Biography

 8/20/1928 Born Tunis 1946 Moved to Italy Rome 1946-49 Attended Liceo A. Righi (High School) Rome 1949 Graduated from Liceo Augusto Righi Rome 1949-52 School of Engineering Univ. of Rome Rome Fall 1953 School of Mathematics Univ. of Rome Rome 1953-57 Graduate student Stanford Univ. Math. Palo Alto Cal. 1955-57 Research Ass. Stanford Research Institute Palo Alto Cal. Sept. 1957 PhD in Mathematics Stanford University "Thesis: On Surfaces with a rectilinear Geodesic Circle" Palo Alto Cal. 1957-1959 C. L. E. Moore Instructor Mass. Inst. of Tech Cambridge Mass. Summer 1959 Research Fellow Bell Laboratories. Murray Hill N.J. 1959-61 Assistant Prof. of Math. Univ. of Minnesota Mineapolis Minn. Summer 1960 Int. Congress on Diff. Geometry, I. S. Zurich 1961-62 O. N. R. Postdoctoral Cal. Inst. of Tech. Pasadena Cal. 1962-64 Associate Prof. of Math. Cal. Inst. of Tech. Pasadena Cal. 1964-66 Prof. of Math. Cal. Inst. of Tech Pasadena Cal. 1966-72 Consultant Jet Propulsion Lab. Pasadena Cal. 1966 Prof. of Math. Univ. of Cal. San Diego La Jolla Cal. 1969 Venezuelan Inst. of Scien. Research, V. Caracas 1971 Year in Probability Mittag-Leffler Inst., V. Stockholm 1974 Int. Congress on Gaussian Processes, I. S. Strasbourg 1974 Annual Meeting Amer. Math. Society, I. S. San Francisco 1977 Int. Congress on Prob. Japan, I. S. Kyoto 1978 Int. Congress of Math, I. S. Helsinki 1980 Year in Comm. Algebra Mittag-Leffler Inst., V. Stockholm 1981 Int. Colloquium On Ordered sets, I. S. Banff 1985 Int. Symposium Combinatorics of Symm. Group I. S. Durham England 1985 Spent Fall semester at MIT (Navy res. Grant) Cambridge Mass. June 1987 Visiting professor U. Paris VII Paris Sept. 1988 Visiting professor U.Bordeaux Bordeaux Dec. 1989 Visiting professor U.Q.A.M. Montr\'eal Dec. 1990 Visiting professor U.Q.A.M. Montr\'eal June. 1991 Conf. in Algebraic Combinatorics I.S. Ann Arbor Apr.-May 1992 Year in Algebraic Comb. Mittag-Leffler Inst., V. Stockholm June 1992 4th Int. Colloquium Alg. Comb. UQAM, I.S. Montr\'eal July 1992 Colloquium on Representation Theory, I.S. Lyons March 1993 Special Session in Algebraic Combinatorics, I.S. Knoxville

I.S. = Invited Speaker, V. = Visitor

Prior and Current PhD students

 Stanley Sawyer Almost Everywhere Convergence 1964 Charles Greenhall Orthogonal Series 1965 Luis Baez-Duarte Ergodic Theory 1966 Chris Preston Fourier Analysis 1970 Tom Crocker Interpolation Theory 1971 Rex Page Numerical Analysis 1973 Paul Deland Real Analysis 1974 T. H. Park Sobolev Type Inequalities 1974 Steve Milne Comb. Methods in Real Analysis 1975 S. A. Joni Formal power series inversion 1976 Michelle Wachs Algorithms for Minimal Search Trees 1976 Don Rawlings Permutation Enumeration 1977 Roger Whitney Theory of Symmetric Functions 1980 Y. M. Chen Plethysm 1983 Omer Egecioglu Symmetric Function Algorithms 1984 Timothy McLarnan Robinson-Schensted Correspondences 1986 H\'el\ene Barcelo Combinatorics of Representation Theory 1988 Nantel Bergeron Structure of Descent Algebras 1990 Ed Allen Computational commutative algebra 1991 Arun Ram(cochair) Matrix units for Brauer algebras 1991 Ethan Reiner Invariants of reflection Groups 1993 Joe Alfano Harmonics for diagonal actions 1994 Sara Billey Schubert Polynomials 1994 Mike Zabrocki Hall-Littlewood Vertex Operator 1998 Jennifer Morse Macdonald Polynomials 1999 Theresa Gallo Combinatorial Bases for Modules of Coinvariants 2000 Ezra Halleck Magic Squares 2000 David Little Bijective combinatorics 2002 Gregg Musiker Combinatorics of Elliptic Curves over finite fields 2007 Jason Bandlow Extensions of Macdonald Polynomials 2007

