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Project Summary: Manifolds of Positive and Nonnegative Sectional Curvature
Megan M. Kerr
I propose research to find new examples of spaces of nonnegative and positive curvature
and to understand the essential features these examples share.
Left invariant metrics on Lie groups. All known examples of manifolds of nonnegative
curvature are obtained by starting with a compact Lie group with a left-invariant metric
with nonnegative sectional curvature. We still do not have a complete understanding of the
starting point of this set-up: all left-invariant metrics with nonnegative sectional curvature.
I will investigate the simple compact Lie groups SU (3) and G2 , the automorphism group of
the Cayley numbers. The exceptional Lie group G2 has several large subgroups (e.g., SU (3)
and SO(4)). I have two goals: a classification of the nonnegatively curved left-invariant
metrics on SU (3) and G2 , and a better understanding of the role large subgroups play in
left-invariant metrics of Lie groups.
A deformation on homogeneous spaces. Via a scaling up, scaling down procedure,
Grove and Ziller find new nonnegative curvature metrics on G/H where H ⊂ K ⊂ G. Under
the hypothesis that K/H = S 1 , they get strong results. I am interested in generalizing their
procedure when one has H ⊂ K ⊂ G and the quotient spaces G/K and K/H are sufficiently
nice. The idea is to attempt to expand a biinvariant metric on G in the direction of K and
yet maintain non-negative curvature on G/H. It is known one can do this via shrinking,
but expanding would be new. Efforts so far have avoided the algebraic properties of specific
candidates G and triples of nested subgroups H ⊂ K ⊂ G. My approach will be from the
algebraic perspective, using my familiarity with the simple compact Lie groups.
A non-existence example. For a compact simple Lie group G and an abelian subgroup
K, let Qt be the one-parameter family of left invariant metrics on G achieved by stretching in
the vertical directions but not in the horizontal directions. Then we know Qt has nonnegative
sectional curvature as long as t ≤ 4/3. If K is instead a non-abelian subgroup, I will try to
show the metric Qt , for any t > 1, must always have some negative sectional curvatures. One
hopes that this will shed some light on the cause for the scarcity of examples of manifolds
of positive sectional curvature.
• Intellectual merit The study of Riemannian manifolds of positive sectional curvature
is one of the original questions motivating global Riemannian geometry. It has a rich history;
its questions have motivated deep and beautiful mathematical results. However, this is still
an area of geometry that is characterized more by its open questions than by its known
theorems. Recent exciting breakthroughs have made the search for new examples of spaces
of positive—as well as nonnegative, quasi positive and almost positive—sectional curvature
quite active, full of new interest and new understanding.
• Broader impact NSF data show that 201 Wellesley alumnae earned science doctorates in the years 2000-04. This is approximately 7% of Wellesley’s alumnae in a five year
period. When considered as a percentage of the total number of women alumnae, Wellesley
outperforms the top five schools, ranked by total number of alumnae who earned a doctorate
in science in 2000-04. I am not only a professor at Wellesley, I am an alumna. There are
still too few women in mathematics who establish and maintain excellent research records.
Receipt of this grant would give me the best opportunity to provide another role model
and to continue to develop the next generation of students who may someday have similar
professional success.
1
TABLE OF CONTENTS
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PROJECT DESCRIPTION:
MANIFOLDS OF POSITIVE AND NONNEGATIVE
SECTIONAL CURVATURE
MEGAN M. KERR
DEPARTMENT OF MATHEMATICS
WELLESLEY COLLEGE
1. Introduction
The study of Riemannian manifolds of positive sectional curvature is one of the original
questions of global Riemannian geometry. It has a rich history; its questions have motivated
deep and beautiful mathematical results. However, this is still an area of geometry that is
characterized more by its open questions than by its known theorems.
On the one hand, we know only a few obstructions to strictly positive curvature: there
are two classical theorems about topological restrictions, Bonnet-Myers and Synge’s Theorem. While there are other known restrictions, they hold already for manifolds of nonnegative sectional curvature, a much weaker condition. On the other hand, there are few
known examples of spaces with positive curvature. Up to diffeomorphism, there are the rank
one symmetric spaces, and then only a handful of other examples. Homogeneous spaces
which admit a homogeneous metric with positive curvature are classified: even-dimensional
examples by Wallach [Wa] and odd-dimensional examples by B´erard-Bergery [BB]. They
are the flag manifolds found by Wallach: W 6 = SU (3)/T 2 , W 12 = Sp(3)/(Sp(1))3 , and
W 24 = F4 /Spin(8); the Berger spaces B 7 = SO(5)/SO(3) (here SO(3) is maximal subgroup) and B 13 = SU (5)/Sp(2) · S 1 [Be]. There are families of inhomogeneous examples:
7
in dimension 7 we have the Aloff-Wallach spaces Wp,q
= SU (3)/diag(z p , z q , z¯p+q ), where
(p, q) = 1. In dimensions 6 and 7 we have the Eschenburg spaces, which are biquotients,
E 6 = SU (3)//T 2 where T 2 acts with different circle actions on the right and on the left,
7
and Ek,l
= SU (3)//S 1 where the circle acts on the right and the left (with different actions,
determined by k and l). All are obtained by taking isometric quotients of compact Lie groups
with biinvariant metrics. The only examples in dimensions greater than 24 are the classical
rank one symmetric spaces. There are many more examples of manifolds with nonnegative
sectional curvature, many of these discovered within the past ten years. They also come
from two constructions. One takes an isometric quotient of a compact Lie group with a
Date: November 5, 2007.
1
2
M. M. KERR
biinvariant metric, or one applies a gluing procedure, first described by Cheeger [Ch, 1973]
(referred to as a Cheeger deformation) and recently generalized by Grove and Ziller [GZ2].
My experience in working with homogeneous manifolds and manifolds of low cohomogeneity lends itself well to this arena. Recent exciting breakthroughs have made the search
for new examples of spaces of positive—as well as nonnegative, quasi positive and almost
positive—sectional curvature quite active, full of new interest and new understanding.
2. Proposed Research
It is natural to begin a search for new examples among spaces with lots of symmetry. This
has been the guiding principle for the past 20 years. In what follows, I list three problems
related to finding more examples of spaces of non-negative and (quasi and almost) positive
curvature and to understanding the essential features these examples share. In previous
research, I pursued new examples of Einstein manifolds, spaces of constant Ricci curvature.
