The famous French mathematician. Is so far won the Nobel prize in mathematics " Fields Medal The youngest winner.

Searl Profile

Jean-Pierre Serre (French: Jean-Pierre Serre, September 15, 1926 -), French mathematician, the main contribution to the field is topology , Algebraic geometry And number. He has received many awards including the 1954 mathematics. Fields Medal And 2003 abel prize .
J P Searl (Serre, Je
Date of birth: September 15, 1926.
By Fields Medal Age: 28 years old
Origin: france.
In 1954, the year location: Amsterdam .
Winning and working place: The University of Paris .

Searl The main achievement

The development of the Are all finite group The introduction; localization The method for homotopy The problem of the group to be decomposed, obtained a series of important results. The mathematician Jean Pierre Sal created "algebra and condensed layer"" Algebraic geometry With analytic geometry, a new "classic" of modern mathematics literature. He is due to the Algebraic topology The outstanding achievements gained Fields Medal .

Searl Paul Mauriat's History

Then, Commutative algebra and Algebraic geometry Mainly, using layer theory and homological algebra techniques. Searl's doctoral dissertation a Leray - fibrosis mapping Searl spectral sequence . Searl and Cartan With the calculation of the ball with the spirit of space based cohomology group, which at the time was topology The main subject.
In 1954 Fields Medal The award ceremony, Weyl Searl praised the contribution, and points out that this is the first prize awarded to scientists since the development of mathematics algebra; prove to be the Weyl on Abstract algebra Attention. Searl then changed the research direction, he clearly believes that homotopy theory has become overly technical.
stay Algebraic geometry and weil The work on 1950-60's conjecture, Searl and his younger than two years grothendieck Cooperation, leading to Algebraic geometry The basic work, its motivation stems from the Weil conjecture. Searl in the aspects of two algebraic geometry based algebra Condensed layer (Faisceaux Alg briques Coh rents, referred to as FAC) and algebraic geometry and analytic geometry (G om trie Alg briqueet G om trie Analytique, referred to as GAGA).
Searl was already aware to generalized cohomology theory to solve layer weil Guess. The key lies in the condensed cohomology layer not as integer coefficient singular cohomology algebra general master cluster topology Nature。 Searl early (1954/55) tried to value cohomology for Witt vector, this idea was later absorbed crystalline cohomology.
In 1958, Searl suggested that the study of algebraic varieties such as ordinary coverage, this is in a limited coverage of change after the end of a class of ordinary coverage coverage. This idea can be regarded as etale cohomology The origin of. grothendieck And its partners finally establish a complete theory in SGA4.
Searl is often overly optimistic that provide some Counterexample Also, he and Belgium Mathematician Pierre Delinemice cooperation. Finally, the completion of the dream weil Proof of a conjecture.
Other work from 1959, Searl's interest to number theory, especially Class field theory With the theory of complex multiplication of elliptic curve.
His most original contribution is: algebraic K- theory ideas, l- cohomology of Galois representation theory, and representation of the Searl conjecture modulo P.

Searl Figure effect

The mathematician, Searl belongs to a class of broad and profound. This is the traditional Bourbaki tradition. The second half of the twentieth Century mathematics is created in the glorious tradition of the. They do not love mathematics split into small branches, every little bit forward in every branch stenosis. Their slogan is the unity of mathematics. A symbol of unity is the abstract algebra and topology . While Searl is using the topology and algebraic topology transformation -- the homology mathematics main characters to a new level of mathematics.
The first major work of Searl is greatly the development of topology. After the Second World War, the topology was a Cinderella, and because Searl, tom, Wentsun WU Who work in elegant mathematical topology become queen. Although the topology has a history of half a century, but every step is very difficult, especially the homology (homology) theory, although some development, homotopy (homotopy) theory has come to a standstill, calculated the head of a stumbling block is the homotopy group. many A great mathematician As the Soviet Union, especially under the academician of gold (pontjagin) calculation error. The application of this tool and Searl spectral sequence, solve many issues of principle. Fundamental change Homotopy theory and even topology Look. This is a 24 year old student's PhD thesis. Because of this work and the subsequent development of topology, in 1954 under the age of 28 Searl won the most important Mathematics prize - Fields Medal . Today, this award-winning age still no break.
The last century since 60s, Searl's work mainly in the aspects of number theory. He introduced Galois Cohomology and some other tools to become the key to solve many important problems in number theory. stay Wiles The proof of Fermat's last theorem of epsilon conjecture of Searl is an important step.
Searl's mathematical achievements are widely recognized by the international mathematical community. Thus, he received many honors, in 1970s, he was elected academician of the French Academy of sciences, The Royal Society Foreign member, American Academy of Sciences foreign academician of the three crown is the highest honor a scientist can get. In mathematics, besides the Fields Medal, he won Wolf Prize Also, the international scientific awards Barr Chan (Balzan) award.

