*
*

Jessica Striker:

Abstract: We extend results in dynamical algebraic combinatorics connecting the actions of promotion on (standard Young and increasing) tableaux and rowmotion on order ideals to a more general setting. This is joint work with Kevin Dilks and Corey Vorland.

Ben Noteboom:

Abstract: Betti numbers are a widely studied invariant of homogeneous ideals, but can be difficult to calculate, since to find them one must usually construct a minimal free resolution of the ideal. A Betti splitting of an ideal is a tool which allows us to calculate the Betti numbers of an ideal by breaking it up into smaller pieces and finding the Betti numbers of those pieces. In this talk I will discuss how to determine if a splitting of an ideal is a Betti splitting, then I will go over some applications of these splittings. This will mostly follow a paper by Christopher Francisco, Huy Tai Ha, and Adam Van Tuyl.

Brandon Allen:

Abstract: One hard concept to handle in the beginning of Category Theory is the natural transformation. However, thanks to the Poincare Dual, we have an efficient way to visualize the relations that the natural transformation has with our categorical diagram known as a string diagram. We shall delve into some basic proofs using string diagrams. The talk we based mostly on about the first 25 pages of the following document listed below.

https://arxiv.org/pdf/math/0307200v3.pdf

Sara Solhjem:

Abstract: Motivated by the study of the polytopes formed by the convex hull of permutation matrices and alternating sign matrices, we will define two new families of polytopes. The first as the convex hull of certain \( \{0,1,−1 \} \) matrices in bijection with semistandard Young tableaux. The second are defined as the convex hull of m by n sign matrices. We investigate various properties of these polytope families, including their inequality descriptions, vertices, and facets.

Corey Vorland:

Abstract: The actions of rowmotion and promotion on order ideals of a poset have generated a significant amount of interest in recent algebraic combinatorics research. One property associated to rowmotion and promotion that might suggest a poset is "nice" is the homomesy property. In this talk, we will discuss homomesy on the product of chains poset using a beautiful technique called recombination.

Jim Coykendall

Abstract: A CK (Cohen-Kaplansky) domain is an atomic integral domain that contains only finitely many irreducible elements. Of course, PIDs with only finitely many primes are examples, but there are myriad other examples (e.g. if \( F \) is a finite field then any proper subring of \( F[x] \) generated over \( F \) by powers of \(x \) is a CK domain that is not a PID). We will consider some examples and give some relevant (and reasonably new) results on CK-domains. From there we will see how this class of rings naturally segues into a class of domains with a condition that is stronger than the Noetherian property. And in fact, this property lends itself nicely to (certain aspects of) topology.

14 February 2017

Jessica Striker:

Abstract: In a discrete dynamical system, such as a random juggling pattern, a natural question is to find the probability that the system will be in a given state after running for a long time. This is called the stationary state distribution. In this expository talk, I’ll show how to compute the stationary state distribution for random juggling patterns, using only linear algebra, and then mention an idea for a related research project.

26 April 2016

Chelsey Morrow:

Abstract: We will cover basic factorization properties and how these properties give "nice" factorization in rings.

12 April 2016

Jessica Striker:

Abstract: We introduce the notion of combinatorial dynamics on algebraic ideals by translating combinatorial results involving rowmotion and other toggle group actions on order ideals of posets to the setting of monomial ideals. This is joint work with David Cook.

Trevor McGuire: Resolutions of \(k[M]\)-modules

Abstract: Resolutions of \( k[x_1,...x_n]\)-modules have been widely studied, and in particular, combinatorial methods have been applied to large classes of modules. If we replace the variables with more general objects, the problems get proportionally more difficult. Specifically, we will investigate \(k[M]\)-modules where \(M\) is a monoid. There are two equally realistic avenues to take with \(M\), and we will discuss both avenues. The presentation will begin with a review of aforementioned combinatorial methods for the traditional case.

9 February 2016

Cătălin Ciupercă: Reduction numbers of equimultiple ideals

Fall 2015 Schedule

Cluster algebras are commutative algebras which are generated by a distinguished set of (usually infinitely many) generators, called cluster variables. Starting from a finite set \(x_1, x_2, \ldots, x_n \), the cluster variables can be computed by an iterated elementary process. They miraculously turn out to always be Laurent polynomials in \(x_1, x_2,\ldots, x_n \), with positive coefficients. Finding a closed-form formula for the cluster variables is one of the main problems in the theory of cluster algebra.

In this talk, I will discuss such a closed-form formula for the class of cluster algebras which can be modeled after triangulations of orientable Riemann surfaces with marked points (my running examples will be a pentagon and an annulus). The formula is given in terms of paths (called T-paths) along the edges of a fixed triangulation. The T-paths can be used to give a combinatorial proof for a natural basis (consisting of elements which are indecomposable and positive in some sense) for some types of cluster algebras.

In this talk, I will discuss the relation of squarefree monomial ideals to combinatorics. In particular, I will explain some combinatorial properties of simplicial complexes which can be used to describe the graded Betti numbers of associated ideals.

In this talk, we will go over the history of Horn's conjecture, describe its connection to the Grassmannian, and discuss how it comes up in other areas of mathematics.

**Location:
**ABEN 215**
Time: **Tuesday, 10:00-10:50 a.m.

**5 May
2015**

Sean Sather-Wagstaff, NDSU:

10 March 2015

Jessica Striker, NDSU:

Abstract:

We apply this perspective to model gyration on fully-packed loops, an action whose analysis by L. Cantini and A. Sportiello let to their proof of the Razumov-Stroganov conjecture, an intriguing link between combinatorics and statistical physics. We prove an instance of the homomesy phenomenon of J. Propp and T. Roby, which when specialized to the setting of the Razumov-Stroganov conjecture, yields a key component of this proof.