I propose to pursue examples of positive (or nonnegative) sectional curvature within the
arena of manifolds with homogeneity or low-cohomogeneity. This area of global Riemannian
geometry has a lot of research activity now as well as an extensive array of open questions
and avenues of approach.
All known examples of compact irreducible manifolds of nonnegative curvature come from
constructions that begin with a compact Lie group. One method is to take an isometric
quotient of a compact Lie group with a biinvariant metric, or, more generally, taking a
Riemannian submersion. By O’Neill’s formula, we know that the submersion metric on the
base space will have sectional curvature no less than the sectional curvature of the total
space, thus when the total space has positive sectional curvature, so does the base space.
The second method is via a gluing construction. The second method can also be viewed as a
quotient, or Riemannian submersion, in the following way. If (M, g) is a Riemannian manifold
with a Lie group G acting by isometries on M , we consider the quotient (M × G)/∆G where
the action of G on the product is g ? (p, h) = (gp, gh) for any g in G and for any (p, h) in
M × G. We get a fibration M × G → (M × G)/∆G. The base space is M , the fibers are
G. Deform the metric on the total space by scaling in the direction of the orbits of G. We
then consider the resultant deformation of the submersion metric on the base space. This
method not only does not decrease sectional curvature, in fact, it tends to increase it.
2.1. Left invariant metrics on Lie groups. Many (almost all known) examples of manifolds of non-negative curvature are obtained by starting with a compact Lie group with a
left-invariant metric with non-negative sectional curvature. We still do not have a complete
understanding of the starting point of this set-up: all left-invariant metrics with non-negative
sectional curvature. The only groups where a complete answer is known are SU (2) and U (2)
(which are 3- and 4-dimensional, respectively) [BFSTW]. Partial results have been obtained
3
on SO(4) (6-dimensional) by J. Huizenga and K. Tapp [HT]. In their paper, they use the
Cheeger deformation and develop some new techniques for classifying the non-negatively
curved left invariant metrics on a compact Lie group G.
I propose to apply the techniques of [HT] to other Lie groups, especially some simple
compact rank two Lie groups such as SU (3) and the exceptional Lie group G2 . In previous
research [K1] and [DK] I worked closely with the group G2 and its subgroups. As the automorphism group of the Cayley numbers, G2 has a lot of structure (see [M]). The subgroups
SU (3) and SO(4) of G2 each have the property that their isotropy action is transitive on
their complement in G2 . In searching for the non-negatively curved left-invariant metrics on
SU (3) and G2 , one can hope for a classification. One can also hope to explore the interplay
of the (large) subgroups inside G2 : there are two different embedded subgroups of G2 isomorphic to U (2), one lying in both SU (3) and SO(4), the other in SO(4) but not in SU (3).
We do not know very much about what happens if we diverge from the biinvariant metric.
2.2. A deformation on homogeneous spaces. Consider a compact Lie group G with
corresponding Lie algebra g. Let Q denote a biinvariant metric on G. For k an abelian
subalgebra of g, consider the family of metrics on g obtained by stretching in the k directions.
Lemma 1. [Z1, Lemma 2.9] Let G be a compact Lie group and k ⊂ g be an abelian subalgebra.
Consider the left invariant metric on G whose value at Te G = g is given by Qt = tQ|k + Q|k⊥ ,
where Q is a biinvarian t metric on G. Then Qt has nonnegative sectional curvature as long
as t ≤ 34 .
Grove and Ziller use the lemma above to prove the following
Proposition 2. [Z1, Prop. 2.8] Let H ⊂ K ⊂ G be Lie groups with K/H = S 1 = ∂D2 and
fix a biinvariant metric Q on G. On the disk bundle G×K D2 there exists a G-invariant metric
with non-negative sectional curvature, which is a product near the boundary G ×K S 1 = G/H
with a metric on G/H induced by Q.
The proposition, in turn, is used to prove the very nice theorem below.
Theorem 3. [Z1, Theorem 2.5 (Grove-Ziller)] A compact cohomogeneity one G-manifold
with codimension of the nonprincipal orbits `± ≤ 2 has a G-invariant metric with nonnegative
sectional curvature.
I am interested in generalizing the “scaling up, scaling down” procedure of Grove-Ziller
[Z1]. While a theorem as general as the one above requires the hypothesis that K/H be
S 1 , one can still hope to apply their procedure when one has H ⊂ K ⊂ G and the quotient
spaces G/K and K/H are sufficiently nice. The idea is to attempt to expand a biinvariant
metric on G in the direction of K and yet maintain non-negative curvature on G/H. It is
known one can do this via shrinking, but expanding would be a new approach.
4
M. M. KERR
In [DK], Will Dickinson and I give a complete list of all homogeneous spaces M = G/H
for which the isotropy representation of H on Tp M decomposes into exactly two irreducible
summands (for G a simple compact Lie group and H a connected, closed subgroup). Almost
all of our examples come from the structure due to the presence of an intermediate subgroup
H ⊂ K ⊂ G needed above. In all of our examples (where H ⊂ G is not maximal), both G/K
and K/H are isotropy irreducible spaces. And in many such examples, one or both of the
base space G/K and the fibre K/H are symmetric spaces. I hope to use this set of spaces as
a good testing ground and set of potential new examples. This work would contribute to our
understanding which G-invariant metrics on a homogeneous space G/H admit nonnegative
sectional curvature.
Some initial progress on this problem of homogeneous metrics on G/H with non-negative
sectional curvature is underway by Tapp [T3]. He considers this case when there is an intermediate subgroup H ⊂ K ⊂ G. He makes great strides from the analytic approach. If
there exists a homogeneous metric g with non-negative sectional curvature, he shows via
the Cheeger deformation that the “inverse linear” path from g to g0 , the normal homogeneous metric induced from a biinvariant metric on G, is through nonnegatively curved
G-invariant metrics. Tapp has some general conditions under which one can find the infinitesimal directions in g/h where scaling up (and scaling down) will lead to a deformation of the
homogeneous metric which maintains nonnegative curvature. The efforts so far have avoided
the complicated (but beautiful) algebraic properties of specific candidates G and triples of
nested subgroups H ⊂ K ⊂ G. My approach will be from the algebraic perspective, using
my familiarity with the simple compact Lie groups.
In my papers [K1, K2] I used some beautiful results of A.L. Oniˇsˇcik [O1]: In 1962 he
classified all simple compact Lie algebras g with subalgebras g0 and g00 , such that g = g0 + g00 .
