New York Number Theory Seminar

The New York Number Theory Seminar is a research seminar devoted to the theory of numbers and related parts of mathematics and physics. In this seminar, mathematicians gather to discuss and explore different notions in Number Theory. The United States is one of the most invested countries in Number Theory as it holds numerous conferences with mathematicians participating from around the world and it is the country with the most Number Theory centres, the New York Number Theory Seminar being just one of them.[1] The New York Number Theory Seminar also organizes an annual Workshop on Combinatorial and Additive Number Theory (CANT) at the CUNY Graduate Center. The seminar began in 1981 with members working for the City College (CUNY), Columbia University, and Rutgers–Newark, and some still currently at Lehman College (CUNY) and the Polytechnic University of New York.

Proceedings
The Graduate Center, where the New York Number Theory seminars take place, is located in the former B. Altman and Company Building at 365 Fifth Avenue.

The New York Number Theory Seminar originally began when Number Theorists Harvey Cohn, David and Gregory Chudnovsky and Melvyn B. Nathanson met regularly, usually on Tuesday afternoons, during the academic year at the CUNY Graduate Center of the City University of New York, at 365 Fifth Avenue between 34th and 35th Streets. The location was convenient to all parts of the city and major transportation hubs as it is located in the New York City central business district. These members were the founders of the seminar and continued to host it for many years.

The Graduate Center currently holds 30 research centres and institutes, with the New York Number Theory Seminar being one of them. Information for attending the New York Number Theory seminars is available on their website.[2] This includes the speaker for the session and the chosen topic. During the 2020 COVID-19 pandemic, all in-person seminars at the Graduate Center CUNY), including the New York Number Theory Seminar, were temporarily suspended. No online seminars replaced the in-person seminars.

Support from third parties

The seminar is awarded support by the National Science Foundation (NSF). The NSF runs a program called the Research Training Group[3] which the aim is to encourage more individuals to pursue a career in mathematics so that there can be more in-depth scientific research, the idea revolves around a competitiveness between mathematicians to pursue great achievements. The Research Training Group involves a variety of people with different educational background ranging from undergraduate students to postdoctoral associates. The NSF funds the Research Training Group program which supports the New York Number Theory Seminar. This support is provided directly through the universities collaborating in this seminar, those three different universities working in Number Theory: City University of New York (CUNY), University of New York (UNY) and Columbia University.[4] These universities qualify for the help from the program as they organise the New York Number Theory seminar which is a research group in Number Theory.

The New York Number Theory Seminar has also received support from the U.S. Air Force in the field of computer assisted Number Theory. The U.S. Air Force donated funds to support the New York Number Theory Seminar. They support the development of Number Theory because it contributes to expand knowledge on computer science and engineering.

Notable hosts and other collaborators of the seminar

Hosts and co-founders

The first ever meeting of the New York Number Theory seminar was held exclusively between these four individuals. The meeting was encouraged by the universities where the co-founders each worked at. The seminars expanded in the number of members by involving more mathematicians with different academic standards in Number Theory.

David and Gregory Chudnovsky are two brothers who are currently distinguished professors at the New York University Tandon School of Engineering. According to The New Yorker in 1992[5], Gregory Chudnovsky is one of the greatest living mathematicians in the world. He suffers from myasthenia gravis, a neuromuscular disease, and is followed closely by his brother David. The brothers have participated heavily in number theory with the publishing of the Chudnovsky algorithm which is still used to this very day to calculate more precisely the infinite decimals of π. Their contribution to the New York Number Theory Seminar is important as they have released at least one chapter in every publication since 1982 and are recognised as editors on the front cover of all of these publications.They are also the members who work with the publishing company Springer on behalf of the other members of the seminars.

Harvey Cohn was a professor of Mathematics at the City College of New York[2].[6] In 1948, he accomplished a PhD at Harvard University specialising in Diophantine aspects of Poincaré Theta functions, a subset of Number Theory.[7] The Institute for Advanced Study recognises that Harvey Cohn's main field of study was Number Theory. He has also been an active member and host of the New York Number Theory, participating in every publication whilst he was still involved. He was both a writer and an editor in the books. However, he announced his retirement from the seminar and withdrew in December 1995. He recently died in 2014.

Melvyn B. Nathanson

Melvyn B. Nathanson is a professor of Mathematics at Lehman college and The Graduate Center (CUNY). In 1974–1975, after his studies in mathematics and early on in his professional life, he was an assistant to the mathematician André Weil in the Institute for Advanced Study. His mentor André Weil was a specialist in the field on number theory. Melvyn B. Nathanson, often abbreviated in his work to M.B. Nathanson, released over 150 research papers and contributed either as author or editor to 20 books, counting the lecture notes released by the New York Number Theory seminars. He is considered the main host and organiser of the seminars, according to the other hosts in the group. His contributions include organising the annual Workshop on Combinatorial and Additive Number Theory, writing and editing the publications of the seminars. He is now based in the City University and continues to act as the host to the seminar.

