WGT-Workshop on Graph Theory and Its Applications-X
Diophantine Computations
Andrew Sutherland
Massachusetts Institute of Technology
Abstract: Diophantine problems, in which one seeks integer solutions to a polynomial equation, include some of the oldest problems in mathematics. There is a notable disparity between the difficulty of stating a Diophantine problem and that of solving it. This feature was formalized in the 20th century by the negative answer to Hilbert’s tenth problem: It is impossible to determine whether some Diophantine equations have solutions or not. One need not look very far to find examples whose status is unknown. A striking example noted by Mordell in 1953 involves the Diophantine equation x^3 +y^3 + z^3 = 3. In this talk I will discuss the resolution of Mordell's question and some related problems. I will also offer some thoughts on how we may approach questions that might be undecidable, and the role that computation can and cannot play.
Mathematics Days VI
IMBM is a center of research in diverse aspects of mathematics and its applications. The center aims to create an environment which encourages interaction of researchers by providing adequate space, time and services. One of the aims is to promote interdisciplinary research based on mathematics.
Although independently administrated, particular collaborative ties exist with the Boğaziçi University where the center is located.
The center has no formal curriculum, degree programs. Nevertheless, it aims to contribute to the development of young scientists through graduate seminars and postdoctoral training. Also, one of its purposes is to raise the public awareness for mathematical research.
Resources come from endowment income, grants and collaboration agreements with public and private institutions and gifts from corporations and individuals. Funding for researchers is provided from a variety of sources such as the center itself, home institutions or grants from collaborating research centers and universities.
IMBM is governed administratively by two committees.
A brief history of our center's establishment years as presented by Betül Tanbay, one of the founders of the center and one of the first co-directors (served between 2006-2012) and published in EMS Newsletter September 2010 can be found in this link.
IMBM is administrated by a management committee with a representation from major funding bodies. The management committee oversees the administration of the Center. A scientific steering committee, composed of internationally qualified researchers, determines the scientific policy and the programs. An international scientific advisory board evaluates the scientific programs and other activities.
Name | Years | |
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Ekin Özman - Turgay Bayraktar | 2022 - |
Name | Years | |
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Mete Soner - Betül Tanbay | 2006 - 2008 | |
Betül Tanbay - Ali Ülger | 2008 - 2010 | |
Rahmi Güven - Betül Tanbay | 2010 - 2012 | |
Ferit Öztürk - Mete Soner | 2012 - 2016 | |
Kazım Büyükboduk - Ferit Öztürk | 2016 - 2017 | |
Ferit Öztürk - Burak Özbağcı | 2017 - 2019 | |
Olcay Coşkun - Selda Küçükçiftçi | 2019 - 2022 | |
Ekin Özman - Turgay Bayraktar | 2022 - |
Name | Institution | |
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Alp Bassa | Boğaziçi University | |
Kazım Büyükboduk | UC Dublin | |
Olcay Coşkun | Boğaziçi University | Codirector (2019-today) |
Tınaz Ekim | Boğaziçi University | |
Ayhan Günaydın | Boğaziçi University | |
Burak Gürel | Boğaziçi University | |
Varga Kalantarov | Koç University | |
Özgür Kişisel | Middle East Technical University | |
Selda Küçükçifçi | Koç University | Codirector (2019-today) |
Burak Özbağcı | Koç University | |
Ekin Özman | Boğaziçi University | |
Ferit Öztürk | Boğaziçi University | |
Devin Sezer | METU Institute of Applied Mathematics | |
Ergün Yalçın | Bilkent University |
Name | Institution | |
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Feza Sefa Arslan | Mimar Sinan University | 2012 - 2016 |
Alp Bassa | Boğaziçi University | 2012 - |
Kazım Büyükboduk | UC Dublin | 2016 - |
Olcay Coşkun | Boğaziçi University | 2019 - |
Alp Eden | Boğaziçi University | 2006 - 2012 |
Tınaz Ekim | Boğaziçi University | 2016 - |
