University of Kansas Algebra Seminar

All seminar talks will take place from 2:30pm to 3:30pm in Snow Hall 306

Name: Osamu Iyama, Nagoya University

Title: *Calabi-Yau reduction for hypersurface singularities *

Abstract :

Name: David Fu, National Security Agency

Title: *Cyclic groups in cryptography*

Abstract :

At the heart of modern cryptography lies an almost trivial mathematical object, the humble finite cyclic group. We will discuss the Diffie-Hellman key agreement, the related computational problem, and the mathematics involved in solving said problem in varying amounts of time. To enjoy this talk one should have knowledge of cyclic groups and a non-disdain for things finite.

Name: Paolo Mantero, Purdue University

Title: *Minimal representatives of even linkage classes*

Abstract :

In linkage, most of the work has been done to understand, classify and describe the properties of ideals lying in the linkage class of a complete intersection (licci and glicci ideals). Licci and glicci ideals have very clear minimal representatives of their linkage class (i.e. ideals having, in some sense, the best possible homological properties): complete intersection ideals. However, if an ideal is not licci or glicci, it is not even clear if one could define a minimal representative of its even linkage class and how to define it. In this talk (where we will focus only on the CI-linkage case) we will explore homological properties that can make an ideal a minimal of its even linkage class and provide a definition of this minimality. We will then discuss upper bounds to the number of steps needed to link an ideal to a minimal representative of its even linkage class. In general these bounds are pretty large (as in the licci case). However, for special classes of ideals, smaller and more interesting bounds will be presented.

Name: Satya Mandal, University of Kansas

Title: *Excision in Algebraic Obstruction Theory*
Abstract :

All seminar talks will take place from 2:30pm to 3:30pm in Snow Hall 306

Name: Kevin Tucker, University of Utah/Princeton

Title: *Generalized F-signature*

Abstract :

In positive characteristic, the existence of a splitting of the Frobenius map has strong algebraic and geometric consequences. In this talk, we will consider a local numerical invariant called the F-signature which roughly gives an asymptotic measure of the number of splittings of the iterates of Frobenius. This invariant was first formally defined by C. Huneke and G. Leuschke, and until recently has been shown to exist only in special cases. In joint work with M. Blickle and K. Schwede, we generalize the F-signature to incorporate divisors and ideal pairs. After discussing these generalizations, we shall describe how they can be used to show the positivity of a related numerical invariant called the F-splitting ratio. This answers an open question of I. Aberbach and F. Enescu.

Name: Ngo Viet Trung, Institute of Mathematics, Hanoi

Title: *Cohen-Macaulayness of monomial ideals *

Abstract :

A combinatorial criterion for the Cohen-Macaulayness of monomial ideals will be the presented. This criterion helps to explain allmost all previous results on this topics. As applications, I will show that there are some striking relationships between the Cohen-Macaulayness of powers of Stanley-Reisner ideals and special classes of simplicial complexes (or hypergraphs).

Name: Bangere Purnaprajna, University of Kansas

Title: * Why study fundamental groups of algebraic varieties?*

Abstract :

We all seem to have fun with fundamental groups. Fun without meaning is usually equated with hedonism. In this talk we show that fun with fundamental groups is not hedonism after all, for studying fundamental groups has some serious consequences in the world of algebraic geometry and that includes connections with holomorphic convexity, a notion in several complex variables, structure and classification of algebraic varieties, diffeomorphism types among other things.

Name: Russ Woodroofe, Washington University

Title: *Matchings, coverings, and
Castelnuovo-Mumford regularity *

Abstract :

I will use a theorem of Kalai and Meshulam to calculate (or at least bound from above) the Castelnuovo-Mumford regularity of the edge ideal of a graph. The bounds will come from covers of the edges of the graph by subgraphs whose complements are chordal. I'll also show how such a covering can be obtained from, for example, any maximal matching, and review related results from the graph theory literature.

All seminar talks will take place from 2:30pm to 3:30pm in Snow Hall 306

Name: Bangere Purnaprajna, University of Kansas

Title: *On moduli problems in algebraic geometry *

Abstract :

This will be a general talk accessible to students. Moduli space is one of the premier topics in algebraic geometry due to its enormous applications to various problems in algebraic geometry. The moduli of curves are well studied. There are still many open questions in the topic of moduli of curves. But the moduli of surfaces of general type (think of surfaces of general type as two dimensional analogues of curves of genus greater than or equal to 2) is a totally different ball game altogether. In this talk various aspects of these moduli spaces will be discussed.