Other collaborators
Paul Erdős in 1992

Paul Erdős was a renowned in the mathematics community and has published more papers in the field of mathematics than any other person, a record that still stands to this day.[8] He was acknowledged as one of the greatest contributors to mathematics in the 20th Century.[9] Erdős has collaborated with over 500 people and he frequently worked with the main host of the seminar Melvyn B. Nathanson. Together they wrote chapters in the publications of the New York Number Theory Seminar.

Publications

General information on the publications

Proceedings of the seminar have been published regularly by Springer-Verlag, an global publishing company. David and Gregory Chudnovsky, on behalf of the other co-organisers of the seminars, contacted the publishing company who then accepted their request to publish the seminar's lecture notes in mathematics.

Publications of the seminars started in 1982, a year after the seminar's foundation. To this day, Springer-Verlag continue to publish the proceedings of the seminar. They can be found on their website and on other platforms such as Amazon.

Specifically for the publications of the entire lecture notes in Mathematics series, there were two editors: Beno Eckmann [10] and Albrecht Dold[11] who did not participate in the seminars or present any ideas. However, they contributed to shaping and defining the Editorial Policy of the series.

Different editions of the lecture notes from the seminars are available worldwide, both online and as a hard copy. These lecture notes can be used as references during other seminar proceedings.

Different editions

The very first publications of the New York Number Theory seminar appeared in a series called “Lecture Notes in Mathematics”. The series holds a total of four different editions starting in 1982 and finishing in 1988.

The first edition to be released was published in 1982 and presents 11 different articles. It is the very first edition ever to be published by the New York Number Theory Seminar.

The second edition in the series was published in 1984 and corresponds to the lecture notes of the seminars during the years 1983 and part of 1984. The edition also holds 11 different articles.

The third edition was published in 1985. The work undergone during the seminars has recognised the support of the NSF and the U.S. Air Force on the introduction page of the edition. They also acknowledge the help of the Computer Algebra Group of the T.J. Watson Research Center who contributed with extended research and provided knowledge on certain topics. This edition holds the lectures notes of the remaining seminars of 1984 (those which have not already been published in the previous edition) and part of 1985. There is a total of 16 articles in this edition with P. Erdos having contributed to 2 of them (Problems and Results on Minimal Bases in Additive Number Theory and On the Number of False Witnesses for a Composite Number).

ISBN 0-387-17669-1

The last edition was published in 1988. It is the edition that holds the work of the most seminars in this series as it holds the records of the lectures notes of the rest of 1985 and the whole of the years 1986, 1987 and 1988.

ISBN 0-387-51549-6

After the series “Lecture Notes in Mathematics”, the volumes are all published separately.[1] They appear under the name “Number Theory” and the names of the editors of the volumes appear on the cover.

The first separately published volume is the fifth volume of papers presented at the New York Number Theory Seminar covering the lecture notes from the seminars in the years 1989 and 1990. There is a total of 13 different articles.

ISBN 0-387-97670-1

The next volume was published in 1995. It is the sixth volume of papers presented at the New York Number Theory Seminar. This volume is dedicated to Harvey Cohn who was one of the main organisers of the seminar who actively participated from 1982 to 1995, as stated above. He retired in December 1995, thus making this volume his last contribution to the New York Number Theory seminar. This volume covers the work of the seminars from the years 1991 to early 1995 with a total of 22 different articles.

ISBN 0-387-94826-0

The seventh volume was published in 2003 and covers the work of the years 1995 to 2003. There is a total of 16 different articles.

ISBN 0-387-40655-7

The latest volume published by the New York Number Theory seminar is entitled the "Combinatorial and Additive Number Theory III" published in 2020. It concerns the lecture notes of the seminars of the years 2017 and 2018. The only remaining co-founder is Melvyn B. Nathanson who is also the editor of this volume.

ISBN 9783030311056

References
  1. "NUMBER THEORY CENTRES". www.numbertheory.org. Retrieved 2020-05-26.
  2. "New York Number Theory Seminar". sites.math.rutgers.edu. Retrieved 2020-05-26.
  3. "Research Training Groups in the Mathematical Sciences | NSF - National Science Foundation". www.nsf.gov. Retrieved 2020-05-26.
  4. "Joint-NTS.html". www.math.columbia.edu. Retrieved 2020-05-26.
  5. "The Mountains of Pi"The New Yorker
  6. Birth and career data according to American Men and Women of Science , Thomson Gale 2004
  7. "Harvey Cohn". Institute for Advanced Study. Retrieved 2020-05-26.
  8. "2. What Next Taylorism is all about? Facts and Challenges", Next Taylorism, Peter Lang, 2012, doi:10.3726/978-3-653-01686-4/10, ISBN 978-3-631-62405-0
  9. Bollobás, Béla (2013), "Paul Erdős: Life and Work", The Mathematics of Paul Erdős I, Springer New York, pp. 1–41, doi:10.1007/978-1-4614-7258-2_1, ISBN 978-1-4614-7257-5
  10. "Beno Eckmann (1917 - 2008)". mathshistory.st-andrews.ac.uk. Retrieved 2020-05-26.
  11. "Dold, Albrecht". 2012-03-16. Archived from the original on 2012-03-16. Retrieved 2020-05-26.
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