Ayhan Günaydın | Boğaziçi University | 2016 - |
Burak Gürel | Boğaziçi University | 2016 - |
Varga Kalantarov | Koç University | 2016 - |
Özgür Kişisel | Middle East Technical University | 2016 - |
Selda Küçükçifçi | Koç University | 2019 - |
Burak Özbağcı | Koç University | 2016 - |
Ekin Özman | Boğaziçi University | 2016 - |
Ferit Öztürk | Boğaziçi University | 2012 - |
Devin Sezer | METU Institute of Applied Mathematics | 2016 - |
Mete Soner | Bilkent University | 2006 - 2012 |
Betül Tanbay | Boğaziçi University | 2006 - 2012 |
Ali Ülger | Koç University | 2006 - 2012 |
Sinan Ünver | Koç University | 2012 - 2016 |
Ergün Yalçın | Bilkent University | 2016 - |
Cem Yalçın Yıldırım | Boğaziçi University | 2006 - 2012 |
Atilla Yılmaz | Boğaziçi University | 2012 - 2016 |
Name | Institution | Years |
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Victor Kac | MIT | |
David Mumford | Brown University | |
Mete Soner | ETH | |
Gilles Pisier | Texas A&M University | |
Edriss Titi | Weizmann Institute and University of California Irvine | |
Cem Yalçın Yıldırım | Boğaziçi University |
Name | Institution | Years |
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Selman Akbulut | Michigan State University | 2006 - 2016 |
Victor Kac | MIT | 2006 - |
David Mumford | Brown University | 2006 - |
Mete Soner | ETH | 2016 - |
Gilles Pisier | Texas A&M University | 2006 - |
Edriss Titi | Weizmann Institute and University of California Irvine | 2006 - |
Cem Yalçın Yıldırım | Boğaziçi University | 2016 - |
Name | Institution (During establisment) | |
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Selman Akbulut | Michigan State University | as Counselor |
Attila Aşkar | Koç University | as Rector |
Rahmi Güven | Boğaziçi University | |
Ayşe Soysal | Boğaziçi University | as Dean and Rector |
Betül Tanbay | Boğaziçi University | as Chairwoman |
Sabih Tansal | Boğaziçi University | as Rector |
Tosun Terzioğlu | Sabancı University | as Rector |
Ali Ülger | Koç University |
Name | Institution (During establisment) | Years |
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Attila Aşkar | Koç University | 2006 - 2016 |
Alp Eden | Boğaziçi University | 2012-2016 |
Rahmi Güven | Boğaziçi University | 2006-2016 |
Mete Soner | ETH | 2006-2016 |
Betül Tanbay | Boğaziçi University | 2012-2016 |
Tosun Terzioğlu | Sabancı University | 2006-2012 |
Ali Ülger | Koç University | 2006-2016 |
Cem Yalçın Yıldırım | Boğaziçi University | 2012-2016 |
Name | Institution | Years |
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Name | Institution | Years |
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Pınar Adanalı | Boğaziçi University | 2016 - 2018 |
Berrenur Saylam | Boğaziçi University | 2018 - 2022 |
IMBM has been supported by the following universities/institute. We thank for the support we received.
September 3, 2020
September 24, 2019
October 10, 2018
September 01, 2014
November 09, 2012
April 13, 2012
April 4, 2012
December 17, 2010
October 12, 2006
October 12, 2006
October 12, 2006
October 19, 2006
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October 19, 2006
October 19, 2006
October 19, 2006
October 19, 2006
May 28, 2004
Rahmi Güven, Betül Tanbay, Ali Ülger, Attila Aşkar, Tosun Terzioğlu, Ayşe Soysal,
Istanbul is a very large city. However it has an extensive public transportation network. The fare for transportation is reasonable. Getting from one place to the other may take long. Do not get intimidated. Be patient. Depending on the route you choose, you will either take a metro, a Metrobüs, a bus, a Dolmuş, a HAVABUS shuttle , a HAVAIST shuttle , a taxi or a sequence of these. Here are some general tips:
You cannot buy ticket on a vehicle. If you plan to use public transport many times, buy a prepaid ISTANBULKART from a vending machine in the metro stations or kiosks all around the city. While buying an IstanbulKart, you must pay a non-refundable 6 TL fee (for the actual card and the service), plus an amount of your choice to load onto the card. You get transfer discount automatically if you use an IstanbulKart. If you will not use public transport except coming from/going to airports, you might buy cards that have several rides in them. With those cards, you do not have transfer discount.