Searl Awards

Searl in 1945 Fields Medal At that time, only 28 years old, he is still the youngest winner. Then he was awarded the Balzan Award (1985), Steele Award (1995) and Wolf Prize (2000), he is also abel prize The first winner (2003). The Fields prize and the Abel prize is generally considered the highest honor of the mathematician Searl, is so far the only one both.

Searl The Searl conjecture

(Serre'sconjecture) In 1955, the French mathematician Searl conjecture: projective module over polynomial ring is a free module. This is a topic of algebraic theory, and it topology Has the close relation, the popular formulation is: a Invertible matrix The first line is what? This of course depends on what elements are. When the element is real, in addition to (0, 0,... 0) can be. If the limit value in the integer ring, then (2,4,6). That, as long as a line of not greater than 1 Common factor And it can become a reversible matrix The first line. Then for general commutative rings (with Unit ), still has the similar properties? For one order and two order matrix is all right, but for the three order matrix is not established. The Searl conjecture: for some special ring domain variables in polynomial ring, matrix composed of the element, the fan can be on a line Invertible matrix The first line. The original form of the Searl conjecture is related to that on the ring die. After this conjecture announced that the first step of non trivial (Seshardi) given by Seshadi (1958), he proved that when =2 Searl conjecture. 1964 Horrocks (Horrocks) is an important step, he is a local ring (only one of the biggest ideal ring) proved similar results. In 1976, the United States and the former Soviet mathematician mathematician quelen Seuss Lin independently proved Searl's conjecture. Quelen therefore won the 1978 annual Fields Medal .

Searl Related reports

The French mathematician Searl won the first Abel Mathematics prize
CCTV International (04 2003 05 August 13:32)
The Xinhua News Agency Stockholm In April 4th the industry newspaper news Norway Academy of Sciences in April 3rd in the capital of Norway Oslo Announced that the first abel prize The French mathematician Jean Pierre Sal award, in recognition of his remarkable contributions in the field of mathematics.
In the decision, the Norway Academy of Sciences praised Searl for giving through hard work topology , Algebraic geometry And many other areas of mathematics to learn digital "modern form", become one of the most outstanding contemporary mathematicians". The 76 year old Searl is a French College de France emeritus professor And, by many National University Honorary doctor Title。
The Abel prize is norwegian government In 2002 to commemorate the Norway genius mathematician Niels Henrik Abel A mathematics award funded. Abel In the 5 equation and elliptic function Study on far ahead at the level of research, but could not be recognized and academic research has always been plagued by poverty and ill health less than 27 years old, because of contracted tuberculosis and died.
abel prize Awarded annually, the award amount is 6 million Norway. ($830 thousand). The award ceremony in June 3rd each year Oslo Held, known as the "Nobel prize in mathematics". Earlier, set up in 1936 Fields Medal Is widely regarded as the International Mathematics highest honor award. But the Fields Medal is awarded once every four years, the winners of the prize winning achievements obtained shall not exceed 40 years of age. ( Wu ping1 )

