On this webpage I try to describe how children effect publishing
in my field of mathematics (where publication rates are low, papers
are long, and referees often take 2 years), or at least my own publishing.
Publication dates are misleading when papers are refereed for over a year
and people have often said to me they never saw a gap in my publishing when
I had kids. In fact the gaps are there, but the effect of
random refereeing time has averaged out the appearance of my papers.
Here is a tale of how the research actually progressed since I graduated
through the births of three children, tenure and promotion. My
homepage is here.
The dates in parenthesis indicate the date the preprint was posted on the
arxiv.
Graduate School and First Postdoc (Fall 1994-Spring 1997):
In graduate school I worked for 2 years fulltime on research alone
teaching only one course. The resulting thesis was then broken up
during my first postdoc into two papers. A third, very short paper
was also written during that first postdoc. At these times I could
spend hours every week on reading relevant papers and hours on research.
Teaching was a distraction but only 1 course at a time. The biggest difficulty
was the job hunt which had to be repeated two years in a row because
my first postdoc was a one year postdoc. I snail mailed 63 applications
for my first job hunt and 120 for my second job hunt. During the two months
dedicated to job hunts each of those years,
I did no research.
"Busemann Functions on Manifolds with
Lower Ricci Curvature
"The Rigidity and Almost Rigidity
of Manifolds with Lower Bounds on
Ricci Curvature and Minimal Volume Growth",
by Christina Sormani
Communications in Analysis and Geometry.
Vol 8, No. 1, 159-212, January 2000.
Download
a copy or view the
abstract. (May 1996, March 1999)
"Harmonic Functions on Manifolds with
Nonnegative Ricci Curvature
Second Postdoc and Still No Children (Fall 1997-Fall 1998):
At this point I had no job hunts and enough knowledge to focus
purely on research. I tackled the Milnor Conjecture, which is still
open and a very serious question. I would spend days straight
thinking of nothing but mathematics and I have two very strong papers
as a result. The first was immediately recognized as important,
the second was difficult to publish until it was later applied.
At the time I was desperately focussed on the idea of getting a
tenure track job back in NYC and so I left this postdoc early
when I landed such a job.
"Nonnegative Ricci Curvature, Small Linear
Diameter Growth, and
"On Loops Representing Elements of the Fundamental
Group of a
Complete Manifold with Nonnegative Ricci Curvature"
by Christina Sormani.
Indiana Journal of Mathematics, 50 (2001) no. 4, 1867-1883.
reprint
Download a copy or view the abstract (April 1999)
During a Healthy Pregnancy and Infancy of First Child
(Spring 1999-Fall 2000):
I was contacted by Zhongmin Shen who had ideas of how to apply the loops paper
and we quickly come up with a very nice new result. This was
completed start to finish during my first pregnancy which was healthy
and uneventful. I also work with Guofang Wei who was
a mother and a roll model for me and willing to work by email
in the middle of the night. During the infancy and during the first summer
we wrote our first paper together. My inlaws helped watch the baby
and I started a tenure track job at this time with only a six
month Fall semester unpaid maternity leave.
"The Codimension One Homology of a Complete
Manifold with
"Hausdorff Convergence and Universal Covers"
In Fall 2000 I focused on the tenure track job, and a succesful NSF proposal.
I planned to have a second and final child quickly and take a long
maternity leave for this child. I also expected to do research during the
pregnancy again, thinking I would have plenty of time to recover before
applying for a next NSF grant and before going up for tenure.
During an Unhealthy Pregnancy (Spring 2001):
After being hospitalized and almost losing the pregnancy,
I did nothing at all while on bedrest except read. So I read
Peebles "Principles of Modern Cosmology" which made me question
various presumptions in the Friedmann model.
Infancy of Second Child (Spring 2001 - Fall 2001):
I spent time with my two daughters and did no mathematics
planning to restart research when they could both start daycare.
I organized a seminar at the CUNY Graduate Center
and did significant other service at Lehman College to
ensure that there is no resentment for taking a long leave
while tenure track. Organizing the seminar was a great benefit,
keeping my mind in touch with the latest mathematics and
keeping me in touch with mathematicians.
Recovering a Research Program (Spring 2002-Spring 2003):
During an extended unpaid maternity leave in Spring 2002
I recovered my research program with children in fulltime daycare
completing a second paper with Guofang Wei by midnight emails
and starting the investigation of the Friedmann Cosmology
to address questions from Peebles. The cosmology
paper became an obsession as it drew up more and more
need for original ideas. I completed it
while working tenure track by February 2003 taking great advantage of the
January break to finalize details.
"Universal Covers for Hausdorff Limits of Noncompact Spaces"
by Christina Sormani and
Guofang Wei
Transactions of the American Mathematical Society 356 (2004),
no. 3 pp. 1233-1270.
reprint.