In terms of transitive group actions, let G be the simply connected compact Lie group
corresponding to g and let G0 , G00 be subgroups corresponding to g0 , g00 , respectively, then
G/G0 = G00 /(G0 ∩ G00 ) and G/G00 = G0 /(G0 ∩ G00 ). That is, one can view a manifold presented
homogeneously one way as M = G/H, where G = Isom0 (M ) is simple, and we consider the
cases where there exists a closed subgroup G0 ⊂ G which acts transitively on M . Denote by
H 0 the isotropy subgroup in G0 , then M = G0 /H 0 . Since G0 is smaller than G, we expect
more G0 -invariant metrics on M than G-invariant metrics. Via Oniˇsˇcik’s list, one knows
when a subgroup of G still acts transitively on G/H. I will explore ways in which Oniˇsˇcik’s
Lie triple systems can be used to provide some new directions for the “scaling up, scaling
down” procedure.
2.3. A non-existence example. For a compact simple Lie group G and an abelian subgroup K, consider the one-parameter family of left invariant metrics on G given by Qt =
tQ|k + Qk⊥ where Q is a biinvariant metric on G and k is the abelian Lie subalgebra of g
5
corresponding to K. One can view this as stretching in the vertical directions but not in
the horizontal directions. Then Qt has non-negative sectional curvature as long as t ≤ 4/3
[Z1, Lemma 2.9]. If now we instead require that K be a non-abelian subgroup, it is believed
that the metric Qt , for any t > 1, has some negative sectional curvatures. I plan to pursue
this avenue as well as the one above, using the simple examples listed in my paper with
Dickinson [DK].
One hopes that a resolution of the question above would shed some additional light on
the reason for the rarity of examples of manifolds of positive sectional curvature. One of
the exciting new results in this area is Wilking’s proof of the relation of the dimension of a
strictly positive curvature manifold M and the dimension of the isometry group of M [Wi1].
Theorem 4. If M n admits a positively curved metric with an isometric action of cohomogeneity k ≥ 1 with n > 18(k + 1)2 , then M is homotopy equivalent to a rank one symmetric
space.
Clearly, as the dimension of M goes up, the cohomogeneity will need to up as well. But
there are still many unanswered questions in the homogeneous setting as well.
3. Broader Impact
Wellesley College has a strong tradition of educating women scientists. Women and scientists hold key leadership positions at Wellesley. The new president of Wellesley College,
Kimberly Bottomly, is a biologist whose last position was the Deputy Provost at Yale University. Two of the three academic deans are female scientists: a chemist and a biologist. More
than half the faculty at Wellesley College are women, providing excellent role models for our
students. The most recent National Science Foundation data, which ranks baccalaureate
institutions by the total number of women alumnae who earned science and engineering doctorates in the years 2000-2004, show that 201 Wellesley alumnae earned science doctorates.
This is approximately 7% of Wellesley’s alumnae in a five year period. When considered
as a percentage of the total number of women alumnae, this is significantly better than the
top five schools on the list. Even considering the total numbers, Wellesley College was the
highest ranked liberal arts college. 1 I am an alumna of Wellesley College and thus represent
a concrete example of Wellesley’s success in preparing women for a career in mathematics.
The Mathematics Department consists of 13 faculty members in tenured or tenure-track
positions, 5 of whom are women. All mathematics classes are taught in small sections (maximum of 25 students) by regular faculty. Our department has no regular adjunct faculty.
The department typically graduates 15 – 25 majors and 10 minors each year. Graduates
1NSF
Division of Science Resources Statistics, Women, Minorities and Persons with Disabilities in Science
and Engineering, Table Survey of Earned Doctorates, 2000-2004, Table F-4. Wellesley ranked 27th in this
list.
6
M. M. KERR
go on to a variety of careers from medical school to finance with a significant number attending Ph.D. programs in mathematics and related fields (e.g., computer science, statistics,
economics). The cross-registration program with MIT provides an opportunity for Wellesley
College students to take graduate-level mathematics courses. In the last year the Mathematics Department has established a faculty seminar series of talks by and for faculty members
of the mathematics department to supplement the long-standing colloquium series in which
outside speakers give talks designed for undergraduates. Our students are highly aware of
this visible example of faculty engaged in research.
In my teaching as well as in my own research, I work to raise the visibility of mathematics
research, especially in geometry and topology. I created a new course in Knot Theory,
which, as a field, is both accessible, in its three-dimensional setting, and young enough so
that students see open questions that they can understand. In Spring 2008 I will be teaching
a senior level course in Matrix Groups: an Introduction to Lie groups. I love the beautiful
interplay of algebra and geometry and am excited to show students how these seemingly
unrelated subjects are intimately connected. I look forward to describing my own research
to my students, including the open problems I describe in this proposal and what makes
them interesting.
At the national level, I am an active member of the Association for Women in Mathematics.
My involvement has had a focus on the promotion of women just embarking on their careers
in mathematics, providing encouragement and mentoring at a critical point in their careers. I
served for three years on the annual Alice T. Shafer Prize for the best woman undergraduate
in mathematics (as Chair in my third year). I am currently a member of the Organizing
Committee, as well as the Postdoctoral Selection Committee, for the AWM Workshop to be
held in January 2008 at the Joint AMS-MAA Meetings.
Just as colleges and universities seek a balance between research, teaching and service
in granting tenure and promotion, the mathematical community values our colleagues who
excel in all of these areas. There are, unfortunately, still too few women in mathematics who
establish and maintain excellent research records. Receipt of this grant would give me the
best opportunity to provide another leader and to continue to develop the next generation
of students who may someday have similar professional success.
References
[BB]
L. B´erard-Bergery, Les vari´et´es riemanniennes homog`enes simplement connexes de dimension impaire
a courbure strictement positive, J. Math. Pures Appl. (9) 55 (1976), no. 1, 47–67.
`
[Be] M. Berger, Les vari´et´es riemanniennes homog`enes normales simplement connexes `
a courbure strictement positive, Ann. Scuola Norm. Sup. Pisa (3) 15 (1961), 179–246.
[BK] C. B¨ohm, M. Kerr, Low dimensional homogeneous Einstein manifolds, Transactions of the A.M.S.
358 (2006), no. 4, 1455–1468.
[BWi] C. B¨ohm, B. Wilking, Manifolds with positive curvature operators are space forms, International
Congress of Mathematicians. Vol. II, 683–690, Eur. Math. Soc., Zrich, 2006.
[BFSTW] N. Brown, R. Finck, M. Spencer, K. Tapp, Z. Wu, Invariant metrics with nonnegative curvature
on compact Lie groups, Canad. Math. Bull. 50 (2007), no. 1, 24–34.