Postdoctoral scholars

 Mei Yang S-series expansions April 88 - July 89 N. Buzeteanu q-Series and q-analogs Jan 91- Sept 91 A. Goupil Conjugacy Classes of Coxeter Groups Sept 91- ???? Glenn Tesler Macdonald Poynomials Sept 96-2000

Courses Developed

• Introduction to Cryptography (Upper Division)
• Computer Graphics with $\scriptstyle MATHEMATICA$ (Upper Division).
• Introduction to Combinatorial Mathematics (Lower Division)
• Computer Animated Statistics

Miscelanea

Public service

Member of the Editorial Board

• Editor of Journal of Combinatorial Theory Series A
• Analysis

Member of the Advisory board of the {\ita Institut des Sciences Math\'ematiques de Montr\'eal}.

Reviewer for the Natural Sciences and Engineering Research Council of Canada.

Publications

[1] "On surfaces with a rectlinear geodesic circle," Ann. Mat. Pura. Appl . Serie IV-XLVI (1958), 201-203.

[2] "Some models of explosive line detonators," J. Math. Phys ., XXIX (1960), 54-57.

[3] "The calculation of conformal parameters for some imbedded Riemann surfaces," Pacific J. Math., 10 (1960), 121-165.

[4] (with E. Rodemich) "An embedding of Riemann surfaces of genus one," Pacific J. Math., 11 (1961), 193-204.

[5] "An imbedding of closed Riemann surfaces in Euclidean space," Comment. Math . Helv, 35 , 93-110.

[6]"Imbeddings of some closed Riemann surfaces by canal surfaces," Rend. Circ. Mat . Palermo, Ser. II, IX (1960), 1-21.

[7]} "Arithmetic properties of Bernoulli convolutions," Trans. Am. Math. Soc., 102 (1962), 409-432.

[8] "A note on the mean value property," Trans. Am. Math. Soc., 102 (1962), 181-186.

[9] "On the conformal types of algebraic surfaces of Euclidean space," Comment. Math , Helv., 37 (1962), 49-60.

[10] (with J. Lamperti) "A discrete renewal theorem with infinite mean," Comment. Math , Helv. 37 (1963), 221-234.

[11] "Some Tauberian theorems and the asymptotic behavior of probabilities of recurrent events," J. Math. Anal. Appl., 7 (1963), 146-162.

[12] (with S. Orey and E. Rodemich) "Asymptotic behavior of successive coefficients of some power series," Illinois J. Math., 6 (1962), 620-629.

[13] "Entropy and singularity of infinite convolutions," Pacific J. Math., 13 (1963), 1159-1169.

[14] "A new proof of Beurling's theorem on the spectrum of bounded functions on the real axis," J. Math. Anal. Appl., 7 (1963), 436-439.

[15] "Existence of almost everywhere convergent rearrangements for Fourier series of $L_2$ functions," Ann. of Math., 79 (1964), 623-629.

[16] (with S. Sawyer) "On some classes of continuous functions with convergent Fourier series," J. Math. Mech., 13 (1964), 589-602.

[17] "A simple proof of Hopf's maximal ergodic theorem," J. Math. Mech., 14 (1965), 381-382.

[18] "Some bounds on best uniform linear approximation," Numer. Math., 7 (1965), 197-205.

[19] (with E. Rodemich) "On functions satisfying the mean value property with respect to a product measure," Proc. Am. Math. Soc., 17 , No. 3 (1966), 592-594.

[20] "More about the maximal ergodic lemma of Brunel," Proc. Nat'l Acad. Sci., 57 , No. 1 (1965), 21-24.

[21] (with E. C. Posner and E. Rodemich) "Some properties of the measures on function spaces induced by Gaussian processes," J. Math. Anal. Appl., 21 (1968), 150-160.

[22] "Combinatorial inequalities and convergence of some orthonormal expansions and their continuous analogues , S.I.U. Press, 1968, pp. 75-91.

[23] (with E. Rodemich and H. Rumsey) "On some extremal positive definite functions," J. Math. Mech., 18 (1969), 805-834.

[24] "Topics in almost everywhere convergence," Markham , Chicago, 1970. 154 pages research monograph.

[25] (with C. A. Greenhall) "Positive orthonormal systems," Acta. Math. Acad. Soc , Hungary, 21 (1970), 47-63.

[26] (with E. Rodemich and H. Rumsey) "A real variable lemma and the continuity of paths of Gaussian processes," Indiana University Math. J., 20 , No. 6 (1970), 565-578.

