Algebra & Discrete Mathematics Seminar

Spring 2013 Schedule

Location: Minard 210
Time: Tuesday, 10:00-10:50 a.m.
Organizer: Cătălin Ciupercă




2 April  2013
Sean Sather-Wagstaff, NDSU: Rings of Prime Characteristic (part III)


26 March  2013
Sean Sather-Wagstaff, NDSU: Rings of Prime Characteristic (part II)


19 March  2013
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.



26 February  2013
Azer Akhmedov, NDSU:  Left-orderable groups with almost free actions



19 February  2013
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


Location: Minard 340
Time: Tuesday, 10:00-10:50 a.m.
Organizer: Cătălin Ciupercă



4 September  2012
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.

11 September  2012
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.

25 September 2012
Sean Sather-Wagstaff, NDSU: Applications of semidualizing modules IV
Abstract: see above.

2 October 2012  no seminar

9 October  2012
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.


16 October  2012
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



30 October  2012
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)

Abstract: PDF

28 February 2012
Jason Boynton, NDSU: An introduction to the ring Int(D)

Abstract: PDF


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)


7 February 2012 
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

        

    


      Location:













        Minard 336 

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

        Organizer: Cătălin Ciupercă

        

        

      
      


            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.




      
      


          25









            October 2011

        
      
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: A classical
        non-trivial example of a vertex operator algebra constructed in
        full from scratch (part II)

      

      
      


      27 September 2011

        
      
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.


       
      


      20 September 2011

          

        
      
Jim Coykendall, NDSU: A survey of Factorization (part II)

      

      
      


      13 September 2011

          

        
      
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

    

    

    

    


    3 May 2011

        

      Pye Aung, NDSU: Baer's Criterion
      and Whitehead Problem

    Abstract:  This talk
        is an expository talk about tests for injectivity and
        projectivity of modules, and their connection to the Whitehead
        Problem. Projectivity and injectivity can be viewed as dual
        concepts, hence many definitions and theorems are possible to be
        "dualized" including some equivalent conditions (or tests) of
        projectivity and injectivity. Those facts will be formulated
        using the functor Ext. However, when one attempts to find a
        projective counterpart of the Baer's criterion for injectivity,
        difficulties arise leading to the first-known undecidable
        statement outside set theory.

      

    


    26 April 2011

        

      Saeed Nasseh, NDSU: Lifting of DG
      modules over DG algebras

    Abstract:  We are
        mainly concerned with the generalizations of a result of
        Auslander, Ding and Solberg about lifting of modules. In
        particular, we apply DG techniques to investigate lifting
        properties for DG-modules over DG algebras.

      

    


    19 April 2011

        

      Rich Wicklein, NDSU: A connection
      between the Koszul complex and Tor

    Abstract:  Let (R, m,
        k) be a local ring and M an R-module. A result of Lescot relates
        vector space dimension over k of H_i(M \otimes_R K(x)), where
        K(x) is the Koszul complex, and vector space dimension of
        Tor^R_i(k,M). I will discuss an alternate proof of Lescot’s
        result. This talk should be accessible to anyone who has
        completed 721 or has a basic understanding of modules.

      

    

    

    
12













            April 2011

        

      Tom Dunn, NDSU: Multiplicities
      in Local Rings

    

    

    

    
1
            March 2011

        

      Jim Coykendall, NDSU: Norms in
      Rings of Algebraic Integers (Part II)

    

    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.
    


    

    

    
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

    

    


    

    
Location: Minard












        304A (Seminar Room) 

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

        Organizer: Cătălin Ciupercă

        

      
      


            16 November 2010 

        Jason Boynton, NDSU: The
      D+M Construction and a Generalization

      Abstract: In













      1976 J.W. Brewer and E.A. Rutter investigated certain ring and
      ideal theoretic properties that behave nicely in the now
      well-studied D+M construction. In more recent years, it has become
      fashionable to consider such pullback constructions in greater
      generality. We will survey some past and present results
      concerning the transfer of ring and ideal theoretic properties in
      a special case of a pullback diagram called a conductor square.