[Ch] J. Cheeger, Some examples of manifolds of nonnegative curvature, J. Diff. Geom. 8 (1973), 623–628.
[DK] W. Dickinson, M. Kerr, The geometry of compact homogeneous spaces with two isotropy summands,
preprint 2007 (available at palmer.wellesley.edu/˜mkerr/).
[GZ1] K. Grove, W. Ziller, Cohomogeneity one manifolds with positive Ricci curvature, Inv. Math. 149
(2002), 619–646.
[GZ2] K. Grove, W. Ziller, Lifting group actions and nonnegative curvature, preprint 2007.
[HT] J. Huizenga, K. Tapp, Invariant metrics with nonnegative curvature on SO(4) and other Lie groups,
arXiv:math.DG/0702241v1.
[K1] M. Kerr, Some New Homogeneous Einstein Metrics on Symmetric Spaces, Transactions of the A.M.S.
348 (1996), no. 1, 153–171.
[K2] M. Kerr, New Examples of Homogeneous Einstein Metrics, Michigan Mathematical Journal, 45
(1998), 115–134.
[M]
S. Murakami, Exceptional Simple Lie Groups and Related Topics in Recent Differential Geometry,
Diff. Geom. and Topol. Proceedings, (Tianjin, 1986–87), vol. 1369, Springer, 1989.
[O1] A. L. Oniˇsˇcik, Inclusion Relations Among Transitive Compact Transformation Groups, Trans. Am.
Math. Soc., ser. 2, 50, (1966), 5–58.
[O2] A. L. Oniˇsˇcik, Transitive Compact Transformation Groups, Trans. Am. Math. Soc., ser. 2, 55, (1966),
153–194.
[O3] A. L. Oniˇsˇcik, Lie Groups Transitive on Grassmann and Stiefel Manifolds, Math. USSR, Sb., 12,
(1970), 405–427.
[OW] Y.-L. Ou, F. Wilhelm, Horizontally homothetic submersions and nonnegative curvature, Indiana Univ.
Math. J. 56 (2007), no. 1, 243–261.
[T1] K. Tapp, Obstruction to positive curvature on homogeneous bundles, Geom. Dedicata 119 (2006),
105–112.
[T2] K. Tapp, Flats in Riemannian submersions from Lie groups, arXiv:math.DG/0703389v1.
[T3] K. Tapp, Homogeneous metrics with nonnegative curvature, preprint 2007.
1
[Wa]
N. Wallach, Compact homogeneous Riemannian manifolds with strictly positive curvature, Ann. of
Math. (2) 96 (1972), 277–295.
[W] F. Wilhelm, An exotic sphere with positive curvature almost everywhere, J. Geom. Anal. 11 (2001),
no. 3, 519–560.
[Wi1] B. Wilking, Positively curved manifolds with symmetry, Ann. of Math. (2) 163 (2006), no. 2, 607–668.
[Wi2] B. Wilking, Nonnegatively and positively curved manifolds, Metric and Comparison Geometry, Surv.
Diff. Geom. v. 11, ed. K. Grove and J. Cheeger, International Press, to appear (available at
arXiv:math.DG/07073091).
[VZ] L. Verdiani, W. Ziller, Positively curved homogeneous metrics on spheres,
arXiv:math.DG/07073056.
[Z1] W. Ziller, Examples of Riemannian manifolds with non-negative sectional curvature, Metric and Comparison Geometry, Surv. Diff. Geom. v. 11, ed. K. Grove and J. Cheeger, International Press, to appear
(available at arXiv:math.DG/0701389).
[Z2] W. Ziller, On the geometry of cohomogeneity one manifolds with positive curvature, Proceedings of
Riemannian Topology: Geometric Structures on Manifolds, Progress in Mathematics, Birkhauser, to
appear (available at arXiv:math.DG/07073345).
MEGAN M. KERR
Biographical Sketch
Department of Mathematics
Wellesley College
Wellesley, MA 02481
email: mkerr@wellesley.edu
phone: (781) 283-3144
fax: (781) 283-3642
(a.) Professional Preparation
Wellesley College: B.A. (1989) in Mathematics.
The University of Pennsylvania: Ph.D. (1995) in Mathematics.
Dartmouth College: Postdoctoral Instructorship (95–97) in Mathematics.
(b.) Appointments
2003–pres: Associate Professor, Wellesley College.
1998–2003: Assistant Professor, Wellesley College.
2001–2002: Radcliffe Fellow, Radcliffe Institute for Advanced Study (for sabbatical).
2001–2002: Visiting Scholar, Brown University (for sabbatical).
Spring 1998: Visiting Assistant Professor, University of Arizona.
Fall 1997: Assistant Professor, Wellesley College.
1995–1997: John Wesley Young Research Instructor, Dartmouth College.
1991–1995: Summer Instructor, The University of Pennsylvania.
1992–1994: T.A.-Training Instructor, The University of Pennsylvania.
1989–1994: Graduate Teaching Assistant, The University of Pennsylvania.
(c.) Publications
(i) Five publications most closely related to the project.
1. The geometry of compact homogeneous spaces with two isotropy summands (joint with
Will Dickinson), submitted September 2007.
2. Low-dimensional homogeneous Einstein manifolds (joint with Christoph B¨ohm),
Transactions of the AMS, 358 (2006), no. 4, 1455–1468.
3. New Examples of Homogeneous Einstein Metrics, Michigan Mathematical Journal,
45 (1998), 115–134.
4. Homogeneous Einstein–Weyl Structures on Symmetric Spaces, Annals of Global Analysis and Geometry, 15 (1997), no. 5, 437–445.
5. Some New Homogeneous Einstein Metrics on Symmetric Spaces, Transactions of the
AMS, 348 (1996), no. 1, 153–171.
1
(ii) Other significant publications.
1. New Homogeneous Einstein Metrics of Negative Ricci Curvature (joint with Carolyn
Gordon), Annals of Global Analysis and Geometry, 19 (2001), no. 1, 75–101.
2. A Deformation of Quaternionic Hyperbolic Space, Proceedings of the AMS, 134
(2006), no. 2, 559–569.
3. The geometry of filiform nilpotent Lie groups (joint with Tracy Payne), preprint 2007.
(d.) Synergistic Activities – Examples
1. I am an active member of the Association for Women in Mathematics. Currently, I am
a member of the Organizing Committee and Postdoctoral Speaker Selection Committee
for AWM Workshop at the January 2008 Joint AMS-MAA Meetings. At the AWM
workshop, I will serve on an advice panel “Establishing a Career in Mathematics.”