[27] "On the smoothness of functions satisfying certain integral inequalities," Proc. Functional Analysis Symposium , Academic Press, 1970, pp. 127-162.

[28] "Continuity properties of Gaussian processes with a multidimensional time parameter," Proc. of the VI Berkeley Symposium in Probability and Statistics , 1971, pp. 369-374.

[29] "An expose of the Mullin-Rota theory of polynomials of binomial type," J. Linear and Multilinear Algebra, 1 (1973), 47-65.

[30] "The Burgess Davis inequalities via Fefferman's inequality," Arkiv fur Mathematik, 11 , No. 2 (1973), 229-237.

[31] "On a convex function inequality for Martingales," Ann. Prob., 1 , No. 1 (1973), 171-174.

[32] (with E. Rodemich) "The monotonicity of certain functionals under rearrangement," Annales de l'Institut Fourier , T.XXIV F.2 (1974), 67-116.

[33] "Martingale inequalities," Seminar Notes on Recent Progress (184-page monograph), W. A. Benjamin Math. Lecture Note Series, 1973.

[34] "A remarkable inequality and the uniform convergence of Fourier series," Indiana Math. J., 25 , No. 1 (1976), 85-102.

[35] "Combinatorial inequalities and the smoothness of functions," Bull. Am. Math. Soc., 82 , No. 2 (1976), 157-170.

[36] (with M. Wachs) "A new algorithm for minimum cost binary trees," SIAM J. on Computing, 6 , No. 4 (1977), 622-642.

[37] (with J. Shapiro) "Polynomials of binomial type and Lagrange inversion," Proc. Am. Math. Soc., 64 , No. 4 (1977), 179-185.

[38] (with J. Shapiro) "Higher dimensional polynomials of binomial type and formal power series inversion," Communications in Algebra, 6 (1978), 1187-1215.

[39] "Some combinatorial methods in real analysis," Proc. of the Int'l Congress of Mathematicians , Helsinki, 1978, 331-340.

[40] "On the "maj" and "inv" q-analogues of Eulerian polynomials," Linear and Multilinear Algebra, 8 , No. 1 (1979-80), 21-34.

[41] (with D. Foata) "A combinatorial approach to Mehler's formulas for Hermite polynomials," Proc. of the Symposium on Relations Between Combinatorics and Other Parts of Mathematics , AMS, Columbus, Ohio, March 20-23, 1978, 34 , 1979, pp. 163-179.

[42] (with J. Remmel) "On the raising operators of A. Young," Proc. of the Symposium on Relations Between Combinatorics and Other Parts of Mathematics , Columbus, Ohio, March 20-23, 1978, 34 , 1979, pp. 181-198.

[43] (with I. Gessel) "Permutation statistics and partitions," Advances in Math., 31 , No. 3 (1979), 288-305.

[44] "Methodes combinatories dans la theorie des anneaux de Cohen-Macaulay," C. R. Acad. Sci ., Paris, 288 (1979), Serie A-371-374.

[45] (with S. A. Joni) "Composition sequences," Communications in Algebra, 8 (13) (1980), 1195-1266.

[46] (with J. Remmel) "A combinatorial interpretation of Q-derangement and Q-Laguerre numbers," European J. of Combinatorics, 1 (1980), 47-59.

[47] "Combinatorial methods in the theory of Cohen-Macaulay rings," Advances in Math., 38 (1980), 229-266.

[48] (with J. Remmel) "Symmetric functions and raising operators," Linear and Multilinear Algebra, 10 (1981), 15-43.

[49] (with K. Baclawski) "Combinatorial decompositions of a class of rings," Advances in Math., 39 (1981), 155-184.

[50] "A Q-analogue of the Lagrange inversion formula," Houston J. Math., 7 No. 2 (1981), 205-237.

[51] (with Stephen Milne) "A Rogers-Ramanujan bijection," J. Combinatorial Theory, Ser. A., 31 No. 3 (1981), 290-339.

[52] (with Stephen Milne) "Method for constructing bijections for classical partition identities," Proc. Nat'l Acad. Sci., USA, 78 (4) (April 1981), 2026-2028.

[53] (with J. Remmel) "A combinatorial view of Andrews' proof of the L-M-W conjectures," European J. Combinatorics , 6 (1985), 335-352.

[54] (with A. Bjorner and R. Stanley) "An introduction to Cohen-Macaulay partially ordered sets," Proc. of the Banff Conference on Ordered Sets , NATO Advanced Study Institute series C-83, D. Reider (1982), 583-615.

[55] (with D. Stanton) "Group actions on Stanley-Reisner rings and the construction of invariants," Advances in Math 351 (1984), 107-201.

