Radix sort

Template:BLP sources Template:Infobox scientist Robert Phelan Langlands (born October 6, 1936) is a Canadian mathematician best known as the founder of the Langlands program, a vast web of conjectures and results connecting representation theory and automorphic forms to the study of Galois groups in number theory. He is an emeritus professor at the Institute for Advanced Study.

Career

Langlands received an undergraduate degree from the University of British Columbia in 1957, and continued on there to receive an M. Sc. in 1958. He then went to Yale University where he received a Ph.D. in 1960. His academic positions since then include the years 1960-67 at Princeton University, ending up as Associate Professor, and the years 1967-72 at Yale University. He was appointed Hermann Weyl Professor at the Institute for Advanced Study in 1972, becoming Professor Emeritus in January 2007.

Research

His Ph.D. thesis was on the analytical theory of semi-groups, but he soon moved into representation theory, adapting the methods of Harish-Chandra to the theory of automorphic forms. His first accomplishment in this field was a formula for the dimension of certain spaces of automorphic forms, in which particular types of Harish-Chandra's discrete series appeared.

He next constructed an analytical theory of Eisenstein series for reductive groups of rank greater than one, thus extending work of Maass, Roelcke and Selberg from the early 1950s for rank one groups such as $SL(2)$. This amounted to describing in general terms the continuous spectra of arithmetic quotients, and showing that all automorphic forms arise in terms of cusp forms and the residues of Eisenstein series induced from cusp forms on smaller subgroups. As a first application, he proved the Weil conjecture on Tamagawa numbers for the large class of arbitrary simply connected Chevalley groups defined over the rational numbers. Previously this had been known only in a few isolated cases and for certain classical groups where it could be shown by induction.

As a second application of this work, he was able to show meromorphic continuation for a large class of $L$-functions arising in the theory of automorphic forms, not previously known to have them. These occurred in the constant terms of Eisenstein series, and meromorphicity as well as a weak functional equation were a consequence of functional equations for Eisenstein series. This work led in turn, in the winter of 1966/67, to the now well known conjectures making up what is often called the Langlands program. Very roughly speaking, they propose a huge generalization of previously known examples of reciprocity, including (a) classical class field theory, in which characters of local and arithmetic abelian Galois groups are identified with characters of local multiplicative groups and the idele quotient group, respectively; (b) earlier results of Eichler and Shimura in which the Hasse-Weil zeta functions of arithmetic quotients of the upper half plane are identified with $L$-functions occurring in Hecke's theory of holomorphic automorphic forms. These conjectures were first posed in relatively complete form in a famous letter to Weil, written in January 1967. It was in this letter that he introduced what has since become known as the $L$-group and along with it, the notion of functoriality.

Functoriality, the $L$-group, the rigorous introduction of adele groups, and the consequent application of the representation theory of reductive groups over local fields changed drastically the way research in automorphic forms was carried out. Langlands's introduction of (or in cases where others had done previous work, emphasis on) these notions broke up large and to some extent intractable problems into smaller and more manageable pieces. For example, they made the infinite-dimensional representation theory of reductive groups into a major field of mathematical activity.

Functoriality is the conjecture that automorphic forms on different groups should be related in terms of their $L$-groups. As one example of this conjecture the letter to Weil raised the possibility of solving the well known conjecture of Emil Artin regarding the behaviour of Artin's $L$-functions, a hope partly realized in Langlands' later work on base change. In its application to Artin's conjecture, functoriality associated to every $N$-dimensional representation of a Galois group an automorphic representation of the adelic group of $GL(N)$. In the theory of Shimura varieties it associates automorphic representations of other groups to certain $l$-adic Galois representations as well.

The book by Hervé Jacquet and Langlands on $GL(2)$ presented a theory of automorphic forms for the general linear group $GL(2)$, establishing among other things the Jacquet–Langlands correspondence showing that functoriality was capable of explaining very precisely how automorphic forms for $GL(2)$ related to those for quaternion algebras. This book applied the adelic trace formula for $GL(2)$ and quaternion algebras to do this. Subsequently James Arthur, a student of Langlands while he was at Yale, successfully developed the trace formula for groups of higher rank. This has become a major tool in attacking functoriality in general, and in particular has been applied to demonstrating that the Hasse-Weil zeta functions of certain Shimura varieties are among the $L$-functions arising from automorphic forms.

The functoriality conjecture is far from proved, but a special case (the octahedral Artin conjecture, proved by Langlands and Tunnell) was the starting point of Andrew Wiles' attack on the Taniyama–Shimura conjecture and Fermat's last theorem.

In the mid-1980s Langlands turned his attention to physics, particularly the problems of percolation and conformal invariance.

In recent years he has turned his attention back to automorphic forms, working in particular on a theme he calls `beyond endoscopy'.

In 1995 Langlands started a collaboration with Bill Casselman at the University of British Columbia with the aim of posting nearly all of his writings—including publications, preprints, as well as selected correspondence—on the Internet. The correspondence includes a copy of the original letter to Weil that introduced the $L$-group.

Awards and honors

Langlands has received the 1996 Wolf Prize (which he shared with Andrew Wiles), the 2005 AMS Steele Prize, the 1980 Jeffery-Williams Prize, the 1988 NAS Award in Mathematics from the National Academy of Sciences, the 2006 Nemmers Prize in Mathematics, and the 2007 Shaw Prize in Mathematical Sciences (with Richard Taylor) for his work on automorphic forms.

He was elected a Fellow of the Royal Society of London in 1981. In 2012, he became a fellow of the American Mathematical Society.

Personal life

Langlands spent a year in Turkey in 1967/68, where his office at the Middle East Technical University was next to that of Cahit Arf's. He speaks Turkish.

Publications

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  Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.
  
  In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.
  
  Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region
  
  Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.
  
  15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.
  
  To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010
• Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.
  
  Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.
  
  In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.
  
  Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region
  
  Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.
  
  15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.
  
  To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010

See also

• Langlands classification
• Langlands decomposition
• Langlands–Deligne local constant
• Langlands dual
• Langlands group
• Langlands program

References

43 year old Petroleum Engineer Harry from Deep River, usually spends time with hobbies and interests like renting movies, property developers in singapore new condominium and vehicle racing. Constantly enjoys going to destinations like Camino Real de Tierra Adentro.

External links

• Template:MacTutor Biography
• 50 yr old Print Journalist Broadbent from Deep River, has hobbies and interests which includes r/c helicopters, property developers in singapore house for rent and scrabble. Suggests that you go to Tomb of Askia.
• The work of Robert Langlands (a nearly complete archive)
• Faculty page at IAS

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