Name: Huy Tai Ha, Tulane University

Title: *Linearity of regularity and the a*-invariant*

Abstract :

Let X = Proj R be a projective scheme over a field k. Let I be an ideal generated by forms of degree d, and let Y --> X be the blowing up of X along the subscheme defined by I. We shall discuss how the asymptotic linearity of the regularity and a*-invariant of powers of I can be related to a set of local data associated to fibers of a projection map from Y.

Name: Huy Tai Ha, Tulane University

Title: *Pure O-sequences and h-vectors of matroids*

Abstract :

A long-standing conjecture of Stanley states that the h-vectors of matroid simplicial complexes are pure O-sequences. We shall discuss a new conjecture on pure O-sequences that implies, in particular, Stanley's conjecture for matroids of rank 3.

Name: Roger Wiegand, University of Nebraska

Title: * Brauer-Thrall Theorems in Various Contexts*

Abstract :

Let (R,m,k) be a local ring (commutative and Noetherian). Roughly speaking, the Brauer-Thrall theorems, transplanted to commutative algebra, say this: If a class C of finitely generated R-modules contains infinitely many non-isomorphic indecomposable modules, then it contains arbitrarily large indecomposables. Moreover, if k is infinite, then there are infinitely many n for which C contains |k| non-isomorphic indecomposables of size n. (Here "size" might be number of generators, length, multiplicity, ... .) I will survey some situations where these conjectures hold, situations where they do not, and situations where we don't know the answer. I will also indicate how one can build large indecomposable modules.

Name: Yi Zhang, University of Minnesota

Title: *A property of local cohomology modules of polynomial rings*

Abstract :

Let R=k[x_1,...,x_n] be a polynomial ring over a field k of characteristic p, and let I=(f_1,...,f_s) be an ideal of R. Then every associated prime P of H^i_I(R) satisfies dim R/P is greater than or equal to n-deg f_1 - deg f_2 -...-deg f_n.

Name: Bangere Purnaprajna, University of Kansas

Title: *Deformation theory and moduli spaces*

Abstract :

Cancelled.

Name: Olgur Celikbas, University of Kansas

Title: *Vanishing of Ext for modules over complete intersection rings*

Abstract :

Let R be a local complete intersection and let M and N be finitely generated R-modules. We will discuss, under certain conditions, a pairing that generalizes Buchweitz's notion of the Herbrand difference. We use this pairing to examine the number of consecutive vanishing of Ext^{i}_{R}(M,N) needed to ensure that Ext^{i}_{R}(M,N)=0 for all postive i$. This is joint work with Hailong Dao.

Name: Bangere Purnaprajna, University of Kansas

Title: *Syzygies and geometry*

Abstract :

Name: Bangere Purnaprajna, University of Kansas

Title: *Fundamental groups of surfaces and two conjectures in algebraic geometry*

Abstract :

Name: Hailong Dao, University of Kansas

Title: *On the structure of Hom(M,N)*

Abstract :

Let R be a regular local ring and M,N be reflexive, non-free R-modules. We describe restrictions on the direct summands of Hom(M,N). We will relate our results to earlier ones by Auslander, Auslander-Goldman, and Griffith.

Name: Bangere Purnaprajna, University of Kansas

Title:

Abstract :

Name: Emily Witt, University of Michigan

Title: *Local cohomology with support in ideals of maximal minors*

Abstract :

Name: H. Dao, University of Kansas

Title: *Endomorphism rings of finite global dimension and cluster tilting objects over Gorenstein rings, I*

Abstract :

Let *M* be a reflexive modules over a local ring *R* and *A = Hom _{R}(M,M)*.
If

Name: H. Dao, University of Kansas

Title: *Endomorphism rings of finite global dimension and cluster tilting objects over Gorenstein rings, II*

Name: D. Katz, University of Kansas

Title: *The e _{1} coefficient in the Hilbert polynomial of a parameter ideal*

Abstract :

We will discuss recent work of Goto, Vasconcelos, et. al. concerning the *e _{1}* coefficient in the Hilbert polynomial of an ideal generated by a system of parameters.

Name: B. Purnaprajna, University of Kansas

Title: *Geometry and syzygies of an algebraic surface*

Abstract :

In the last 25 years or so, after the work of M. Green, the topic of syzygies of algebraic varieties has attracted special attention. The relation between the geometry of an embedding and the algebra of the associated free resolution is to some extent clear for curves but mostly open for an algebraic surface and higher dimensional varieties. I will speak about my recent work with Krishna Hanumanthu that relates the syzygies and geometry of an algebraic surface. This lecture will be accessible to graduate students as well.

Name: S. Cooper, University of Nebraska

Title: *Invariants Related to Symbolic Powers of Ideals of Points *

Abstract :

Many algebraic tools have been developed to gain insight into 0-dimensional schemes. In particular, the Hilbert function and graded Betti numbers of the homogeneous ideal of the scheme have played a central role in many intriguing problems. Hilbert functions of ideals defining reduced 0-dimensional schemes have a well-known characterization. However, we are left perplexed when trying to characterize Hilbert functions of symbolic powers of such ideals (which define non-reduced schemes called fat point schemes). In this talk we'll compare the two situations and provide some insight into the case for fat points. By "trimming down" fat point schemes as a sequence of residuals with respect to lines, we will obtain upper and lower bounds for the Hilbert function of any fat point scheme in projective 2-space. This reduction procedure can be applied to also obtain bounds on Betti numbers, regularity and initial degree. This is joint work with B. Harbourne and Z. Teitler.

Name: G. Leuschke, Syracuse University

Title: *Wild Hypersurfaces*

Abstract :

In the representation theory of finite-dimensional algebras over a field, Drozd's dichotomy theorem says that an algebra has either tame module type or wild module type. Loosely, these two possibilities correspond to: hoping for a classification theorem, or throwing up our hands in dismay. We'd very much like a similar dichotomy result in other representation-theoretic contexts, specifically for maximal Cohen--Macaulay modules over a Cohen--Macaulay local ring. I'll give a little background on the problem, including definitions of tame and wild CM type, and talk about recent work with Andrew Crabbe (Syracuse) which shows that hypersurfaces of multiplicity four or more, in three or more variables, have wild CM type.

Name: Bangere Purnaprajna, University of Kansas

Title: *Geometry and syzygies of an algebraic surface, continued*

Abstract : see above

Name: Bhargav Bhatt, Princeton University

Title: *Derived direct summands*

Abstract :

A scheme satisfies the direct summand condition if its structure sheaf is a summand of that of a finite cover; in characteristic 0, this is equivalent to normality. We will discuss a derived category analogue of this condition. The two conditions diverge in characteristic 0 (the latter characterises rational singularities by a theorem of Kovacs), but turn out to be very closely related in positive and in mixed characteristic. Using this relation, I will also discuss some applications to extensions of standard cohomological vanishing results beyond the ample cone in positive characteristic algebraic geometry.

Name: Ryan Kinser, University of Connecticut

Title: *Rank functions and tensor products of quiver representations*

Abstract :

We'll start with an overview of quiver representations, giving the basic definition and examples, then provide a brief summary their use in algebra, geometry and combinatorics. Next we'll discuss rank functions, which assign a nonnegative integer to any quiver representation, generalizing the notion of the rank of a linear map. They have algebraic properties similar to the classical rank function (additive with respect to direct sum, multiplicative with respect to tensor product, invariant under duality). A "global rank function" can be constructed for any quiver and then maps between directed graphs can be used to derive more rank functions. These can be applied to study the structure of the representation ring (i.e., split Grothendieck ring) of a quiver. Time permitting, we'll also discuss the constructibility of rank functions on representation spaces of quivers.

Name: P. Blass

Title: *
*

Abstract :

Name: Ben Williams, Stanford University

Title: *Motovic cohomology and problems in commutative algebra*

Abstract :

Let *R=k[x _{1}, ... , x_{m}]* be a graded polynomial ring over a field, and let

We try to understand the space of complexes *C* by constructing a moduli space *X* of
exact sequences, and then exhibiting *C* as a map from a punctured affine space to such
*X*. Our space *X* has a presentation as a homogeneous space of linear groups. Using
methods stolen from classical algebraic topology, we can compute the motivic cohomology
of the space *X*, and consequently find numerical restrictions on the existence of such
complexes *C*, including a mild generalization of the Herzog-Kuehl equations.

Name: S. Sather-Wagstaff, North Dakota State University

Title: *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 the 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).