[56] (with Y. M. Chen and J. Remmel ) "Algorithms for Plethysm", Contemporary Math. \# 34 . Combinatorics and Algebra , Curtis Greene ed. (1984) pp.

[57] (with J. Remmel), Shuffles of permutations and the Kronecker product, Graphs and Combinatorics, (1985) 217-263.

[58] (with J. Remmel) "q-Counting Rook placements and a formula of Frobenius", J. Comb. Theory, ser. A 341 (1986) 246-275.

[59] (with J. Remmel) "A novel form of q-Lagrange inversion", Houston J. of Math. V. 12 N. 4 (1986).

[60] "Raising operators and Young's Rule", Proceedings of the Montreal Colloquium of Enumerative Combinatorics, U.Q.A.M, Springer L. N. \# 1234 (1987).

[61] A. Garsia and T. McLarnan, Relations between Young's natural and the Kazhdan-Lusztig representations of $S_n$, Adv. in Math. V. 69, N. 1 May 1988 pp. 32,92.

[62] A. Garsia and M. Wachs, Combinatorial Aspects of Skew Representations of the Symmetric Group, J. Comb. Theory, {\bf A} V. 50 (1989) 47-81.

[63] A. Garsia and C. Reutenauer, A decomposition of Solomon's descent algebra, Adv. Math. {\bf 77} (1989) 189-262.

[64] A. Garsia, Combinatorics of the Free Lie Algebra and the Symmetric Group, Analysis et Cetera, (J\"rgen Moser festschrift), Academic Press (1990) 309-382.

[65] F. Bergeron, N. Bergeron and A. Garsia, Idempotents of the Free Lie Algebra and q-enumeration, Invariant Theory and Tableaux, The IMA volumes in Mathematics and its Applications, {\bf 19} Springer-Verlag (1990) 166-190.

[66] N. Bergeron and A. M. Garsia, Sergeev's Formula and the Littlewood-Richardson Rule, Linear and Multilinear Algebra, 27 (1990) 79-100.

[67] A. M. Garsia and C. Procesi, On certain graded $S_n$-modules and the q-Kostka polynomials, Advances in Mathematics {\bf 94} (1992) 82-138.

[68] N. Bergeron and A. M. Garsia, On Certain Spaces of Harmonic Polynomials, Hypergeometric Functions on domains of Positivity, Jack polynomials and Applicatioions, Contemporary Mathematics, {\bf 138} (1992) 51-86.

\item {[69] A. F. Bergeron, A. Garsia and C. Reutenauer, Homomorphisms between Solomon's descent algebras, Journal of Algebra, {\bf 150} \#2 (1992) 503-519.

[70] N. Bergeron and A. M. Garsia, Zonal Polynomials and Domino Tableaux, Discrete Mathematics {\bf 99} (1992) xxx-xxx.

[71] A. Garsia, Orthogonality of Milne's polynomials and raising operators, Discrete Mathematics {\bf 99} (1992) 247-264.

[72] A. Garsia, Recent Progress on the Macdonald q,t-Kostka conjecture, Actes du $4^e$ Colloque sur les S\'eries Formelles et Combinatoire Alg\'ebrique, U.Q.A.M. , Pub. L.A.C.I.M. Montr\'eal, (1992) 249-255.

[73] A. M. Garsia and M. Haiman, Factorizations of Pieri rules for Macdonald polynomials, To appear in the Proceedings of the $IV^{th}$ Colloquium on Algebraic Combinatorics

[74] A. M. Garsia and M. Haiman, A Graded Representation Model for Macdonald's Polynomials, Proceedings of The National Academy.

[75] A. Garsia and M. Haiman, Some bigraded $S_n$-modules and the Macdonald q,t-Kotska coefficients, (in preparation)

[76] A. 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)

[77] A. Garsia and M. Haiman, Some remarkable q,t-analogues of the Catalan numbers,

[] A. Garsia and M. Zabrocki, Polynomiality of the q,t-Kotska revisited To appear in a Volume dedicated to the memory of G. C. Rota edited by Domenico Senato U. of Basilicata. math.QA/0008199

[] A. M. Garsia and M. Haiman, Factorizations of Pieri rules for Macdonald polynomials Discrete Mathematics 139 (1995) 219-256.

[] A. M. Garsia and J. Haglund, A Proof of the q,t-Catalan Positivity Conjecture Submitted to Discrete Math,

[] A. M. Garsia The Saga of Reduced Factorizations of Elements of the Symmetric Group

[] A. M. Garsia Pebbles and expansions in the Polynomial ring

[] A. M. Garsia and N. Wallach Qsym over Sym is Free