      

        

      
      


        

      9 November 2010
      

          

          Sean Sather-Wagstaff, NDSU: Bass Numbers and
      Semidualizing Modules (part III)

      Abstract: Let













      (R,m,k) be a Cohen-Macaulay local ring. We are interested in a
      question of Huneke on the rate of growth of the sequence of Bass
      numbers m^i = rank_k(Ext^i(k,R)). In previous work, we showed
      that, if R has a semidualizing module that is not free and not
      dualizing, then the sequence {m^i} is unbounded. This reduces the
      original question of Huneke down to the case where R has only
      trivial semidualizing modules. We discuss a method for reducing
      generalizations of Huneke's question down to the same case.

      

      
      


      2 November 2010
      

          

          Sean Sather-Wagstaff, NDSU: Bass Numbers and
      Semidualizing Modules (part II)

      Abstract: Let













      (R,m,k) be a Cohen-Macaulay local ring. We are interested in a
      question of Huneke on the rate of growth of the sequence of Bass
      numbers m^i = rank_k(Ext^i(k,R)). In previous work, we showed
      that, if R has a semidualizing module that is not free and not
      dualizing, then the sequence {m^i} is unbounded. This reduces the
      original question of Huneke down to the case where R has only
      trivial semidualizing modules. We discuss a method for reducing
      generalizations of Huneke's question down to the same case.

      

      
      


      26 October 2010
      

          

          Sean Sather-Wagstaff, NDSU: Bass Numbers and
      Semidualizing Modules

      Abstract: Let













      (R,m,k) be a Cohen-Macaulay local ring. We are interested in a
      question of Huneke on the rate of growth of the sequence of Bass
      numbers m^i = rank_k(Ext^i(k,R)). In previous work, we showed
      that, if R has a semidualizing module that is not free and not
      dualizing, then the sequence {m^i} is unbounded. This reduces the
      original question of Huneke down to the case where R has only
      trivial semidualizing modules. We discuss a method for reducing
      generalizations of Huneke's question down to the same case.

      

        

      
      


            12 October 2010 

          

          Cătălin Ciupercă, NDSU: Constructing prime ideals

      

      


            5 October 2010 

          

          Azer Akhmedov, NDSU: Some examples of finitely
      generated infinite simple groups

      

      

      
      


      28 September 2010
      

          

          Azer Akhmedov, NDSU: Some examples of finitely
      generated infinite simple groups

      

      

      


    

    


    

    


        

    


        

    
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)

    

    


      

    
26
          January 2010 

          

          Sean Sather-Wagstaff, NDSU: Extension and
      Torsion Functors for Artinian Modules

      

    

          Abstract: Let R be a commutative noetherian ring. It is
        well known that if N and N' are noetherian R-modules, then the
        modules Ext^i_R(N,N') and Tor^R_i(N,N') are also noetherian.
        Similarly, if N is a noetherian R-module and A is an artinian
        R-module, then the modules Ext^i_R(N,A) and Tor^R_i(N,A) are
        artinian. We will discuss basic properties of artinian modules.
        Then we will state and prove some properties of Ext and Tor
        modules when applied to other combinations of noetherian
        modules, artinian modules, and Matlis reflexive modules. This is
        joint work with Bethany Kubik (NDSU) and Micah Leamer (UNL).

          

        
    


        

    

    


        

    


        

    
Fall
          2009 Schedule

    


    

    
Location:













        Minard 304A (Seminar Room) 

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

        Organizer: Cătălin Ciupercă

      

    


      

    
8
          December 2009 

          

          Azer Akhmedov, NDSU: On linear groups

    

          Abstract: A
      group is linear if it admits a faithful representation in GL(n,k)
      for some natural number n and some field k. In this talk I will
      present some (well known) results about linear groups. The talk is
      aimed at a general audience.

      
    

    
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.