Sunday, September 2, 2012

Uri Rothblum's intellectual legacies

The journal Linear Algebra and its Applications has published an article in memoriam of Uri Rothblum, who passed away in March of this year:   Uriel G. Rothblum (1947–2012) by Raphael Loewy.

The article has discussions of aspects of Uri's work by a number of his collaborators, one of whom is Hans Schneider, a longtime editor of LAA. I recently corresponded with Professor Schneider about the beginning of his long and productive collaboration with Uri, and (with his permission) here is some of that correspondence.

 Dear Professor Schneider: Eric Denardo shared with me the memoir of Uri Rothblum, and encouraged me to write a note to you about his very first interaction with you. My memory of it isn't all that clear.

It must have been in 1974 (the year that he and I graduated from Stanford) that you contacted him about his paper on nonnegative matrices. As I recall, your letter suggested that perhaps his results and some of yours should appear in collaboration. He wasn't sure that his English was up to the task of saying "no" in a diplomatic way, and so he asked me to help draft the letter, which explained that he had a special emotional attachment to that paper since it was a central part of his dissertation.

He valued enormously his subsequent collaboration with you, and never tired of telling me that the letter I had drafted for him might be the most productive piece I have written.

The world is certainly less complete without Uri in it.

All the best,

Al Roth

 From: Hans Schneider []
 Sent: Saturday, September 01, 2012 1:15 PM
 To: Roth, Alvin
 Cc: Eric Denardo
 Subject: Re: Uri's write-up in Linear Algebra and its Applications
 Dear AL,
 Thank you for your very interesting letter and  apologies for my slow reply. 

 But now to your remarks. You are right, I proposed that Uri and I combine our papers and he turned this  down. I did not know that you were involved until Eric told me this year.

 It was a good decision on his part and I need to thank you for your help to Uri.  The sequence of letters (mine, his) spectacularly achieved what I desired, viz. cooperation with a young mathematician who was interested in the same area as I. I think it is impossible for me to explain how mathematically isolated I felt at the time without sounding like a petulant child.

 BTW, I first saw Uri's paper #3 in early 1975. The correction is worth making for I spent calendar 1974 at  TU Munich and before I left my student Richman had essentially completed results for his Ph.D. which  were  waiting to be writtten up when I saw Uri's paper. That's the paper I offered to combine with Uri's. I recall that Uri said there was room for both papers; I wish I still had his letter. Richman-S finally appeared in LAMA in 1978.

 I have never again offered to make a joint paper of a submission to LAA, even when I felt I could improve it significantly. I got increasingly worried that this is crossing a line for an EIC.  (Full disclosure, there is another paper joint with me that was originally submitted by my co-authors, but it became joint at the suggestion of an editor when he saw my referee's report.)

 Finally , I am very glad to hear from you, AL, that Uri saw the events that brought us together so positively. To my recollection, we never discussed them in any meaningful way.

 best wishes


 ps The obit is now on line on the LAA site under 'articles in press'. 


Some quick recollections of my own, of an intellectual history sort.

Uri and I were office mates in grad school, and I often benefited from his advice. I recall one time in particular, when I needed to prove that a certain interval was compact, and he showed me a proof that allowed me to complete the theorem that formed the basis for my dissertation. I later realized that a corollary of his proof was that _every_ interval was compact, so unfortunately I had to use another proof (and I recall a tense week between weekly visits to my advisor, at the end of which I was able to say "there was a problem with the proof I outlined last week" instead of "...with the theorem...").

Uri and I didn't collaborate as grad students, but we eventually wrote four papers together:

Roth, A.E. and Rothblum, U. "Risk Aversion and Nash's Solution for Bargaining Games With Risky Outcomes," Econometrica, Vol. 50, 1982, 639‑647.

Roth, A.E., Rothblum, U.G., and Vande Vate, J.H. "Stable Matchings, Optimal Assignments, and Linear Programming," Mathematics of Operations Research, 18, 1993, 803-828. 

 Blum, Y., A.E. Roth, and U.G. Rothblum "Vacancy Chains and Equilibration in Senior-Level Labor Markets," Journal of Economic Theory, 76, 2, October 1997, 362-411.

Roth, A.E. and U.G. Rothblum "Truncation Strategies in Matching Markets--In Search of Advice for Participants," Econometrica, 67, January, 1999, 21-43.

The two two-author papers each began when, in the course of a long walk somewhere, I indicated that I was working on a problem that was too hard for me to solve.  The paper with John Vande Vate came about by combining two different such conversations. But the most unusual of the collaborations was initiated by Uri in connection with work he had started with his student Yossi Blum. I believe they figured out that a paper by Blum and Rothblum would look better if they had a third author named Roth.

Readers of this blog may already be familiar with his other papers on matching and market design:

H. Abeledo and U.G. Rothblum, “Stable matchings and linear inequalities,” Discrete Applied Mathematics 54 (1994), pp. 1-27.

H. Abeledo and U.G. Rothblum, “Courtship and linear programming,” Linear Algebra and Its Applications 216 (1995), pp. 111-124.

H. Abeledo and U.G. Rothblum, “Paths to marriage stability,” Discrete Applied Mathematics 63 (1995),  pp. 1-12

H. Abeledo, Y. Blum and U.G. Rothblum, “Canonical monotone decompositions of fractional stable matchings,” The International Journal of Game Theory 25 (1996), pp. 161-176.

Y. Blum and U.G. Rothblum, “ ‘Timing is everything’ and marital bliss,” Journal of Economic Theory 103 (2002), pp. 429-443.

N. Perach, J. Polak and U.G. Rothblum, “Stable matching model with an entrance criterion applied to the assignment of students to dormitories at the Technion,” The International Journal of Game Theory 36 (2008),
pp. 519-535.

N. Perach and U.G. Rothblum, “Incentive Compatibility for the Stable Matching Model with an Entrance Criterion,” accepted for publication in The International Journal of Game Theory, 17 pages.

Book review: U.G. Rothblum, Two Sided Matchings: A Study in Game-Theoretic Modeling and Analysis (by A.E. Roth and M.A. Oliviera Sotomayor), Games and Economic Behavior 4 (1992), pp.161-165

Here is Uri's listing on Google Scholar.
Here is his list of publications in chronological order.
Here is the obituary by Boaz Golany in INFORMS online.

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