2. I was a member of the AWM’s Alice T. Schafer Prize Selection Committee of the
AWM, 2003 - 05, Chair 2005 - 06. The Alice T. Schafer Prize is awarded annually to the
best undergraduate woman in mathematics.
3. I co-organized of a Workshop on “Geometry in Materials Physics: making the connection,” at the Aspen Center for Physics, June 2004. This workshop succeeded in bringing
together physicists and mathematicians (pure and applied) to share expertise.
4. I was a Project NExT Fellow in 1997 - 98. I served as a panelist at the Project NExT
Workshop at MAA Mathfest, Brown University, August 2004: “The faculty member as
teacher and scholar.”
5. In 2001, I served as mentor and presenter at Pathways, Boston University. For Bostonarea high school girls, Pathways provided an opportunity to learn about career options
in science, mathematics and engineering.
6. As a Fellow at the Radcliffe Institute for Advanced Study in 2001 - 02, I gave a public
lecture: Symmetries: Spaces of Constant Curvature.
(e.) Collaborators and other Affiliations
(i) Collaborators during the last 48 months: Christoph B¨ohm (Westf¨alische Wilhelms –
Universit¨at M¨
unster), Will Dickinson (Grand Valley State University), Carolyn Gordon
(Dartmouth College), Tracy Payne (Idaho State University), Alan Shuchat (Wellesley
College), Ann Trenk (Wellesley College).
(ii) Graduate Advisors and postdoctoral sponsors: Wolfgang Ziller (University of Pennsylvania), Carolyn S. Gordon (Dartmouth College).
SUMMARY
PROPOSAL BUDGET
YEAR
1
FOR NSF USE ONLY
PROPOSAL NO.
DURATION (months)
Proposed Granted
AWARD NO.
ORGANIZATION
Wellesley College
PRINCIPAL INVESTIGATOR / PROJECT DIRECTOR
Megan M Kerr
A. SENIOR PERSONNEL: PI/PD, Co-PI’s, Faculty and Other Senior Associates
(List each separately with title, A.7. show number in brackets)
NSF Funded
Person-months
CAL
ACAD
1. Megan M Kerr - PI
0.00 0.00
2.
3.
4.
5.
6. ( 0 ) OTHERS (LIST INDIVIDUALLY ON BUDGET JUSTIFICATION PAGE)
0.00 0.00
7. ( 1 ) TOTAL SENIOR PERSONNEL (1 - 6)
0.00 0.00
B. OTHER PERSONNEL (SHOW NUMBERS IN BRACKETS)
1. ( 0 ) POST DOCTORAL SCHOLARS
0.00 0.00
2. ( 0 ) OTHER PROFESSIONALS (TECHNICIAN, PROGRAMMER, ETC.)
0.00 0.00
3. ( 0 ) GRADUATE STUDENTS
4. ( 0 ) UNDERGRADUATE STUDENTS
5. ( 0 ) SECRETARIAL - CLERICAL (IF CHARGED DIRECTLY)
6. ( 0 ) OTHER
TOTAL SALARIES AND WAGES (A + B)
C. FRINGE BENEFITS (IF CHARGED AS DIRECT COSTS)
TOTAL SALARIES, WAGES AND FRINGE BENEFITS (A + B + C)
D. EQUIPMENT (LIST ITEM AND DOLLAR AMOUNT FOR EACH ITEM EXCEEDING $5,000.)
TOTAL EQUIPMENT
E. TRAVEL
1. DOMESTIC (INCL. CANADA, MEXICO AND U.S. POSSESSIONS)
2. FOREIGN
F. PARTICIPANT SUPPORT COSTS
0
1. STIPENDS
$
0
2. TRAVEL
0
3. SUBSISTENCE
0
4. OTHER
TOTAL NUMBER OF PARTICIPANTS
(
0)
G. OTHER DIRECT COSTS
1. MATERIALS AND SUPPLIES
2. PUBLICATION COSTS/DOCUMENTATION/DISSEMINATION
3. CONSULTANT SERVICES
4. COMPUTER SERVICES
5. SUBAWARDS
6. OTHER
TOTAL OTHER DIRECT COSTS
H. TOTAL DIRECT COSTS (A THROUGH G)
I. INDIRECT COSTS (F&A)(SPECIFY RATE AND BASE)
SUMR
Funds
Requested By
proposer
Funds
granted by NSF
(if different)
2.00 $
21,411 $
0.00
2.00
0
21,411
0.00
0.00
0
0
0
0
0
0
21,411
7,044
28,455
0
5,000
0
0
TOTAL PARTICIPANT COSTS
0
0
0
0
0
0
0
33,455
77.0% of salaries and wages (Rate: 77.0000, Base: 21411)
TOTAL INDIRECT COSTS (F&A)
J. TOTAL DIRECT AND INDIRECT COSTS (H + I)
K. RESIDUAL FUNDS
L. AMOUNT OF THIS REQUEST (J) OR (J MINUS K)
M. COST SHARING PROPOSED LEVEL $
Not Shown
PI/PD NAME
Megan M Kerr
ORG. REP. NAME*
16,486
49,941
0
49,941 $
$
AGREED LEVEL IF DIFFERENT $
FOR NSF USE ONLY
INDIRECT COST RATE VERIFICATION
Date Checked
Date Of Rate Sheet
fm1030rs-07
Initials - ORG
Elizabeth Lieberman
1 *ELECTRONIC SIGNATURES REQUIRED FOR REVISED BUDGET
SUMMARY
PROPOSAL BUDGET
YEAR
2
FOR NSF USE ONLY
PROPOSAL NO.
DURATION (months)
Proposed Granted
AWARD NO.
ORGANIZATION
Wellesley College
PRINCIPAL INVESTIGATOR / PROJECT DIRECTOR
Megan M Kerr
A. SENIOR PERSONNEL: PI/PD, Co-PI’s, Faculty and Other Senior Associates
(List each separately with title, A.7. show number in brackets)
NSF Funded
Person-months
CAL
ACAD
1. Megan M Kerr - PI
0.00 0.00
2.
3.
4.
5.
6. ( 0 ) OTHERS (LIST INDIVIDUALLY ON BUDGET JUSTIFICATION PAGE)
0.00 0.00
7. ( 1 ) TOTAL SENIOR PERSONNEL (1 - 6)
0.00 0.00
B. OTHER PERSONNEL (SHOW NUMBERS IN BRACKETS)
1. ( 0 ) POST DOCTORAL SCHOLARS
0.00 0.00
2. ( 0 ) OTHER PROFESSIONALS (TECHNICIAN, PROGRAMMER, ETC.)