Finally, we abstract the notion of the toggle group to any finite set of subsets. Interesting special cases of this general setting include chains and antichains of a poset, independent sets, acyclic subgraphs, and vertex or edge covers of a graph. We conclude with many accessible open problems.

17 February 2015

Sean Sather-Wagstaff, NDSU:

10 February 2015

Sean Sather-Wagstaff, NDSU:

3 February 2015

**
Fall 2014 Schedule**

**Location:
**Minard 214**
Time: **Tuesday, 10:00-10:50 a.m.

**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.

**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.

29 October 2013

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.

Sean Sather-Wagstaff, NDSU: Rings of Prime Characteristic (part III)

Sean Sather-Wagstaff, NDSU: Rings of Prime Characteristic (part II)

Sean Sather-Wagstaff, NDSU: Rings of Prime Characteristic

Abstract: Let (R,m,k) be a commutative noetherian local ring. A famous result of Auslander, Buchsbaum, and Serre says that R is regular if and only if the residue field k has finite projective dimension. Other ring-theoretic properties (e.g., complete intersection and Gorenstein) have similar characterizations. If R contains a field of characteristic p > 0, then the Frobenius module R' has a similar ability to characterize properties of R. Essentially, R' is a copy of R viewed as an R-module via the ring homomorphism R \to R given by r \mapsto r^p. We will discuss various aspects of this parallel world, beginning with basic computations, and ending with a recent characterization of dualizing complexes which is joint work with Saeed Nasseh.

Azer Akhmedov, NDSU: Left-orderable groups with almost free actions

Azer Akhmedov, NDSU: Left-orderable groups with almost free actions

Abstract: I will prove a classical result that any countable left-orderable group is isomorphic to a subgroup of Homeo(R). If the action is free, then the group is Archimedean and therefore Abelian. It is also a classical result (Barbot-Kovacevic) that if every non-identity element has at most one fixed point then the group is metaabelian. We'll discuss almost free actions in a more relaxed sense and study the algebraic consequences.

**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
**

Time:

Sean Sather-Wagstaff, NDSU: Applications of semidualizing modules

Abstract: In these
talks, I will present some applications of semidualizing
modules. The
point is to explain some motivation for studying these gadgets.
Applications will include the following: compositions of ring
homomorphisms of finite G-dimension, growth rate bounds for Bass
numbers, and structure results for quasi-deformations. I will
include
plenty of background. In particular, I will not assume any prior
background knowledge about semidualizing modules. These talks
will be
geared toward graduate students.

Sean Sather-Wagstaff, NDSU: Applications of semidualizing modules II

Abstract: see above.

**18
September 2012**

Sean Sather-Wagstaff, NDSU: Applications of semidualizing modules III

Abstract: see above.

Sean Sather-Wagstaff, NDSU: Applications of semidualizing modules III

Abstract: see above.

25 September 2012

Sean Sather-Wagstaff, NDSU: Applications of semidualizing modules IV

Abstract: see above.

2 October 2012 no seminar

Jessica Striker, University of Minnesota: Toggle group actions on posets

Abstract: In this
talk, we introduce the toggle group, which acts on the order
ideals of
a partially ordered set, or poset. We use the toggle group to
model
actions on various objects important in combinatorics, including
partitions, plane partitions, Dyck paths, and Young tableaux.
This
perspective allows us to find easy proofs of the cyclic sieving
phenomenon, in which the number of objects invariant under a
cyclic
action is given by specializing the generating function at a
certain
root of unity. This is based on joint work with Nathan Williams.

Rich Wicklein, NDSU: Codualizing Modules

Abstract: We'll define the concepts of semidualizing and quasidualizing modules. We'll then define a codualizing module, which is a common framework for discussing both ideas. We'll look at some examples and some natural questions that arise.

Mark Batell, NDSU: A note on factorization in polynomial rings

Tom Dunn, NDSU: A Linear Formula for the Generalized Multiplicity Sequence

6 November 2012

Kosmas Diveris, St. Olaf College: Vanishing of self-extensions over symmetric algebras

Abstract: The
Auslander-Reiten (AR) quiver of an Artin algebra is a
combinatorial
device for organizing the indecomposable modules over the
algebra. In the case of symmetric algebras, the
combinatorial
structure of this quiver is well suited for investigating modules
with
eventually vanishing self-extensions. In fact, one can
determine when the vanishing of self-extensions must begin for any
such
module based on its position in the AR quiver. In this talk,
we will explain how one can use the combinatorial data of the AR
quiver
to prove such a fact and discuss connections with a conjecture of
Auslander and Reiten. This is based on joint work with Marju
Purin of St. Olaf College.

**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
**

22 November 2011

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 m^{^4}=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).

18 October 2011

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.

11 October 2011

Thomas Robinson, NDSU:

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 FactorizationAbstract: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**

16 November 2010

Sean Sather-Wagstaff, NDSU:

Sean Sather-Wagstaff, NDSU:

Sean Sather-Wagstaff, NDSU:

12 October 2010

Cătălin Ciupercă, NDSU:

5 October 2010

Azer Akhmedov, NDSU:

Azer Akhmedov, NDSU:

**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:

**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)

Sean Sather-Wagstaff, NDSU:

Abstract:

**Fall
2009 Schedule**

**Location: **Minard
304A (Seminar Room)

**Time: **Tuesday, 10:00-10:50 a.m.

**Organizer: **Cătălin Ciupercă

Azer Akhmedov, NDSU:

Abstract:

**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:

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
**

Abstract

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.

Title:

Abstract:

2 December 2008

**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

Cătălin Ciupercă, NDSU:

Cătălin Ciupercă, NDSU: