Marie Vitulli - Academia.edu (original) (raw)

Papers by Marie Vitulli

arXiv (Cornell University), Oct 30, 2017

We take a long term look at initial employment trends for new doctorates with an eye towards gend... more We take a long term look at initial employment trends for new doctorates with an eye towards gender, citizenship, and gender and citizenship differences by analyzing data from 1991-2015 AMS-ASA-IMS-MAA-SIAM Annual Surveys. The data show that the unemployment rate for women has been equal to or lower than the rate for men during most of the last quarter century. The one exception is that between 2001 and 2015 the unemployment rate for women who are not U.S. citizens was higher than the rate for non-citizen men. The unemployment rates are higher for males who are U.S. citizens than for non-citizen males in the last fifteen years, a puzzling trend. The data show that men from all pure math programs 1 are considerably more likely than women to take jobs at the top-ranking and top-producing math departments. The data show women take jobs at departments in which the highest degree is a bachelor's degree at much higher rates and men take jobs in business and industry at considerably higher rates. We also find that men from the top-ranking or top-producing doctoral programs tend to be more likely to take jobs at academic institutions or research institutes at least on a par with their degreegranting institutions.

arXiv (Cornell University), Oct 30, 2017

In this article I reflect upon the problems connected with writing women in mathematics into Wiki... more In this article I reflect upon the problems connected with writing women in mathematics into Wikipedia. I discuss some of the current projects and efforts aimed at increasing the visibility of women in mathematics on Wikipedia. I present the rules for creating a biography on Wikipedia and relate my personal experiences in creating such articles. I hope to provide the reader with the background and resources to start editing existing Wikipedia articles and the confidence to create new articles. I would also like to encourage existing editors to look out for and protect new articles about women mathematicians and submit new articles.

In the 1990s some mathematicians questioned whether affirmative action efforts were skewing the j... more In the 1990s some mathematicians questioned whether affirmative action efforts were skewing the job market in favor of women. With this in mind, twelve years ago we analyzed the 1991– 1995 employment data collected by the AMS for possible gender bias in the employment of new Ph.D. mathematicians. A summary of our analysis appeared in [1], where we reported that the data showed that women were not getting more than their share of first jobs, but that there were gender differences in the type of employment. In the current article we summarize what has happened in the intervening years. We thank Jim Maxwell of the AMS for supplying the data collected from the AMS-ASA-IMS-MAA-SIAM Annual

Fifty Years of Women in Mathematics

The core of an ideal is the intersection of all its reductions. We describe the core of a zero-di... more The core of an ideal is the intersection of all its reductions. We describe the core of a zero-dimensional monomial ideal I as the largest monomial ideal contained in a general reduction of I. This provides a new interpretation of the core in the monomial case as well as an efficient algorithm for computing it. We relate the core to adjoints and first coefficient ideals, and in dimension two and three we give explicit formulas.

In this note we characterize the affine semigroup rings K[S] over an arbitrary field K that satis... more In this note we characterize the affine semigroup rings K[S] over an arbitrary field K that satisfy condition R_l of Serre. Our characterization is in terms of the face lattice of the positive cone pos(S) of S. We start by reviewing some basic facts about the faces of pos(S) and consequences for the monomial primes of K[S]. After proving our characterization we turn our attention to the Rees algebras of a special class of monomial ideals in a polynomial ring over a field. In this special case, some of the characterizing criteria are always satisfied. We give examples of nonnormal affine semigroup rings that satisfy R_2.

We describe some basic facts about the weak subintegral closure of ideals in both the algebraic a... more We describe some basic facts about the weak subintegral closure of ideals in both the algebraic and complex-analytic settings. We focus on the analogy between results on the integral closure of ideals and modules and the weak subintegral closure of an ideal. We start by giving a geometric interpretation of the Reid-Roberts-Singh criterion for when an element is weakly subintegral over a subring. We give new characterizations of the weak subintegral closure of an ideal. We associate with an ideal I of a ring A an ideal I_>, which consists of all elements of A such that v(a)>v(I), for all Rees valuations v of I. The ideal I_> plays an important role in conditions from stratification theory such as Whitney's condition A and Thom's condition A_f and is contained in every reduction of I. We close with a valuative criterion for when an element is in the weak subintegral closure of an ideal. For this, we introduce a new closure operation for a pair of modules, which we cal...

Notices of the American Mathematical Society, Mar 1, 2018

We take a long term look at initial employment trends for new doctorates with an eye towards gend... more We take a long term look at initial employment trends for new doctorates with an eye towards gender, citizenship, and gender and citizenship differences by analyzing data from 1991-2015 AMS-ASA-IMS-MAA-SIAM Annual Surveys. The data show that the unemployment rate for women has been equal to or lower than the rate for men during most of the last quarter century. The one exception is that between 2001 and 2015 the unemployment rate for women who are not U.S. citizens was higher than the rate for non-citizen men. The unemployment rates are higher for males who are U.S. citizens than for non-citizen males in the last fifteen years, a puzzling trend. The data show that men from all pure math programs 1 are considerably more likely than women to take jobs at the top-ranking and top-producing math departments. The data show women take jobs at departments in which the highest degree is a bachelor's degree at much higher rates and men take jobs in business and industry at considerably higher rates. We also find that men from the top-ranking or top-producing doctoral programs tend to be more likely to take jobs at academic institutions or research institutes at least on a par with their degreegranting institutions.

Pacific Journal of Mathematics, 1979

Consider a semigroup ring B H =k[t h lheH] where t is a transcendental over an algebraically clos... more Consider a semigroup ring B H =k[t h lheH] where t is a transcendental over an algebraically closed field k of characteristic 0. Let T X {B) denote T x (BIJc,B) where T^B/k,-) is the upper cotangent functor of Lichtenbaum and Schlessinger. Then T 1 (B) is a graded ά-vector space of finite dimension and B is said to be negatively graded if T 1 (B)+= 0. It is known that a versal deformation T/S of B/k exists in the sense of Schlessinger, where (S, m s) is a complete noetherian local A-aigebra. We say that the formal moduli space is unobstructed if S is a regular local ring. In this paper we restrict our attention to the negatively graded semigroup rings. In this case we compute the dimension of T 1 (B) and are thus able to determine which formal moduli spaces are unobstructed. Let U denote the (open) subset of Spec (S) consisting of all points with smooth fibres. In a previous paper [5] we computed the dimension of U. We always have inequalities: dim U ^ (Krull) dim S ^ [m s /m 2 s : k]. Consequently S is a regular local ring if and only if dim U-[m s j m|: k] = [T^B): k]. In the general case the difference [T^B): k]dim U gives some indication of the extent of the obstruction. I would like to express my gratitude to Dock S. Rim for stimulating my interest in the subject and for his valuable suggestions and advice.

Communications in Algebra, 1989

American Journal of Mathematics, 1983

Advances in Mathematics, 2011

Advances in Mathematics, 2007

The core of an ideal is the intersection of all its reductions. We describe the core of a zero-di... more The core of an ideal is the intersection of all its reductions. We describe the core of a zero-dimensional monomial ideal I as the largest monomial ideal contained in a general reduction of I. This provides a new interpretation of the core in the monomial case as well as an efficient algorithm for computing it. We relate the core to adjoints and first coefficient ideals, and in dimension two and three we give explicit formulas.

Communications in Algebra, 1990

The core of an ideal is the intersection of all its reductions. We describe the core of a zero-di... more The core of an ideal is the intersection of all its reductions. We describe the core of a zero-dimensional monomial ideal I as the largest monomial ideal contained in a general reduction of I. This provides a new interpretation of the core in the monomial case as well as an efficient algorithm for computing it. We relate the core to adjoints and first coefficient ideals, and in dimension two and three we give explicit formulas.

Notices of the American Mathematical Society, Mar 1, 2018

In this article I reflect upon the problems connected with writing women in mathematics into Wiki... more In this article I reflect upon the problems connected with writing women in mathematics into Wikipedia. I discuss some of the current projects and efforts aimed at increasing the visibility of women in mathematics on Wikipedia. I present the rules for creating a biography on Wikipedia and relate my personal experiences in creating such articles. I hope to provide the reader with the background and resources to start editing existing Wikipedia articles and the confidence to create new articles. I would also like to encourage existing editors to look out for and protect new articles about women mathematicians and submit new articles.

Nagoya Mathematical Journal

The foundations for this paper were developed in [5], “Seminormal rings and weakly normal varieti... more The foundations for this paper were developed in [5], “Seminormal rings and weakly normal varieties”, where the historical framework and fundamental properties of weakly normal varieties were presented in detail. Here we devote our attention to the study of the multicross singularity and the role of local cohomology in the theory of weakly normal varieties.

Nagoya Mathematical Journal, 1987

In “Seminormal rings and weakly normal varieties” we introduced the notion of a c-regular functio... more In “Seminormal rings and weakly normal varieties” we introduced the notion of a c-regular function on an algebraic variety defined over an algebraically closed field of characteristic zero. Our intention was to describe those k-valued functions on a variety X that become regular functions when lifted to the normalization of X, but without any reference to the normalization in the definition. That is, we aspired to identify the c-regular functions on X with the regular functions on the weak normalization of X

Nagoya Mathematical Journal, 1981

In the late sixties and early seventies the operation of weak normalization was formally introduc... more In the late sixties and early seventies the operation of weak normalization was formally introduced first in the case of analytic spaces and later in the abstract scheme setting (cf. [6] & [4]). The notion arose from a classification problem. An unfortunate phenomenon in this area occurs when one tries to parametrize algebraic objects associated with a space by an algebraic variety; the resulting variety is, in general, not uniquely determined and may, for example, depend on the choice of coordinates. Under certain conditions one does know that the normalization of the parameter variety is unique. The price one pays for passing to the normalization is that often this variety no longer parametrizes what it was intended to; one point on the original parameter variety may split into several in the normalization. This problem is avoided if one passes instead to the weak normalization of the original variety. One then obtains a variety homeomorphic to the original variety with universal ...

arXiv (Cornell University), Oct 30, 2017

We take a long term look at initial employment trends for new doctorates with an eye towards gend... more We take a long term look at initial employment trends for new doctorates with an eye towards gender, citizenship, and gender and citizenship differences by analyzing data from 1991-2015 AMS-ASA-IMS-MAA-SIAM Annual Surveys. The data show that the unemployment rate for women has been equal to or lower than the rate for men during most of the last quarter century. The one exception is that between 2001 and 2015 the unemployment rate for women who are not U.S. citizens was higher than the rate for non-citizen men. The unemployment rates are higher for males who are U.S. citizens than for non-citizen males in the last fifteen years, a puzzling trend. The data show that men from all pure math programs 1 are considerably more likely than women to take jobs at the top-ranking and top-producing math departments. The data show women take jobs at departments in which the highest degree is a bachelor's degree at much higher rates and men take jobs in business and industry at considerably higher rates. We also find that men from the top-ranking or top-producing doctoral programs tend to be more likely to take jobs at academic institutions or research institutes at least on a par with their degreegranting institutions.

arXiv (Cornell University), Oct 30, 2017

In this article I reflect upon the problems connected with writing women in mathematics into Wiki... more In this article I reflect upon the problems connected with writing women in mathematics into Wikipedia. I discuss some of the current projects and efforts aimed at increasing the visibility of women in mathematics on Wikipedia. I present the rules for creating a biography on Wikipedia and relate my personal experiences in creating such articles. I hope to provide the reader with the background and resources to start editing existing Wikipedia articles and the confidence to create new articles. I would also like to encourage existing editors to look out for and protect new articles about women mathematicians and submit new articles.