Name: Bangere Purnaprjana, University of Kansas

Title: *Deformation of maps and moduli space of surfaces of general type
*

Abstract :

Name: A. Hariharan, University of Nebraska

Title: *Connected Sums of Gorenstein Local Rings*

Abstract :

This talk will introduce a new construction of local rings called the connected sum and study its properties. In particular, we will obtain conditions for the connected sum to be Gorenstein. Finally, we will see some applications of this construction. This is joint work with W. Frank Moore (Cornell) and Luchezar L. Avramov (UNL).

Name: Y. Kachi, University of Kansas

Title: *Wallis type formula for the special
value of Riemann's zeta function at positive
odd integers. *

Abstract :

As in the title, I will talk about Wallis type formulas for ζ(3) and also Catalan's number. This is joint work with Joel Font.

Name: K. Schwede, University of Michigan

Title: *Discreteness and rationality of F-jumping numbers*

Abstract :

The jumping numbers of a multiplier ideal are an important set of invariants in algebraic geometry. Since the test ideal is a characteristic *p > 0* analog of the multiplier ideal, it is natural to define and study the associated F-jumping numbers. Two basic questions about these invariants follow:
1. Are they always rational? (rationality)
2. Are there always no limit points? (discreteness)
Several groups have partially answered these questions in the past.
I will discuss joint work with M. Blickle, S. Takagi and W. Zhang, where we affirmatively answer these questions in the same generality as answers are known for multiplier ideals.

Name: K. Lee, Purdue University

Title: *Hilbert schemes of points*

Abstract :

The famous *n*! conjecture can be stated in an elementary
language. In fact it asserts that the dimension of the vector space
spanned by all derivatives of a certain bivariate analogue of the* n x n*
Vandermonde determinant is equal to n!. Earlier results of Haiman and
Garsia had shown that the *n*! conjecture implied the Macdonald positivity
conjecture. Later Haiman proved the *n*! conjecture, and the proof is
closely related to the algebraic and geometric properties of isospectral
Hilbert schemes of points on the plane. I'll discuss how some of the
results in the plane case can or cannot be generalized to the higher
dimensional case.

Name: K. Hanumanthu, University of Kansas

Title: *Koszul rings in geometry*

Abstract :

Koszul rings appear naturally in algebra and geometry. We will discuss a basic question regarding the Koszulness of section rings of powers of a line bundle on a projective variety. This is studied in connection to the regularity of the line bundle in question. The relation to the $N_1$ property will be discussed. We will talk also about an analogous question for adjoint line bundles on certain nice surfaces. An attempt will be made to explore the relevance of and interest in these questions from an algebraic perspective.

Name: Z. Teitler, Texas A&M University

Title: *Ranks of polynomials*

Abstract :

The Waring rank of a polynomial of degree d is the least number of terms in an expression for the polynomial as a sum of dth powers. The problem of finding the rank of a given polynomial and studying rank in general has been a central problem of classical algebraic geometry, related to secant varieties; in addition, there are applications to signal processing and computational complexity. Other than a well-known lower bound for rank in terms of catalecticant matrices, there has been relatively little progress on the problem of determining or bounding rank for a given polynomial (although related questions have proved very fruitful). I will describe new upper and lower bounds, with especially nice results for some examples including monomials and cubic polynomials. The talk will be very elementary. This is joint work with J.M. Landsberg.

Name: N. Epstein, University of Osnabrück

Title: *Homogenous equational tight closure*

Abstract :

The title refers to a new variant of tight closure for ideals and modules over locally excellent rings in positive characteristic and in equal characteristic zero, defined in terms of persistence from `homogeneous instances' of tight closure. Unlike the original notion, it commutes with arbitrary localization! In all cases, it sits between plus closure and tight closure. It agrees with the original notion of tight closure for parameter ideals, and for all ideals and modules over finitely generated positively-graded algebras over any algebraic field extension of a prime field. It captures colons, yields a `Brian\,con-Skoda' type theorem, and gives a theory of phantom homology similar to ordinary tight closure. The new notion works well with module-finite extensions and smooth base change, and generally acts the way one expects a "tight closure theory" to behave. It raises a host of new questions, and provides new criteria for when ordinary tight closure commutes with localization. This is joint work with Mel Hochster.