0.00 0.00
3. ( 0 ) GRADUATE STUDENTS
4. ( 0 ) UNDERGRADUATE STUDENTS
5. ( 0 ) SECRETARIAL - CLERICAL (IF CHARGED DIRECTLY)
6. ( 0 ) OTHER
TOTAL SALARIES AND WAGES (A + B)
C. FRINGE BENEFITS (IF CHARGED AS DIRECT COSTS)
TOTAL SALARIES, WAGES AND FRINGE BENEFITS (A + B + C)
D. EQUIPMENT (LIST ITEM AND DOLLAR AMOUNT FOR EACH ITEM EXCEEDING $5,000.)
TOTAL EQUIPMENT
E. TRAVEL
1. DOMESTIC (INCL. CANADA, MEXICO AND U.S. POSSESSIONS)
2. FOREIGN
F. PARTICIPANT SUPPORT COSTS
0
1. STIPENDS
$
0
2. TRAVEL
0
3. SUBSISTENCE
0
4. OTHER
TOTAL NUMBER OF PARTICIPANTS
(
0)
G. OTHER DIRECT COSTS
1. MATERIALS AND SUPPLIES
2. PUBLICATION COSTS/DOCUMENTATION/DISSEMINATION
3. CONSULTANT SERVICES
4. COMPUTER SERVICES
5. SUBAWARDS
6. OTHER
TOTAL OTHER DIRECT COSTS
H. TOTAL DIRECT COSTS (A THROUGH G)
I. INDIRECT COSTS (F&A)(SPECIFY RATE AND BASE)
SUMR
Funds
Requested By
proposer
Funds
granted by NSF
(if different)
2.00 $
22,482 $
0.00
2.00
0
22,482
0.00
0.00
0
0
0
0
0
0
22,482
7,397
29,879
0
3,000
0
0
TOTAL PARTICIPANT COSTS
0
0
0
0
0
0
0
32,879
77.0% of salaries and wages (Rate: 77.0000, Base: 22482)
TOTAL INDIRECT COSTS (F&A)
J. TOTAL DIRECT AND INDIRECT COSTS (H + I)
K. RESIDUAL FUNDS
L. AMOUNT OF THIS REQUEST (J) OR (J MINUS K)
M. COST SHARING PROPOSED LEVEL $
Not Shown
PI/PD NAME
Megan M Kerr
ORG. REP. NAME*
17,311
50,190
0
50,190 $
$
AGREED LEVEL IF DIFFERENT $
FOR NSF USE ONLY
INDIRECT COST RATE VERIFICATION
Date Checked
Date Of Rate Sheet
fm1030rs-07
Initials - ORG
Elizabeth Lieberman
2 *ELECTRONIC SIGNATURES REQUIRED FOR REVISED BUDGET
SUMMARY
PROPOSAL BUDGET
YEAR
3
FOR NSF USE ONLY
PROPOSAL NO.
DURATION (months)
Proposed Granted
AWARD NO.
ORGANIZATION
Wellesley College
PRINCIPAL INVESTIGATOR / PROJECT DIRECTOR
Megan M Kerr
A. SENIOR PERSONNEL: PI/PD, Co-PI’s, Faculty and Other Senior Associates
(List each separately with title, A.7. show number in brackets)
NSF Funded
Person-months
CAL
ACAD
1. Megan M Kerr - PI
0.00 0.00
2.
3.
4.
5.
6. ( 0 ) OTHERS (LIST INDIVIDUALLY ON BUDGET JUSTIFICATION PAGE)
0.00 0.00
7. ( 1 ) TOTAL SENIOR PERSONNEL (1 - 6)
0.00 0.00
B. OTHER PERSONNEL (SHOW NUMBERS IN BRACKETS)
1. ( 0 ) POST DOCTORAL SCHOLARS
0.00 0.00
2. ( 0 ) OTHER PROFESSIONALS (TECHNICIAN, PROGRAMMER, ETC.)
0.00 0.00
3. ( 0 ) GRADUATE STUDENTS
4. ( 0 ) UNDERGRADUATE STUDENTS
5. ( 0 ) SECRETARIAL - CLERICAL (IF CHARGED DIRECTLY)
6. ( 0 ) OTHER
TOTAL SALARIES AND WAGES (A + B)
C. FRINGE BENEFITS (IF CHARGED AS DIRECT COSTS)
TOTAL SALARIES, WAGES AND FRINGE BENEFITS (A + B + C)
D. EQUIPMENT (LIST ITEM AND DOLLAR AMOUNT FOR EACH ITEM EXCEEDING $5,000.)
TOTAL EQUIPMENT
E. TRAVEL
1. DOMESTIC (INCL. CANADA, MEXICO AND U.S. POSSESSIONS)
2. FOREIGN
F. PARTICIPANT SUPPORT COSTS
0
1. STIPENDS
$
0
2. TRAVEL
0
3. SUBSISTENCE
0
4. OTHER
TOTAL NUMBER OF PARTICIPANTS
(
0)
G. OTHER DIRECT COSTS
1. MATERIALS AND SUPPLIES
2. PUBLICATION COSTS/DOCUMENTATION/DISSEMINATION
3. CONSULTANT SERVICES
4. COMPUTER SERVICES
5. SUBAWARDS
6. OTHER
TOTAL OTHER DIRECT COSTS
H. TOTAL DIRECT COSTS (A THROUGH G)
I. INDIRECT COSTS (F&A)(SPECIFY RATE AND BASE)
SUMR
Funds
Requested By
proposer
Funds
granted by NSF
(if different)
2.00 $
23,606 $
0.00
2.00
0
23,606
0.00
0.00
0
0
0
0
0
0
23,606
7,766
31,372
0
3,000
0
0
TOTAL PARTICIPANT COSTS
0
0
0
0
0
0
0
34,372
77.0% of salaries and wages (Rate: 77.0000, Base: 23606)
TOTAL INDIRECT COSTS (F&A)
J. TOTAL DIRECT AND INDIRECT COSTS (H + I)
K. RESIDUAL FUNDS
L. AMOUNT OF THIS REQUEST (J) OR (J MINUS K)
M. COST SHARING PROPOSED LEVEL $
Not Shown
PI/PD NAME
Megan M Kerr
ORG. REP. NAME*
18,177
52,549
0
52,549 $
$
AGREED LEVEL IF DIFFERENT $
FOR NSF USE ONLY
INDIRECT COST RATE VERIFICATION
Date Checked
Date Of Rate Sheet
fm1030rs-07
Initials - ORG
Elizabeth Lieberman
3 *ELECTRONIC SIGNATURES REQUIRED FOR REVISED BUDGET
SUMMARY
PROPOSAL BUDGET
Cumulative
FOR NSF USE ONLY
PROPOSAL NO.