In the 1990s some mathematicians questioned whether affirmative action efforts were skewing the j... more In the 1990s some mathematicians questioned whether affirmative action efforts were skewing the job market in favor of women. With this in mind, twelve years ago we analyzed the 1991– 1995 employment data collected by the AMS for possible gender bias in the employment of new Ph.D. mathematicians. A summary of our analysis appeared in [1], where we reported that the data showed that women were not getting more than their share of first jobs, but that there were gender differences in the type of employment. In the current article we summarize what has happened in the intervening years. We thank Jim Maxwell of the AMS for supplying the data collected from the AMS-ASA-IMS-MAA-SIAM Annual

Fifty Years of Women in Mathematics

The core of an ideal is the intersection of all its reductions. We describe the core of a zero-di... more The core of an ideal is the intersection of all its reductions. We describe the core of a zero-dimensional monomial ideal I as the largest monomial ideal contained in a general reduction of I. This provides a new interpretation of the core in the monomial case as well as an efficient algorithm for computing it. We relate the core to adjoints and first coefficient ideals, and in dimension two and three we give explicit formulas.

In this note we characterize the affine semigroup rings K[S] over an arbitrary field K that satis... more In this note we characterize the affine semigroup rings K[S] over an arbitrary field K that satisfy condition R_l of Serre. Our characterization is in terms of the face lattice of the positive cone pos(S) of S. We start by reviewing some basic facts about the faces of pos(S) and consequences for the monomial primes of K[S]. After proving our characterization we turn our attention to the Rees algebras of a special class of monomial ideals in a polynomial ring over a field. In this special case, some of the characterizing criteria are always satisfied. We give examples of nonnormal affine semigroup rings that satisfy R_2.

We describe some basic facts about the weak subintegral closure of ideals in both the algebraic a... more We describe some basic facts about the weak subintegral closure of ideals in both the algebraic and complex-analytic settings. We focus on the analogy between results on the integral closure of ideals and modules and the weak subintegral closure of an ideal. We start by giving a geometric interpretation of the Reid-Roberts-Singh criterion for when an element is weakly subintegral over a subring. We give new characterizations of the weak subintegral closure of an ideal. We associate with an ideal I of a ring A an ideal I_>, which consists of all elements of A such that v(a)>v(I), for all Rees valuations v of I. The ideal I_> plays an important role in conditions from stratification theory such as Whitney's condition A and Thom's condition A_f and is contained in every reduction of I. We close with a valuative criterion for when an element is in the weak subintegral closure of an ideal. For this, we introduce a new closure operation for a pair of modules, which we cal...

Notices of the American Mathematical Society, Mar 1, 2018

We take a long term look at initial employment trends for new doctorates with an eye towards gend... more We take a long term look at initial employment trends for new doctorates with an eye towards gender, citizenship, and gender and citizenship differences by analyzing data from 1991-2015 AMS-ASA-IMS-MAA-SIAM Annual Surveys. The data show that the unemployment rate for women has been equal to or lower than the rate for men during most of the last quarter century. The one exception is that between 2001 and 2015 the unemployment rate for women who are not U.S. citizens was higher than the rate for non-citizen men. The unemployment rates are higher for males who are U.S. citizens than for non-citizen males in the last fifteen years, a puzzling trend. The data show that men from all pure math programs 1 are considerably more likely than women to take jobs at the top-ranking and top-producing math departments. The data show women take jobs at departments in which the highest degree is a bachelor's degree at much higher rates and men take jobs in business and industry at considerably higher rates. We also find that men from the top-ranking or top-producing doctoral programs tend to be more likely to take jobs at academic institutions or research institutes at least on a par with their degreegranting institutions.

