i(k,M)=0 for all i \ne dim R.
An endomorphism f: R --> R of rings is called contracting if
f^i(m) \subseteq m2 for some i \geq 1. Letting S denote the R-module
R with action induced by f, we prove: A finite R-module M is
Gorenstein if and only if Hom_R(S,M) \cong M and Ext_R^i(S,M) = 0 for
1 \leq i \leq \depth R.
4
November 2008
Yong Hou, NDSU
Title:
Geometry of Kleinian Group
18
November 2008
Yong Hou, NDSU
Title:
Fractal Dimensions and Geometric Dynamics
25
November 2008
Sean
Sather-Wagstaff, NDSU
Title:
Homological properties of
modules
Abstract:
In this talk, I will present some background information in
preparation for David Jorgensen's seminar scheduled for 02 December.
I will discuss Ext, depth, and some aspects of modules over
Gorenstein rings.
2
December 2008
Dave
Jorgensen, University of Texas at
Arlington
Title:
Existence of
totally reflexive modules
Abstract:
Totally
reflexive modules over a commutative local ring behave much like
maximal Cohen-Macaulay modules do over a Gorenstein ring. The
point of this talk is to investigate the existence of non-free
totally reflexive modules over local (usually Cohen-Macaulay)
non-Gorenstein rings. We will briefly survey what is known, as
well as discuss some recent results from joint work with Kristen
Beck, and with Meri Hughes and Liana Sega.
Spring
2008 Schedule
Location:
Minard 304A
(Seminar Room)
Time:
Thursday,
12:00
- 12:50 p.m
Organizer:
Cătălin
Ciupercă
7
February 2008
Cătălin
Ciupercă, NDSU: Asymptotic properties of
ideals
21
February 2008
Cătălin
Ciupercă, NDSU: Asymptotic properties of
ideals II
28
February 2008
Cătălin
Ciupercă, NDSU: Asymptotic properties of
ideals III
13
March 2008
Sean
Sather-Wagstaff, NDSU: Duality in
algebra
Abstract: I will present some examples, some theory
and some applications of algebraic duality.
20
March 2008
Sean
Sather-Wagstaff, NDSU: Duality in
algebra II
27 March
2008
Sean
Sather-Wagstaff, NDSU: Duality in
algebra III
10 April
2008
Jim Coykendall, NDSU
17
April 2008
Jim Coykendall, NDSU
24
April 2008
Sandra Spiroff, Seattle
University: A New Zero Divisor Graph
Abstract: A zero
divisor graph of a ring R is a visual representation of the zero
divisor activity in R. They have been studied by I. Beck, D. Anderson
& P. Livingston, S. Mulay, and C. Wickham, to name just a few.
Using a new zero divisor graph introduced by Mulay, one which is
constructed from equivalence classes of zero divisors, we identify
ring theoretic properties. We will compare and contrast these graphs
with the original zero divisor graphs and discuss some results
involving the associated primes of the ring. This is joint work with
Cameron Wickham.