Arxiv preprint (July 2002)
"Friedmann Cosmology and Almost Isotropy"
During a Healthy Pregnancy (Spring 2003-Summer 2003):
I was shocked to become pregnant for the third time in five years
that winter. Luckily I was healthy this time and able to work as well
as during my first pregnancy. Wei and I discovered a deeper meaning
in our first two papers together. Suddenly we realised there was a
new kind of spectrum that could
be defined and in a wonderous flurry of email exchanged ideas.
We created an important paper which was immediately published by JDG:
"The Covering Spectrum of a Compact Length Space"
During the Third Child's Infancy (Fall 2003-Spr 2004):
I spent time with all three children for one year maternity leave
doing no research. I went up for tenure during the leave
taking advantage of the
brand new JDG paper and the finally verified GAFA paper both
of which are top journals in my field. I applied for an NSF grant
confident that I will get it and focus on a new concept of convergence.
I continued my extensive departmental service through this year
as well as organizing the seminar.
NSF Rejection (Spring 2004-Summer 2005):
Traumatized by a very harsh NSF rejection despite the appearance of
three articles in 2004 including the lengthy GAFA article, I turned away
from research. I spent more time with my family and focused on
things like explaining Perelman's work to the media, to
popular nonfiction writer George Szpiro and to undergraduates.
I felt that if my research was no longer good enough for
NSF funding, why should I take time away from my family to pursue it?
One potential coauthor I tried working with refused to read emailed proofs
and caused further depressions by insulting my ideas calling them naive. This
destroyed the fun of doing mathematics and delayed work on the convergence
project I had been eagerly to work on. I thought about the length spectrum
on and off but more as fun without a serious intention to write
it up. Most times I tried to do research I just became
depressed. I had been used to being the best of the best and now I
decided I wasn't a worthwhile mathematician anymore. I was tenured
but felt I was already done with my research career.
Invitations to Speak Revive Research (Fall 2005-Spring 2006):
Suddenly invited to speak at Princeton and the Midwest Geometry
Conference about the GAFA and JDG papers respectively
, I regained a sense of purpose and decided to focus strongly
on research again. First I wrote up the various thoughts I had
over the prior two years as a length spectrum paper and then
I wrote a solicitted survey article with Shen. I also began to
work with a doctoral student. Wei and I started to work again
focussing on a new question we call the spherical cap problem
although we did not have as much time as we would like. I also worked
on a solenoid project which turned out to need more computation
than even mathematica can handle.
"Convergence and the Length Spectrum"
"The Topology of Open Manifolds of Nonnegative Ricci Curvature"
In Fall 2007 I became overwhelmed with work partly due to lingering
contacts with the media regarding Perelman's work and partly due to frustration
that I had no time for the cap and solenoid projects as well as all the
service and teaching. I have ideas for a project with Wenger as well.
Essential Unpaid Research Leave (Spring-Summer 2007):
Frustrated, I took an unpaid research leave keeping the three children
in daycare.
Although colleages who started tenure track when I did were already
up to taking paid research leaves, I did not yet qualify due to
my breaks in service. I stopped the calculation intensive
solenoid project but continue to work with Wei on various ideas
from the spherical cap to the covering spectrum. She had a leave
as well at this time so we make great progress on the covering
spectrum writing up a new paper on the topic. I also began and completed
a project with Ravi Shankar.
"The Cut-Off Covering Spectrum"
"Conjugate Points in Length Spaces"
My first doctoral student made great progress on his thesis
at this time
and I enjoy the role of a doctoral advisor very much.
Prioritizing (Fall 2007-Summer 2008):
On returning to a 2:2 teaching load, I set about planning how
to maintain a research program without having to take leaves every few
years. A certain amount of time went to family and moving to
a new home. About 45 hours a week (not including lunch) was
scheduled for teaching, service and research. Since I was tenured
I felt I could easily say no to certain service (like running
a math circle for no released time) if I did something similar
(like teaching college now courses as one of my two courses). I
also went for lucrative service: applying for an NSF MSP grant
with colleagues in math education which covered released time
from teaching.
I prioritized research as well
focusing exclussively on the project I felt would
most likely lead to a seriously important result. This was the
project with
Wenger and we wanted to complete it while he was at NYU.
I abandoned a project with another coauthor that was not going well
dividing up future work on the project to do separately.
Wei and I decided to pospone working on our
fifth paper. Meanwhile I had more and more
invitations to speak, even a summer school 4 lecture series in Switzerland.
My first student defended his doctoral dissertation.
Wenger and I did not finish the project as we had hoped but made
excellent progress proving all our planned theorems
and finalizing definitions.
Going up for Full Professor (Fall 2008 - Spring 2009):
My first doctoral student won an NSF postdoc in September.
Both the paper with Wei and the paper with Shankar were accepted
for publication
in October 2008. Then my colleages and I won the five million dollar
NSF MSP grant. Suddenly an application for full professor seemed
appropriate and the only concern was that the paper with Wenger
was not yet written (although we did have quite a bit texed up).