Pacific Journal of Mathematics, 1979

Consider a semigroup ring B H =k[t h lheH] where t is a transcendental over an algebraically clos... more Consider a semigroup ring B H =k[t h lheH] where t is a transcendental over an algebraically closed field k of characteristic 0. Let T X {B) denote T x (BIJc,B) where T^B/k,-) is the upper cotangent functor of Lichtenbaum and Schlessinger. Then T 1 (B) is a graded ά-vector space of finite dimension and B is said to be negatively graded if T 1 (B)+= 0. It is known that a versal deformation T/S of B/k exists in the sense of Schlessinger, where (S, m s) is a complete noetherian local A-aigebra. We say that the formal moduli space is unobstructed if S is a regular local ring. In this paper we restrict our attention to the negatively graded semigroup rings. In this case we compute the dimension of T 1 (B) and are thus able to determine which formal moduli spaces are unobstructed. Let U denote the (open) subset of Spec (S) consisting of all points with smooth fibres. In a previous paper [5] we computed the dimension of U. We always have inequalities: dim U ^ (Krull) dim S ^ [m s /m 2 s : k]. Consequently S is a regular local ring if and only if dim U-[m s j m|: k] = [T^B): k]. In the general case the difference [T^B): k]dim U gives some indication of the extent of the obstruction. I would like to express my gratitude to Dock S. Rim for stimulating my interest in the subject and for his valuable suggestions and advice.

Communications in Algebra, 1989

American Journal of Mathematics, 1983

Advances in Mathematics, 2011

Advances in Mathematics, 2007

The core of an ideal is the intersection of all its reductions. We describe the core of a zero-di... more The core of an ideal is the intersection of all its reductions. We describe the core of a zero-dimensional monomial ideal I as the largest monomial ideal contained in a general reduction of I. This provides a new interpretation of the core in the monomial case as well as an efficient algorithm for computing it. We relate the core to adjoints and first coefficient ideals, and in dimension two and three we give explicit formulas.

Communications in Algebra, 1990

The core of an ideal is the intersection of all its reductions. We describe the core of a zero-di... more The core of an ideal is the intersection of all its reductions. We describe the core of a zero-dimensional monomial ideal I as the largest monomial ideal contained in a general reduction of I. This provides a new interpretation of the core in the monomial case as well as an efficient algorithm for computing it. We relate the core to adjoints and first coefficient ideals, and in dimension two and three we give explicit formulas.

Notices of the American Mathematical Society, Mar 1, 2018

In this article I reflect upon the problems connected with writing women in mathematics into Wiki... more In this article I reflect upon the problems connected with writing women in mathematics into Wikipedia. I discuss some of the current projects and efforts aimed at increasing the visibility of women in mathematics on Wikipedia. I present the rules for creating a biography on Wikipedia and relate my personal experiences in creating such articles. I hope to provide the reader with the background and resources to start editing existing Wikipedia articles and the confidence to create new articles. I would also like to encourage existing editors to look out for and protect new articles about women mathematicians and submit new articles.

Nagoya Mathematical Journal

The foundations for this paper were developed in [5], “Seminormal rings and weakly normal varieti... more The foundations for this paper were developed in [5], “Seminormal rings and weakly normal varieties”, where the historical framework and fundamental properties of weakly normal varieties were presented in detail. Here we devote our attention to the study of the multicross singularity and the role of local cohomology in the theory of weakly normal varieties.

Nagoya Mathematical Journal, 1987

In “Seminormal rings and weakly normal varieties” we introduced the notion of a c-regular functio... more In “Seminormal rings and weakly normal varieties” we introduced the notion of a c-regular function on an algebraic variety defined over an algebraically closed field of characteristic zero. Our intention was to describe those k-valued functions on a variety X that become regular functions when lifted to the normalization of X, but without any reference to the normalization in the definition. That is, we aspired to identify the c-regular functions on X with the regular functions on the weak normalization of X

Nagoya Mathematical Journal, 1981

In the late sixties and early seventies the operation of weak normalization was formally introduc... more In the late sixties and early seventies the operation of weak normalization was formally introduced first in the case of analytic spaces and later in the abstract scheme setting (cf. [6] & [4]). The notion arose from a classification problem. An unfortunate phenomenon in this area occurs when one tries to parametrize algebraic objects associated with a space by an algebraic variety; the resulting variety is, in general, not uniquely determined and may, for example, depend on the choice of coordinates. Under certain conditions one does know that the normalization of the parameter variety is unique. The price one pays for passing to the normalization is that often this variety no longer parametrizes what it was intended to; one point on the original parameter variety may split into several in the normalization. This problem is avoided if one passes instead to the weak normalization of the original variety. One then obtains a variety homeomorphic to the original variety with universal ...