Adriano Garsia
Encyclopedia
Adriano Mario Garsia is an Italian American
mathematician, a leading expert in combinatorics
, representation theory
, and algebraic geometry
, a student of Charles Loewner
. He has made many deep contributions to representation theory, symmetric function
s and algebraic combinatorics
, which exerted a remarkable influence and opened new subfields. Thus, his famous n!-conjecture
has resulted in new vistas opening up in representation theory.
Born to Italian Tunisians in Tunis
, Garsia moved to Rome
in 1946.
He currently (2008) has 29 students and 73 descendants according to the data at the Mathematics Genealogy Project
.
He is currently on the faculty of the University of California, San Diego
.
Italian American
An Italian American , is an American of Italian ancestry. The designation may also refer to someone possessing Italian and American dual citizenship...
mathematician, a leading expert in combinatorics
Combinatorics
Combinatorics is a branch of mathematics concerning the study of finite or countable discrete structures. Aspects of combinatorics include counting the structures of a given kind and size , deciding when certain criteria can be met, and constructing and analyzing objects meeting the criteria ,...
, representation theory
Representation theory
Representation theory is a branch of mathematics that studies abstract algebraic structures by representing their elements as linear transformations of vector spaces, and studiesmodules over these abstract algebraic structures...
, and algebraic geometry
Algebraic geometry
Algebraic geometry is a branch of mathematics which combines techniques of abstract algebra, especially commutative algebra, with the language and the problems of geometry. It occupies a central place in modern mathematics and has multiple conceptual connections with such diverse fields as complex...
, a student of Charles Loewner
Charles Loewner
Charles Loewner was an American mathematician. His name was Karel Löwner in Czech and Karl Löwner in German.Loewner received his Ph.D...
. He has made many deep contributions to representation theory, symmetric function
Symmetric function
In algebra and in particular in algebraic combinatorics, the ring of symmetric functions, is a specific limit of the rings of symmetric polynomials in n indeterminates, as n goes to infinity...
s and algebraic combinatorics
Algebraic combinatorics
Algebraic combinatorics is an area of mathematics that employs methods of abstract algebra, notably group theory and representation theory, in various combinatorial contexts and, conversely, applies combinatorial techniques to problems in algebra....
, which exerted a remarkable influence and opened new subfields. Thus, his famous n!-conjecture
N!-conjecture
In mathematics, the n! conjecture is the conjecture that the dimension of a certain bi-graded module of diagonal harmonics is n!. It was made by A. M. Garsia and M. Haiman and later proved by M. Haiman...
has resulted in new vistas opening up in representation theory.
Born to Italian Tunisians in Tunis
Tunis
Tunis is the capital of both the Tunisian Republic and the Tunis Governorate. It is Tunisia's largest city, with a population of 728,453 as of 2004; the greater metropolitan area holds some 2,412,500 inhabitants....
, Garsia moved to Rome
Rome
Rome is the capital of Italy and the country's largest and most populated city and comune, with over 2.7 million residents in . The city is located in the central-western portion of the Italian Peninsula, on the Tiber River within the Lazio region of Italy.Rome's history spans two and a half...
in 1946.
He currently (2008) has 29 students and 73 descendants according to the data at the Mathematics Genealogy Project
Mathematics Genealogy Project
The Mathematics Genealogy Project is a web-based database for the academic genealogy of mathematicians. As of September, 2010, it contained information on approximately 145,000 mathematical scientists who contribute to "research-level mathematics"...
.
He is currently on the faculty of the University of California, San Diego
University of California, San Diego
The University of California, San Diego, commonly known as UCSD or UC San Diego, is a public research university located in the La Jolla neighborhood of San Diego, California, United States...
.
Books by A. Garsia
- Garsia, Adriano M. Martingale inequalities: Seminar notes on recent progress. Mathematics Lecture Notes Series. W. A. Benjamin, Inc., Reading, Mass.-London-Amsterdam, 1973.
- Garsia, Adriano M. Topics in almost everywhere convergence. Lectures in Advanced Mathematics, 4 Markham Publishing Co., Chicago, Ill. 1970
- A. M. Garsia and M. Haiman, Orbit Harmonics and Graded Representations, Research Monograph to appear as part of the collection published by the Lab. de. Comb. et Informatique Math\'ematique, edited by S. Brlek, U. du Qu\'ebec \'a Montr\'eal.