DURATION (months)
Proposed Granted
AWARD NO.
ORGANIZATION
Wellesley College
PRINCIPAL INVESTIGATOR / PROJECT DIRECTOR
Megan M Kerr
A. SENIOR PERSONNEL: PI/PD, Co-PI’s, Faculty and Other Senior Associates
(List each separately with title, A.7. show number in brackets)
NSF Funded
Person-months
CAL
ACAD
1. Megan M Kerr - PI
0.00 0.00
2.
3.
4.
5.
6. (
) OTHERS (LIST INDIVIDUALLY ON BUDGET JUSTIFICATION PAGE)
0.00 0.00
7. ( 1 ) TOTAL SENIOR PERSONNEL (1 - 6)
0.00 0.00
B. OTHER PERSONNEL (SHOW NUMBERS IN BRACKETS)
1. ( 0 ) POST DOCTORAL SCHOLARS
0.00 0.00
2. ( 0 ) OTHER PROFESSIONALS (TECHNICIAN, PROGRAMMER, ETC.)
0.00 0.00
3. ( 0 ) GRADUATE STUDENTS
4. ( 0 ) UNDERGRADUATE STUDENTS
5. ( 0 ) SECRETARIAL - CLERICAL (IF CHARGED DIRECTLY)
6. ( 0 ) OTHER
TOTAL SALARIES AND WAGES (A + B)
C. FRINGE BENEFITS (IF CHARGED AS DIRECT COSTS)
TOTAL SALARIES, WAGES AND FRINGE BENEFITS (A + B + C)
D. EQUIPMENT (LIST ITEM AND DOLLAR AMOUNT FOR EACH ITEM EXCEEDING $5,000.)
TOTAL EQUIPMENT
E. TRAVEL
1. DOMESTIC (INCL. CANADA, MEXICO AND U.S. POSSESSIONS)
2. FOREIGN
F. PARTICIPANT SUPPORT COSTS
0
1. STIPENDS
$
0
2. TRAVEL
0
3. SUBSISTENCE
0
4. OTHER
TOTAL NUMBER OF PARTICIPANTS
(
0)
G. OTHER DIRECT COSTS
1. MATERIALS AND SUPPLIES
2. PUBLICATION COSTS/DOCUMENTATION/DISSEMINATION
3. CONSULTANT SERVICES
4. COMPUTER SERVICES
5. SUBAWARDS
6. OTHER
TOTAL OTHER DIRECT COSTS
H. TOTAL DIRECT COSTS (A THROUGH G)
I. INDIRECT COSTS (F&A)(SPECIFY RATE AND BASE)
TOTAL INDIRECT COSTS (F&A)
J. TOTAL DIRECT AND INDIRECT COSTS (H + I)
K. RESIDUAL FUNDS
L. AMOUNT OF THIS REQUEST (J) OR (J MINUS K)
M. COST SHARING PROPOSED LEVEL $
Not Shown
PI/PD NAME
Megan M Kerr
ORG. REP. NAME*
SUMR
Funds
Requested By
proposer
Funds
granted by NSF
(if different)
6.00 $
67,499 $
0.00
6.00
0
67,499
0.00
0.00
0
0
0
0
0
0
67,499
22,207
89,706
0
11,000
0
0
TOTAL PARTICIPANT COSTS
0
0
0
0
0
0
0
100,706
51,974
152,680
0
152,680 $
$
AGREED LEVEL IF DIFFERENT $
FOR NSF USE ONLY
INDIRECT COST RATE VERIFICATION
Date Checked
Date Of Rate Sheet
fm1030rs-07
Initials - ORG
Elizabeth Lieberman
C *ELECTRONIC SIGNATURES REQUIRED FOR REVISED BUDGET
Budget Justification Page
This proposal requests two months summer salary for each of the next thee years. My academic
salary will be paid by Wellesley College for all three years, including in the 2008-09 academic
year, when I am scheduled to be on sabbatical.
In addition, this proposal requests travel funds: $5000 in 2008-09, when I will not be teaching,
and $3000 in each of the two following years. This is travel to attend conferences, such as
the annual East Coast Geometry Festival, and also to work on collaborations which may develop.
Current and Pending Support
(See GPG Section II.C.2.h for guidance on information to include on this form.)
The following information should be provided for each investigator and other senior personnel. Failure to provide this information may delay consideration of this proposal.
Other agencies (including NSF) to which this proposal has been/will be submitted.
Investigator: Megan Kerr
Support:
Current
Pending
Submission Planned in Near Future
*Transfer of Support
Project/Proposal Title: RUI: Manifolds of Positive and Non-Negative Sectional
Curvature
National Science Foundation
Source of Support:
Total Award Amount: $
152,680 Total Award Period Covered: 07/01/08 - 06/30/11
Location of Project:
Wellesley College
Person-Months Per Year Committed to the Project. Cal:0.00
Acad: 0.00 Sumr: 2.00
Support:
Current
Pending
Submission Planned in Near Future
*Transfer of Support
Project/Proposal Title: Manifolds of Positive and Non-negative Sectional
Curvature
AAUW 2008 American Postdoctoral Fellowship
Source of Support:
Total Award Amount: $
30,000 Total Award Period Covered: 07/01/08 - 06/30/09
Location of Project:
Wellesley College
Person-Months Per Year Committed to the Project. Cal:0.00
Acad: 9.00 Sumr: 0.00
Support:
Current
Pending
Submission Planned in Near Future
*Transfer of Support
Project/Proposal Title:
Source of Support:
Total Award Amount: $
Total Award Period Covered:
Location of Project:
Person-Months Per Year Committed to the Project. Cal:
Acad:
Support:
Current
Pending
Submission Planned in Near Future
Sumr:
*Transfer of Support
Project/Proposal Title:
Source of Support:
Total Award Amount: $
Total Award Period Covered:
Location of Project:
Person-Months Per Year Committed to the Project. Cal:
Acad:
Support:
Current
Pending
Submission Planned in Near Future
Sumr:
*Transfer of Support
Project/Proposal Title:
Source of Support:
Total Award Amount: $
Total Award Period Covered:
Location of Project:
Person-Months Per Year Committed to the Project. Cal:
Acad:
Summ:
*If this project has previously been funded by another agency, please list and furnish information for immediately preceding funding period.
