Location:
ABEN 215
Time: Tuesday, 10:00-10:50 a.m.
Organizer: Cătălin Ciupercă
5 May 2015
Fall 2014 Schedule
Location:
Minard 214
Time: Tuesday, 10:00-10:50 a.m.
Organizer: Cătălin Ciupercă
9 December 2014
2 December 2014
25 Nobember 2014
18 Nobember 2014
4 Nobember 2014
28 October 2014
7 October 2014
30 September 2014
9 September 2014
Spring 2014 Schedule
Location:
Minard 210
Time: Tuesday, 10:00-10:50 a.m.
Organizer: Cătălin Ciupercă
6
May 2014
Cătălin Ciupercă, NDSU: The concept of
multiplicity of a point on an algebraic variety (Part II)
29
April 2014
Cătălin Ciupercă, NDSU: The concept of
multiplicity of a point on an algebraic variety (Part I)
22 April 2014
15 April 2014
25 March 2014
4 March 2014
25 February 2014
18 February 2014
Fall 2013 Schedule
Location:
Minard 308
Time: Tuesday, 10:00-10:50 a.m.
Organizer: Cătălin Ciupercă
Jason Boynton, NDSU
22 October 2013
15 October 2013
1 October 2013
24
September 2013
17
September 2013
10 September 2013
Spring 2013 Schedule
Location:
Minard 210
Time: Tuesday, 10:00-10:50 a.m.
Organizer: Cătălin Ciupercă
12
February 2013
Azer
Akhmedov, NDSU: Left-orderable groups
Abstract: This
talk is aimed at a very general audience, and will serve as a
preparation for the next talk. We will study basic properties of
left-orderable and bi-orderable groups. Many examples will be
provided.
Fall
2012 Schedule
Spring 2012 Schedule
Location:
Morrill 109
Time: Tuesday, 10:00-10:50 a.m.
Organizer: Cătălin Ciupercă
1 May 2012
Josef Dorfmeister, NDSU: Calc III meets Homological
Algebra
Abstract: I
will show what Green's Theorem, Stokes' Theorem and Gauss' Theorem
of
Calc III fame have to do with chain maps and (co-)homology. I will
define DeRham cohomology, singular homology and show that Stokes'
Theorem (not the Calc III version) shows that integration of forms
on
simplices is a chain map between DeRham cohomology and (singular
homology)*.
10 April 2012
Pye Aung, NDSU: Nagata’s Idealization and the
Amalgamated
Duplication of a Ring along an Ideal
Abstract: If
R is a commutative ring with identity and E is an R-module, then
the
idealization R \ltimes E, called "Nagata’s idealization" of E, is
a new
ring, containing R as a subring. Marco D’anna and Marco Fontana
introduced in 2007 a new general construction, denoted R \bowtie
E; it
is called the ""amalgamated duplication" of a ring R along an
R-submodule E of T(R), the total ring of fractions of R. When
E^2=0,
this new construction coincides with R \ltimes E. I will present
definitions and some basic properties of these two constructions,
and
briefly discuss the case when E is an ideal in R and E is
semi-dualizing as an R-module.
27 March 2012
Sean Sather-Wagstaff, NDSU: Factorizations of local ring
homomorphisms (Part
II)
20 March 2012
Sean Sather-Wagstaff, NDSU: Factorizations of local ring
homomorphisms
Abstract: Let f: R --> S be a homomorphism of
commutative rings. Many techniques for studying R-modules focus on
finitely generated modules. As a consequence, these techniques are
not
well-suited for studying S as an R-module. However, a technique of
Avramov, Foxby, and Herzog sometimes allows one to replace the
original
homomorphism with a surjective one f': R' --> S where R and R'
are tightly connected. In this setting, S is a cyclic R'-module,
so one
can study it using finitely generated techniques. I will give a
general
introduction to such factorizations, followed by a discussion of
some
new results on "weakly functorial properties" of such
factorizations
and applications. The new results are joint with Saeed Nasseh.