Searl Interview

Q: what makes you in Mathematics for the occupation?
Answer: I remember is probably from the age of seven or eight when the love of mathematics. In high school, I used to do some high grade title. At that time, I hosted by Nimes, together with the big child than I live, they often bullied me to calm them, I often help them to do the math homework. This is one of the best training. My mother is a pharmacist (his father is), and love of mathematics. She was in the pharmacy students at Montpellier University, just out of interest, the first grade elective course in calculus, and passed the exam. She carefully preserved the year The work of (~ 1950), I am confident: given the space X, there must be a X fiber space E substrate, it is contractible. Such a space can indeed make me (by Leray method) to do many To deal with these complex projective clusters: in 1953, I was such a series of thoughts on Riemann-Roch's theorem. But the projective varieties are "(especially the number, (microlocal analysis), super cluster (supervariety), intersection Cohomology (intersection cohomology)...)...
Q: in the face of the explosive development of mathematics, do you think the beginning graduate students can absorb a lot of mathematical knowledge in four or five or six years, and then start doing groundbreaking work?
Answer: why not? For a given problem, you usually do not need to know a lot of, say, is often a very simple idea opens up. Some theories are simplified, some theory of retiring. For example, I remember in 1949 I was frustrated, because every time the Annals of Mathematics has a more difficult than the previous article topology. But now no one would see them at a glance; they are forgotten (should be like this: I think they do not contain any profound things......). Forgetting is a very healthy behavior. Of course, relatively speaking, some subjects need more training, because they need a lot of skills. The classification?
Answer: it is not a letter -- letter letter more ingredients. If some day in the future to find a new powder in the group, I feel funny, but I'm afraid it won't happen. More importantly, the classification theorem is very great. Now as long as the check list of all groups form, can be found in many properties (example: n>4 n- (transitive group) transitive group classification).
Q: your complete classification Finite simple group The vitality of what?
A: are you implying that some finite group Experts in the implementation of classification of morale; they curse (probably told me) "will have nothing to do." I think this is absurd. Do a lot of course! First of all, nature is a simplified proof (that is, Gorenstein said" Revisionism "). You can also find its application in other parts of mathematics, for example, has the Griess-Fischer group (monster group) and strange link mode very wonderful discovery (the so-called "Moonlight" ( Moonshine )). Just ask this Faltings (Faltings) the proof of Mordell conjecture whether the end of the curve Rational point The theory. No This is only the beginning. Many problems remain to be solved. (of course, sometimes it can kill a theory. A famous example is Hilbert Fifth problem: prove that every locally Euclidean topological group is Lie group. When I was a young scientist when I really want to topology, to solve the problem, but I failed to do so. Gleason and Montgomery-Zippin to solve it. Their solution almost killed the subject. What can I do in this direction? I can only think of one problem: p-adic integer group can effectively function in the manifold? It may seem difficult, but I can see is, even if there is no answer with wings).
Q: you can think so, most of the problems in mathematics are like this, that the problem itself may be difficult and challenging, but in solution, without what use. In fact, only a few problems can be like Riemann conjecture So, early before solving, know a lot of theory.
Answer: yes. The Riemann conjecture is wonderful: it gave birth to many things (including pure numerical inequality, for example The number of domain The Discriminant ). But there are also other similar examples: singular resolution theorem of Hironaka (desingularizationtheorem) is a, of course, discussed above Finite simple group The classification. Sometimes, a method used in the proof has many applications: I am sure that this belongs to Faltings. Sometimes, the problem itself does not mean that there are applications, but a kind of experience known theory, it urges us to see farther.
Q: would you still come back to engage in "extension of the problem?
Answer: No. I have to master the latest methods, I do not know the Homotopy Groups of spheres \pi_{n+k} (S_n) has been considered to what extent (I guess people have k=40 or 50. I only know about the case of k=10). But in general, I am still in use in topology theory, such as cohomology, obstacle Stiefel-Wiltney, etc..
Ask: Bourbaki What is the impact on mathematics?
Answer: good question. I know what the things (such as the "new math") are to blame for Bourbaki is very fashionable, but this is not fair. Bourbaki is not responsible, but people misuse of his book. This book is not written for college education, middle school education is not to mention the.
Q: maybe it should give a warning signal?
Answer: the fact that Bourbaki gives a signal, which is discussed in Bourbaki class. This discussion is not the class of their books so formal. It includes all mathematics, physics and even some. If you put the discussion class and books together, you will have more appropriate views.
Q: if you found the effect of Bourbaki on mathematics is weakening?
Answer: the effect is different from the previous. Forty years ago, Bourbaki has a goal, he must prove that there are plans to elaborate system mathematics is possible. Now, this goal has been reached, Bourbaki victory. As a result, his book is now only the technical aspects of importance; the problem is whether they are good on those topics. Some of them do (the book about the "root" has become a standard reference in the field of Literature); and some are not so I don't want to (for example, the more of the same for every taste.
Q: when it comes to taste, can you talk about what style you love most (of books or articles)?
Answer: accurate and non formal combination! This is the most ideal, like the lecture as. You will be in atiyah (Atiyah), Milner (Milnor) and some other authors discover this intoxicating mix. But it is extremely difficult to achieve. For example, I found that many French books (including my own), a little too formal, some Russian books and not so accurate....... I also want to emphasize that the paper should contain more notes and unsolved problems, which often proved more accurate than theorem of interest. Hey, most people are afraid to admit that they do not know the answers to certain questions, the refrain from asking these questions, i.e.
It is natural to make them appear. This is a pity! As for myself, I am very happy to say "I don't know".
Searl (Searle John, R.; 1932)
American philosopher analysis. Once in Oxford Educated at J. Austen P., Steffen Sen et al., 1959 received a doctorate in philosophy, he returned to the United States The University of California Berkeley, Professor of philosophy. He to study speech act theory Known that the smallest unit of language communication is not a number, word or sentence, but some kind of speech act. His speech act is divided into 3 kinds, namely propositional acts, illocutionary act and perlocutionary act. The author of " Speech act "Etc..