Page G-1
USE ADDITIONAL SHEETS AS NECESSARY
FACILITIES, EQUIPMENT & OTHER RESOURCES
FACILITIES: Identify the facilities to be used at each performance site listed and, as appropriate, indicate their capacities, pertinent
capabilities, relative proximity, and extent of availability to the project. Use "Other" to describe the facilities at any other performance
sites listed and at sites for field studies. USE additional pages as necessary.
Laboratory:
Clinical:
Animal:
Computer:
Office:
Other:
MAJOR EQUIPMENT: List the most important items available for this project and, as appropriate identifying the location and pertinent
capabilities of each.
OTHER RESOURCES: Provide any information describing the other resources available for the project. Identify support services
such as consultant, secretarial, machine shop, and electronics shop, and the extent to which they will be available for the project.
Include an explanation of any consortium/contractual arrangements with other organizations.
Research will be carried out at Wellesley College. Office, computing
resources, and secretarial support will be provided by Wellesley College.
I will make use of the Wellesley College Science Library and the
Engineering and Science Libraries at the Massachusetts Institute of
Technology. As a faculty member at Wellesley College, I have access to
library resources at both institutions through the MIT/Wellesley exchange
program.
FACILITIES, EQUIPMENT & OTHER RESOURCES
Continuation Page:
OTHER RESOURCES (continued):
NSF FORM 1363 (10/99)
RUI: IMPACT STATEMENT
MEGAN M. KERR
DEPARTMENT OF MATHEMATICS
WELLESLEY COLLEGE
Wellesley College has a strong tradition of educating women scientists. Women and scientists hold key leadership positions at Wellesley. The new president of Wellesley College,
Kimberly Bottomly, is a biologist whose last position was the Deputy Provost at Yale University. Two of the three academic deans are female scientists: a chemist and a biologist. More
than half the faculty at Wellesley College are women, providing excellent role models for our
students. The most recent National Science Foundation data, which ranks baccalaureate
institutions by the total number of women alumnae who earned science and engineering doctorates in the years 2000-2004, show that 201 Wellesley alumnae earned science doctorates.
This is approximately 7% of Wellesley’s alumnae in a five year period. When considered
as a percentage of the total number of women alumnae, this is significantly better than the
top five schools on the list. Even considering the total numbers, Wellesley College was the
highest ranked liberal arts college. 1 I am an alumna of Wellesley College and thus represent
a concrete example of Wellesley’s success in preparing women for a career in mathematics.
Wellesley College is a highly competitive women’s college with a strong tradition of liberal
arts education. Some of Wellesley College’s enduring strengths throughout its 130 year
history include a high-quality faculty and student body, a small enrollment allowing concern
for the individual student, a commitment to the education of women, an underlying belief
in service to society, and a high level of alumnae interest and support. Today, Wellesley is
one of the top ranked liberal arts colleges in the country (currently ranked 4th by the U.S.
News and World Report). Wellesley is home to 2300 undergraduate students, from all 50
states and more than 65 countries. Wellesley’s student body is diverse with 38% women
of color, 8% international students, and 2% students beyond the traditional undergraduate
age. Wellesley is one of the few schools to maintain need-blind admissions, resulting in a
student body that is also economically diverse.
The Mathematics Department consists of 13 faculty members in tenured or tenure-track
positions, 5 of whom are women. All mathematics classes are taught in small sections (maximum of 25 students) by regular faculty. Our department has no regular adjunct faculty.
The department typically graduates 15 – 25 majors and 10 minors each year. Graduates
go on to a variety of careers from medical school to finance with a significant number attending Ph.D. programs in mathematics and related fields (e.g., computer science, statistics,
1
NSF Division of Science Resources Statistics, Women, Minorities and Persons with Disabilities in Science
and Engineering, Table Survey of Earned Doctorates, 2000-2004, Table F-4. Wellesley ranked 27th in this
list.
1
2
M. M. KERR
economics). The cross-registration program with MIT provides an opportunity for Wellesley
College students to take graduate-level mathematics courses.
Like many departments, the Mathematics Department at Wellesley is experiencing retirements of senior colleagues. As Wellesley has shifted to a more research intensive institution
in the last 20 years, active research programs are now the norm in the Mathematics Department. In the last year the department has established a faculty seminar series of talks by
and for faculty members of the mathematics department to supplement the long-standing
colloquium series in which outside speakers give talks designed for undergraduates. Our
students are highly aware of this visible example of faculty engaged in research.
In my teaching as well as in my own research, I work to raise the visibility of mathematics
research, especially in geometry and topology. I created a new course in Knot Theory,
which, as a field, is both accessible, in its three-dimensional setting, and young enough so
that students see open questions that they can understand. In Spring 2008 I will be teaching
a senior level course in Matrix Groups: an Introduction to Lie groups. I love the beautiful
interplay of algebra and geometry and am excited to show students how these seemingly
unrelated subjects are intimately connected. I look forward to describing my own research
to my students, including the open problems I describe in this proposal and what makes
them interesting.
At the national level, I am an active member of the Association for Women in Mathematics.
My involvement has had a focus on the promotion of women just embarking on their careers
in mathematics, providing encouragement and mentoring at a critical point in their careers. I
served for three years on the annual Alice T. Shafer Prize for the best woman undergraduate
in mathematics (as Chair in my third year). I am currently a member of the Organizing
Committee, as well as the Postdoctoral Selection Committee, for the AWM Workshop to be
held in January 2008 at the Joint AMS-MAA Meetings.
Just as colleges and universities seek a balance between research, teaching and service
in granting tenure and promotion, the mathematical community values our colleagues who
excel in all of these areas. There are, unfortunately, still too few women in mathematics who
establish and maintain excellent research records. Receipt of this grant would give me the
best opportunity to provide another leader and to continue to develop the next generation
of students who may someday have similar professional success.
Certification of RUI Eligibility
By submission of this proposal, the institution hereby certifies that the originating and
managing institution is an institution that offers courses leading to a bachelor's or
master's degree, but has awarded an average of no more than 10 doctoral degrees per
year in NSF-supported disciplines over the 2-to-5-year period preceding proposal
submission.
Andrew B. Evans
Vice President for FinanceITreasurer
Date