6 March 2012
Jason Boynton, NDSU: An introduction to the ring Int(D)
(part II)
28 February 2012
Jason Boynton, NDSU: An introduction to the ring Int(D)
21 February 2012
Azer Akhmedov, NDSU: Hamiltonian cycles in some homogeneous graphs (part III)
14 February 2012
Azer Akhmedov, NDSU: Hamiltonian cycles in some homogeneous graphs (part II)
Azer Akhmedov, NDSU: Hamiltonian cycles in some homogeneous graphs
Abstract: L.Lovasz has conjectured (1970) that all vertex transitive graphs, except 5 of them, are Hamiltonian. We discuss/prove this conjecture for some examples of vertex transitive graphs; these examples turn out to be useful in musical theory.
31 January 2012
Cătălin Ciupercă, NDSU: Kronecker (general) extensions II
24 January 2012
Cătălin Ciupercă, NDSU: Kronecker (general) extensions
Fall
2011 Schedule
Rocío Blanco, Universidad de Castilla-La Mancha: Combinatorial resolution of binomial ideals
Abstract: In this talk we will construct an algorithm of resolution of singularities for binomial ideals in arbitrary characteristic. To resolve binomial ideals we define a modified order function, E-order, as the order along a normal crossing divisor E. With this E-order function we construct a resolution function that drops after blowing up and which provides only combinatorial centers. This kind of centers preserve the binomial structure of the ideal after blowing up. The output of this procedure is a locally monomial ideal that can be easily resolved to achieve a log-resolution.
Kristen Beck, University of Arizona: Asymmetric linear complete resolutions over a short local ring
Abstract: Let (R,m) be a local ring satisfying m4=0. The goal of this talk is to investigate the existence of a certain class of totall reflexive R-modules which are characterized by asymmetry in their complete resolutions. Such a phenomenon is known to occur, by work of Jorgensen and Șega (2005).
Sean Sather-Wagstaff, NDSU: Totally reflexive modules, or How to resolve freely in both directions
Abstract: I will present an introduction to the concept of totally reflexive modules. In particular, I hope to prove that a module over a noetherian ring is totally reflexive if and only if it has a complete resolution. I will define these new terms, and present several examples. This talk is a pre-seminar, in preparation for Kristen Beck's talk on October 25.
Thomas Robinson, NDSU: A classical non-trivial example of a vertex operator algebra constructed in full from scratch
Abstract: I will begin by giving a (very) brief history of the classical algebraic theory of vertex (operator) algebras and why algebraists began studying them. It is somewhat difficult to construct even one interesting example of a vertex algebra. There are two main classical algebraic approaches to do this. I will focus on one of these approaches first developed by Frenkel, Lepowsky and Meurman. Some new techniques streamlining the original approach will allow me to give from scratch a complete construction of one non-trivial example of a vertex algebra in a reasonable amount of time. Then finally this example can be easily used to demonstrate one of the classical applications of vertex algebras, the construction of certain infinite dimensional Lie algebras.
Jim Coykendall, NDSU: A survey of Factorization (part II)
Jim Coykendall, NDSU: A survey of Factorization
Abstract: Since about 1990, there has been much attention paid to the study of factorization in integral domains. Factorization is classically fundamental in number theory and algebra and has myriad applications (perhaps the most familiar of which is the application to coding theory). The general study of factorization in integral domains is the
study of the multiplicative structure of a domain. Familiar examples include Euclidean domains, PIDs, and UFDs, but more exotic examples include finite factorization domains (FFDs), bounded factorization domains (BFDs), and atomic domains (the largest class of domains where irreducible factorizations exist for an arbitrary nonzero nonunit).
In this sequence of two talks, we will review some of these interesting domains (there will be a number of examples for illumination purposes) and some of their fundamental properties and pathologies. We will also explore some natural questions about stability of these factorizations in polynomial, power series, and other extensions. We will also review some very recent developments concerning Kaplansky conditions and the contrast with monoid factorizations.
This talk will be mostly survey and will be aimed at a beginning graduate student audience. All interested parties are encouraged to attend!
Spring
2011 Schedule
Location: Minard 304A (Seminar
Room)
Time: Tuesday, 10:00-10:50 a.m.