Wenger announced the results, so I was able to include a description
of the work and a preliminary preprint
in my Full Professor file. The file went out in December
to a selection of faculty.
Soon after I was invited to speak at the Geometry Festival, one
of the most important conferences in my field.
In January break Wenger finalized
a short paper in specialist style of a few key results of
ours for experts in his
field and posted it on the arxiv:
"Weak Convergence of Currents and Cancellation"
by Christina Sormani and Stefan Wenger
with an appendix by Raanan Schul and Stefan Wenger
Calc. Var. P.D.E., Vol. 38, No 1-2, May, 2010.
arxiv preprint (February 2009)
I was granted Full professorship
that Spring and gave many talks on the work with Wenger.
I feel more confident as a mathematician and ready to spend
more time on mathematics. Although I had released time from teaching
for the work I was doing for the NSF MSP grant, it was not sufficient.
Much time was spent on reporting and organizing, in addition to the expected
work designing courses and teaching them. I determined to take the summer
completely off from the program and finalize the work with Wenger.
Life as a Full Professor (Summer 2009-...)
In the summer of 2009 I worked fulltime on completing the longer
of the two papers with Wenger. I also planned out the first NSF
research proposal
I had written in years, now based on this work and its potential
applications. I was back to working late at night and very lucky
that my kids played well together and would often allow me to work many
hours while they occupied themselves. The oldest was now old enough to
make breakfast and walk her brother and sister to school, allowing me to
sleep late and stay up regularly until 2 am. This allowed me to increase my
workweek back up to 50-55 hours per week. While busy with the NSF MSP grant,
teaching and graduate students in the Fall, I did manage to complete
the second paper with Wenger in January 2010 as well as a survey article
I was solicitted to write for a volume in honor of my advisor:
"The Intrinsic Flat Distance between Riemannian Manifolds and Integral
Current Spaces"
by Christina Sormani and Stefan Wenger,
to appear in the Journal of Differential Geometry
arxiv preprint (February 2010)
"How Riemannian Manifolds Converge: a Survey"
by Christina Sormani
preprint (January 2010)
In Spring 2010 my second doctoral student made excellent progress
on his dissertation and my third student passed his oral qualifying exams.
The NSF MSP grant started taking more and more time away from research,
so I found another member of my department to take over my role and
disconnected myself from the program completely..
In August 2010 I was awarded an NSF Geometric Analysis Research Grant.
It will fund my doctoral students in the summers and CUNY will
award me released time from one course per year for being a successful
research faculty member.
My first paid research sabbatical is approved for Spring 2011 and
Spring 2012. I'm still young, have a number of partial results
ready to be written up and more open problems to start working on.
My kids are independant and involved in their own activities. I
expect this to be a very productive decade.
Luck and Support
I have been very lucky that
on the whole my kids have been healthy and have no disabilities or serious
difficulties with school. I missed one conference due to a brush with
H1N1 and scattered days due to other minor health issues or incidents
at school. All four grandparents have been an amazing help after school
and during the summer and when I am away, making the decision to live in
New York City probably one of the best choices I've made.
Of course, my husband is my biggest supporter. He enabled me to take all
those unpaid leaves (a difficult thing to do in a city with such a high
cost of living) and he has always supported my career in every way. I might
even consider him my most important source of research funding. Of course
he goes beyond that, always encouraging me to pursue my career with as much
intensity as he has pursued his.
Thoughts
In summary, I wrote this page because I felt my research record is misleading. Often people tell me having children was no delay at all. Publishing dates do not match the dates that research was completed. I also feel it is important to record that I did essentially have a breakdown and almost quit doing research largely because no one cared about my work. I want to emphasize how important it is to show interest in someone's research if you care about his or her career and how carefully one should write NSF rejections. It isn't that children make you incapable of doing research (although unhealthy pregnancies and all infancies are exhausting), its that one feels one must sacrifice the children for the research and if no one cares about the research it seems very selfish to continue to conduct it. This is even more true when one is in a department where some faculty do not do research after getting tenure.
Now that I am back doing research, I
occasionally feel
frustration that I don't have enough time to really focus on my work
the way I did before I had kids: the opportunities to spend days on
end on just one thought. But I'm learning to balance it all:
teaching, research, service and family, and trying to find joy in each
task as it is laid before me. I try to imitate the work patterns of the most
successful researchers who are also active members of my department.
It seems one must focus intensively on research during the summers
and yet also constantly keep in touch with ideas during the semester.
If an idea comes up on a weekend, then that weekend becomes a research
weekend. At the same tme I do make a point to spend random afternoons and days
with my kids to make up for the weekends lost to working or
catching up on sleep. I think they understand the importance of
hard work and the desire to strive for success.
by Christina Sormani, written in 2007-2010.