Name: D. Murfet, University of Bonn

Title: *Duality in singularity categories and the Kapustin-Li formula
*

Abstract :

We will discuss the derivation, from Grothendieck duality, of a trace formula for the Serre functor in the singularity category of an isolated hypersurface singularity, first obtained by the string theorists Kapustin and Li.

Name: Y. Xie, University of Notre Dame

Title: *Formulas for the multiplicity of graded algebras*

Abstract :

For simplicity, we will assume that *A = k[A _{1}] ⊆ B = k[B_{1}]* is a homogeneous inclusion of standard
graded Noetherian domains over the field

Observe that dim *A* ≤ dim *B* and they are equal if and only if their quotient field extension is
algebraic of degree *r*. If *B* is integral over *A*, i.e.
dim *B*/*A*_{1}*B* = 0,
then *e(B) = re(A)*. In 2001,
Simis, Ulrich and Vasconcelos gave a formula when dim *A* = dim *B* and
dim *B*/*A*_{1}*B* = 1. We
generalize their formula to arbitrary dimensions of *B*/*A*_{1}*B*.
We also provide the formula for the
case when dim *A* < dim *B*. Thus we give a complete answer to the original question. The techniques
we use are *j*-multiplicities and filter-regular sequences.

The formulas we obtain can be used to find the degree of dual varieties for any hypersurfaces without any restrictions on its dual varieties and singularities. In particular, it gives a generalization of Teissier’s Plücker formula to hypersurfaces with non-isolated singularities.

Name: B. Purnaprajna, University of Kansas

Title: *Fundamental groups of fibrations and conjectures of Nori and Shafarevich*

Abstract :

This is joint work with Rajendra Gurjar.

Name: L. Christensen, Texas Tech University

Title: *The depth formula revisited
*

Abstract :

Let R be a commutative noetherian local ring. A formula that expresses the depth of the tensor product of two R-modules in terms of their individual depths is traditionally called a depth formula. In the talk I will discuss one such formula that specializes to previous versions by Huneke and Wiegand and by Choi and Iyengar. The talk is based on joint work with Dave Jorgensen.

Name: M. Das, Indian Statistical Institute, Kolkata

Title: *On a conjecture of Nori*

Abstract :

Motivated by a topological result, which he proved in an appendix to a paper of Mandal, Nori posed the "homotopy conjecture" for sections of projective modules over a smooth affine domain. The conjecture has been settled in the affirmative by Bhatwadekar-Keshari. In this talk we will outline the impact of Nori's conjecture in the development of Euler class theory. We will also analyze the conjecture in the non-smooth set up, where it is no longer true.

Name: C. Huneke, University of Kansas

Title: *Inequalities between multiplicities in graded rings*

Abstract :

In this talk we discuss a conjecture which related the multiplicites of two systems of parameters in a local or graded Noetherian ring. We prove a recent result of Mustata, Takagi, Watanabe and myself which proves the conejcture for graded rings. The proof uses reduction to characteristic p, and needs the existence of graded big Cohen-Macaulay algebras.

Name: C. Huneke, University of Kansas

Title: *Inequalities between multiplicities in graded rings, cont*

Name: C. Francisco, Oklahoma State University

Title: *Graph colorings via commutative algebra*

Abstract :

I'll discuss joint work with Tai Ha and Adam Van Tuyl in which we explore how powers of the cover ideal of a graph G and their associated primes encode information about the chromatic number of G and its induced subgraphs.

Name: C. Francisco, Oklahoma State University

Title: *Graph colorings via commutative algebra, cont*

Name: A. Hariharan, University of Kansas

Title: *3-Standardness of the maximal ideal*

Abstract :

Let *R * be a Cohen-Macaulay local ring with infinite residue field.
Let *J * be a minimal reduction of the maximal ideal *m*. P. Valabrega and
G. Valla show that the condition *m ^{n} ∩ J = J m ^{n-1}* holds for all

Name: J. Validashti, University of Kansas

Title: *Relative multiplicities of graded algebras*

Abstract :

Let *R* be a Noetherian local ring and *A ⊆ B* be standard graded Noetherian *R*-algebras.
We define a sequence of relative multiplicities for the pair *A ⊆ B* and we study the properties of these
numbers to give numerical criteria for integrality and birationality of the extension *A ⊆ B*,
specially when *A* and *B* are arising from Rees algebras of a pair of modules.