Organizer: Cătălin Ciupercă
12
April 2011
Tom Dunn, NDSU:
Multiplicities in Local Rings
1 March
2011
Jim Coykendall, NDSU:
Norms in Rings of Algebraic Integers (Part II)
22
February 2011
Jim Coykendall, NDSU:
Norms in Rings of Algebraic Integers
Abstract:
We will present from the beginnings the concept of a norm in
a ring of algebraic integers. Some basic number theory will be reviewed
to demonstrate this concept. After the general concept is introduced,
we will concentrate on the utility of the norm in gleaning
factorization information of the ring that can be obtained from the
factorization properties of the multiplicative monoid of norms. Many
examples will be presented to (hopefully) provide clarity. Our aim is
to present this from a basic and intuitive point of view.
15
February 2011
Sean Sather-Wagstaff,
NDSU: Nakayama's Lemma for Ext and ascent of
module structures II
8
February 2011
Sean Sather-Wagstaff,
NDSU: Nakayama's Lemma for Ext and ascent of
module structures
Abstract: Let f: (R,m,k) -> (S,mS,k) be a
flat local ring homomorphism, and let M be a finitely generated
R-module. We show that the following are equivalent:
(i) M has an S-module structure compatible with its R-module structure;
(ii) Ext^i_R(S,M)=0 for i>0;
(iii) Ext^i_R(S,M) is finitely generated over R for i=1,...,dim_R(M);
(iv) Ext^i_R(S,M) is finitely generated over S for i=1,...,dim_R(M);
(v) Ext^i_R(S,M) satisfies Nakayama's Lemma over R for i=1,...,dim_R(M).
This improves upon recent results of Frankild, Sather-Wagstaff, and
Wiegand and results of Christensen and Sather-Wagstaff. This is joint
work with Ben Anderson and Jim Coykendall.
Fall 2010
Schedule
Spring 2010 Schedule
Location: Minard
304A (Seminar Room)
Time: Tuesday, 10:00-10:50 a.m.
Organizer: Cătălin Ciupercă
29 April 2010
Micah Leamer, University of Nebraska, Lincoln:
Torsion in tensor products over commutative rings
Abstract: Let
R be a commutative local domain. We are interested in finding
conditions under which the tensor product of two torsion free modules
is torsion free. In particular when R is one dimensional and
M is a torsion free R-module, which is not free, does M tensored with
Hom(M,R) always have torsion. We explore the special case where R is a
subring of a discrete valuation domain and show that at least for
monomial ideals the problem can be simplified to working with
submonoids of the natural numbers. This work is inspired by
an attempt to make progress on the following conjecture: Let
M be a maximal Cohen-Macaulay R-module. If M tensored with Hom(M,R) is
maximal Cohen-Macaulay then M is free. When R is one dimensional being
maximal Cohen-Macaulay is equivalent to being torsion free.
The one dimensional case is relevant since it has been shown
that proving the conjecture for one dimensional Gorenstein rings is
equivalent to proving the conjecture for Gorenstein rings of arbitrary
dimension.
6 April 2010
Azer Akhmedov, NDSU: On Shreier Graphs of Groups
(II)
30 March 2010
Azer Akhmedov, NDSU: On Shreier Graphs of Groups
2 March 2010
Saeed Nasseh, NDSU: Symmetry in the Vanishing of
Ext (II)
23 February 2010
Saeed Nasseh, NDSU: Symmetry in the Vanishing of
Ext
16 February 2010
Bethany Kubik, NDSU: Evaluation Homomorphisms
Abstract: R is a local noetherian ring and A, N, and I are
R-modules. The Hom evaluation homomorphism is the map
\theta_{ANI}:A\Otimes\Hom{N,I}\rightarrow\Hom{\Hom{A,N},I}.
This map is known to be an isomorphism only under certain conditions
placed upon the modules. We will expand the conditions under
which the Hom evaluation is an isomorphism. In particular we
will show that when A is artinian, N is noetherian and Matlis
reflexive, and I is injective, the Hom evaluation homorphism is an
isomorphism.
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.