On this webpage I try to describe how children affect 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. This was written in 2007-2010.
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 Bounds and Minimal Volume Growth",
by Christina Sormani Journal of Differential Geometry 48, (1998) 557-585.
Email me for a copy or view the abstract. (May 1996, Nov 1997)
"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 and Linear Volume Growth"
by Christina Sormani Pacific Journal of Mathematics.Vol 192, No 1, 183-189, January 2000.
Download a copy or view the abstract. (March 1999)
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
Finite Generation of Fundamental Groups"
by Christina Sormani. Journal of Differential Geometry 54 (2000), no. 3, 547--559 reprint.pdf.
Download a copy or view the abstract (Sept 1998)
"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
Nonnegative Ricci Curvature"
by Zhongmin Shen and Christina Sormani. American Journal of Mathematics 123 (2001), no. 3, 515--524. reprint
Download a postscript copy or view the abstract. (Sep 1999, Nov 2000)
"Hausdorff Convergence and Universal Covers"
by Christina Sormani and Guofang Wei Transactions of the American Mathematical Society 353 (2001), no. 9, 3585--3602. reprint
Download a postscript copy , pdf copy , or view the abstract. (Aug 2000)
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 children 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"
by Christina Sormani GAFA, Geom. funct. anal. Vol. 14 (2004) 853-912. reprint ArXiV preprint (Feb 2003)
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"
by Christina Sormani and Guofang Wei Journal of Differential Geometry, Vol 67 (2004) 35-77. reprint.pdf.
Arxiv posting, (Nov 2003)
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"
by Christina Sormani, Advances in Mathematics, Volume 213, Issue 1, 1 August 2007, Pages 405-439. reprint.
preprint.pdf (Feb 2006)
"The Topology of Open Manifolds of Nonnegative Ricci Curvature"
by Zhongmin Shen and Christina Sormani Midwest Geometry Conference Proceedings 2006, JGPAM, January 2008.
A survey article, 31 pages, many diagrams and open problems preprintnov2006.pdf, (June 2006, Nov 2006)
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 had 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 colleagues 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"
by Christina Sormani and Guofang Wei, Transactions of the American Mathematical Society 362 (2010), 2339-2391.
preprint on arxiv (May 2007, Sept 2008)
"Conjugate Points in Length Spaces"
by Krishnan Shankar and Christina Sormani Advances in Mathematics 220 (2009), pp. 791-830.
preprint on the arxiv (Sept 2007, Nov 2007, Sept 2008),
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 the little ones 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 that my having children was no delay at all. However, 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.