Cabs are usually trustworthy. Yet always make sure that the taxi driver turns the meter on.
The trip durations given below are on the average. There might be drastic traffic jams.
Istanbul Airport (IST) and Boğaziçi University South and North Campuses are on the European side of Istanbul.
Sabiha Gökçen International Airport (SAW) is on the Asian side of Istanbul.
IMBM, and Kennedy Lodge are in the South Campus.
Map.1
Map.2
FROM THE ISTANBUL AIRPORT TO SOUTH CAMPUS (IST) -- This airport is on the European side as well as Boğaziçi University. There are various ways to get to the campus.
1) HAVAIST + METRO: Go out of the arrival hall. In front of the building take the Havaist to Hacıosman or 4. Levent. It costs 18 Liras. From Hacıosman or 4. Levent, take the M2 metro line and change to line M6 at Levent Station. Get off at the last station which is Boğaziçi University.
http://www.istanbul-ulasim.com.tr/passenger-services/network-maps.aspx
http://nasilgiderim.iett.istanbul/
2) HAVAIST + TAXI: Go out of the arrival hall. In front of the building take the Havaist to 4.Levent. It costs 18 Liras. From there, take a yellow cab. Tell the driver that you want to go to "Boazitchi Üniversitesi Ghünei Kampüs" (read all the letters). It takes around 15 minutes to get to the campus and costs ~25 Liras.
3) TAXI (easy, but usually slower): Go out of the arrival hall. In front of the building take one of the (yellow) cabs. Tell the driver that you want to go to "Boazitchi Üniversitesi Ghünei Kampüs" (read all the letters). It takes around 45 minutes to get to the campus and costs ~140 Liras.
FROM SABIHA GÖKÇEN INTERNATIONAL AIRPORT (SAW) TO SOUTH CAMPUS -- This airport is on the Asian side while the university is on the European side.
1) BUS + TAXI: Go out of the arrival hall. In front of the building take the bus number E3. It reads Sabiha Gökçen Havalimanı - 4. Levent Metro. You must buy an IstanbulKart or a card with several rides in it. You will get off at the last stop. The trip takes more than an hour and even more depending on the traffic. On the way you will pass across Bosphorus. As soon as you get off from the bus, (EITHER) use the underground passage to get across the street. At the other side take a (yellow) cab. Tell the driver to take you to "Boazitchi Üniversitesi Ghünei Kampüs" (read all the letters). It takes around 15 minutes to get to the campus and costs around 25 Liras. (OR) keep walking in the same direction until the metor station Levent. Take the metro M6 towards Boğaziçi Üniversitesi. Get off at the last stop.
2) HAVATAŞ + TAXI: Go out of the arrival hall. In front of the building take the shuttle called HAVATAŞ to Taksim. It costs around 15 Liras. Get off at Kavacık. The trip takes nearly an hour and even more depending on the traffic. As soon as you get off, you will be on a very busy intercity road. Take one of the present (yellow) cabs. You will go in the same direction as the shuttle and eventually pass across Bosphorus. Tell the driver to take you to "Boazitchi Üniversitesi Ghünei Kampüs" (read all the letters). It takes around 15 minutes to get to the campus and costs around 20 Liras.
Istanbul Center for Mathematical Sciences
Bogazici University South Campus
Bebek
34342 Istanbul
Turkey
Phone: ++90-212-359-7477
++90-212-359-6602 (Dept. of Math. - in case the center is closed)
Fax: ++90-212-359-7478
E-mail: imbm [at] imbm.org.tr
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Istanbul Center for Mathematical Sciences welcomes applications to visit IMBM or to organize workshops/conferences/seminars. Please fill in the relevant form below.
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2022
Abstract: In this talk we will give a discussion on a program which aims to present a combinatorial approach to the exceptional Lie group G2 and its Lie algebra. We give various results about the algebraic structure. We also prove some of the old results in terms of our approach.