Name: B. Purnaprajna, University of Kansas

Title: *Local algebra and global geometry of canonical covers*

Abstract :

Name: H. Dao, University of Kansas

Title: *On weak lifting of modules*

Abstract :

Let (*S*, *m*) be a local ring and *f* an element in *m*. Let *R=S/(f)*. The lifting question asks whether given a
finite *R*-module *M*,
one can find an *S*-module *N* such that *M=N/fN* and *f* is a nonzerodivisor on *N*. The point is that *M*
would inherit nice homological
properties of *N* if such a lifting exists. In this talk we will discuss various questions and some answers on lifting and a weaker
version of the above question: whether *M* is a direct summand of a liftable module.

Name: S. Ramanan, Chennai Mathematical Institute

Title: *Cohomology of Lie groups*

Abstract :

Heinz Hopf studied the structure of the cohomology of a Lie group treated
as a topological space. The result was a surprisingly simple and elegant
description of this graded algebra in terms of *l* natural numbers *m _{1}*,
... ,

Name: K. Hanumanthu, University of Kansas

Title: *Toroidalization of locally toroidal morphisms*

Abstract :

The toroidalization conjecture of D. Abramovich, K. Karu, K. Matsuki, and J. Wlodarczyk asks whether any given morphism of nonsingular varieties over an algebraically closed field of characteristic zero can be modified into a "toroidal morphism". In these talks, we will try to understand the origins and the significance of this conjecture. Apart from discussing its status, a related local notion will be defined along with a new question and some answers.

Name: K. Hanumanthu, University of Kansas

Title: *Toroidalization of locally toroidal morphisms, continued*

Name: T. Puthenpurakal, IIT Bombay

Title: *Properties of Koszul homology modules*

Abstract :

We investigate various module-theoretic properties of Koszul homology under mild conditions.
These include their depth, *S _{2}*-property and their Bass numbers
This is joint work with Uwe Nagel

Name: T. Marley, University of Nebraska

Title: *Coherent Gorenstein rings*

Abstract :

The concept of Gorenstein dimension, defined by Auslander and Bridger for finitely generated modules over a Noetherian ring, is studied in the context of finitely presented modules over a coherent ring. A generalization of the Auslander-Bridger formula is established and is used as a cornerstone in the development of a theory of coherent Gorenstein rings.

Name: T. Dinh, University of Utah

Title: *Growth of primary decomposition of Frobenius powers*

Abstract :

The linear growth property of primary decompositions of Frobenius powers has strong connection to the localization problem in tight closure theory. The localization problem has recently been settled in the negative, but the linear growth question is still open. I will introduce the linear growth problem and discuss some recent results.

Name: H. Long, University of Kansas

Title: * Almost Cohen Macaulay modules, almost regular sequences and the monomial conjecture: a survey *

Abstract :

In these talks we will give a survey of some new developments in the study of the monomial conjecture. The talk will be based on recent works by Roberts and others on the existence of almost Cohen-Macaulay modules and its consequences.

Name: J. Validashti, University of Kansas

Title: * Numerical Criteria For Integral Dependence.*

Let R be a Noetherian local ring and A ⊆ B standard graded Noetherian R-algebras. We define a few notions of multiplicity for the pair A ⊆ B and we describe numerical criteria for integrality of the extension A ⊆ B, especially when A and B are arising from Rees algebras of a pair of modules.

Name: N. Mohan Kumar, Washington University

Title: *Reducedness of generalized quadrics*

An ubiquitous equation that arises in the study of polynomials is that of a quadric. For definiteness, let *f _{i},g_{i}*,

Name: H. Long, University of Kansas

Title: * Almost Cohen Macaulay modules, almost regular sequences and the monomial conjecture: a survey, II *

Name: S. Sane, Tata Institute of Fundamental Research

Title: *TBA*

Name: D. Katz, University of Kansas

Title: * Multiplicities and Rees valuations*

Abstract :

Let *(R,m)* be a local, Noetherain ring. In these talks we will show that a number of standard relations between multiplicities and Rees valuations of
*m*-primary ideals carry over to Rees valuations and more general multiplicities for ideals that are not necesarily *m*-primary.
In particular, we show that the
*j*-multiplicity of an ideal with maximal analytic spread is determined by the Rees valuations of the ideal centered on *m*.

Name: D. Katz, University of Kansas

Title: * Multiplicities and Rees valuations, II*

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