Michael Schlosser's Home Page
Dr. Michael J. Schlosser
_{X}
Fakultät für
Mathematik
Universität Wien
OskarMorgensternPlatz 1
A1090 Wien
Austria
telephone:

(+431) 427750455

fax:

(+431) 4277850455

email:


Aktuelle Lehre.
Current Teaching.
Sprechstunden nach Vereinbarung,
OMP1,
Zimmer 11.124
Office hours by appointment,
OMP1,
Room 11.124
Scientific publications (in reverse chronological order):
 Papers:
 Bilateral identities
of the RogersRamanujan type
[25 pp., preprint]

Hypergeometric and basic hypergeometric series and integrals
associated with root systems
[Book chapter for the vol. "Multivariable Special Functions"
of the new
AskeyBateman Project, a multivolume Encyclopedia of Special Functions
(ser. eds. M. E. H. Ismail and
W. Van Assche;
vol. eds. T. H. Koornwinder and
J. Stokman),
Cambridge Univ. Press; 39 pp., to appear]

Wronskians of theta functions and series for $1/\pi$
(jointly with Alex Berkovich
and Heng Huat Chan)
[Adv.
Math. 338 (2018), 266304]

Combinatorial interpretations of Ramanujan's tau function
(jointly with Frank Garvan)
[Discrete
Math. 341 (2018), 28312840]

Weightdependent commutation relations and
combinatorial identities
(jointly with Meesue Yoo)
[Discrete
Math. 341 (2018), 23082325]

Elliptic wellpoised Bailey transforms and lemmas over root systems
(jointly with Gaurav Bhatnagar)
[SIGMA
14 (2018), 025, 44 pp.]

Summation formulae for noncommutative hypergeometric series
[in
Frontiers
in Orthogonal Polynomials and $q$Series
(Z. Nashed and
X. Li, eds.),
World Scientific, 2018, pp. 451496]

$q$Analogues of two product formulas of hypergeometric functions by Bailey
[in
Frontiers
in Orthogonal Polynomials and $q$Series
(Z. Nashed and
X. Li, eds.),
World Scientific, 2018, pp. 445449]

Basic hypergeometric summations from rook theory
(jointly with Meesue Yoo)
[in Analytic Number
Theory, Modular Forms and $q$Hypergeometric Series in Honor of
Krishna Alladi's
60th birthday, University of Florida,
Gainesville, March 2016
(G.E. Andrews
and F. Garvan, eds.),
Springer
Proc. Math. Stat. 221 (2017), 677692]

Elliptic rook and file numbers (jointly with Meesue Yoo)
[Electron. J. Combin.
24(1) (2017), #P1.31, 47 pp.]

Elliptic extensions of the alphaparameter model
and the rook model for matchings (jointly with Meesue Yoo)
[Adv. Appl. Math. 84 (2017), 833]

$q$Stirling numbers of the second kind and
$q$Bell numbers for graphs (jointly with Zsófia R.
Kereskényiné Balogh)
[Electronic
Notes Discr. Math. 54 (2016), 361366]

Elliptic hypergeometric summations by
Taylor series expansion and interpolation (jointly with Meesue Yoo)
[SIGMA
12 (2016), 039, 21 pp.]

An elliptic extension of the general product formula for augmented
rook boards (jointly with Meesue Yoo)
[Europ.
J. Combin. 58 (2016), 247266]

Elliptic rook and file numbers
(jointly with Meesue Yoo),
DMTCS
proc. FPSAC'16, 2016, 10871098.

Some combinatorial identities involving noncommuting variables
(jointly with Meesue Yoo),
DMTCS
proc. FPSAC'15, 2015, 961972.

The major index generating function of standard Young tableaux of shapes
of the form "staircase minus rectangle" (jointly with
Christian
Krattenthaler)
[in Ramanujan 125 (K. Alladi
and F. Garvan, eds.),
Amer. Math. Soc.,
Providence, R. I., Contemp.
Math. 627 (2014), 111122]

On the work of Igor Frenkel (jointly with
John Duncan,
Pavel Etingof,
Ivan Ip,
Mikhail Khovanov,
Matvei Libine,
Anthony Licata,
and
Alistair Savage)
[in Perspectives in Representation Theory
(P. Etingof,
M. Khovanov, and
A. Savage, eds.),
Amer. Math. Soc.,
Providence, R. I., Contemp.
Math. 610 (2014), 121]

Multiple hypergeometric series  Appell series and beyond
[in Computer Algebra in Quantum Field Theory:
Integration, Summation and Special Functions
(J. Blümlein and
C. Schneider, eds.),
Texts & Monographs in
Symbolic Computation,
SpringerVerlag,
Heidelberg/Vienna, 2013; pp. 305324]

On an identity by Chaundy and Bullard. II. More history
(jointly with
Tom H. Koornwinder)
[Indag.
Math. (N.S.) 24 (1) (2013), 174180]

New curious bilateral $q$series identities
(jointly with
Frédéric
Jouhet)
[Axioms
2012, 1 (3), 365371]

A noncommutative weightdependent generalization of the binomial theorem
[23 pp., preprint]

Recurrence formulas for Macdonald polynomials of type $A$
(jointly with
Michel Lassalle)
[J.
Algebraic Combin. 32 (1) (2010), 113131]

Noncommutative hypergeometric and basic hypergeometric equations
(jointly with
Alessandro Conflitti)
[J.
Nonlinear Math. Phys. 17 (4) (2010), 429443]

Theta functions, elliptic hypergeometric series, and Kawanaka's Macdonald
polynomial conjecture (jointly with Robin Langer and
S. Ole Warnaar)
[SIGMA
5 (2009), 055, 20 pp.]

Multilateral inversion of $A_r$, $C_r$ and $D_r$
basic hypergeometric series
[Ann.
Comb. 13 (2009), 341363]

On an identity by Chaundy and Bullard. I
(jointly with
Tom H. Koornwinder)
[Indag.
Math. (N.S.) 19 (2) (2008), 239261]

A Taylor expansion theorem for an elliptic extension
of the AskeyWilson operator
[in Special
Functions and Orthogonal Polynomials
(D. Dominici and
R. S. Maier, eds.),
Amer. Math. Soc.,
Providence, R. I., Contemp.
Math. 471 (2008), 175186]

A new multivariable $_6\psi_6$ summation formula
[Ramanujan
J. 17 (3) (2008), 305319]

Curious extensions of Ramanujan's $_1\psi_1$ summation formula
(jointly with
Victor J. W. Guo)
[J. Math. Anal. Appl. 334 (1) (2007),
393403]
 Macdonald
symmetric functions for partitions with complex parts
[FPSAC'07,
Nankai University, Tianjin, China, 10 pp.]

Macdonald polynomials and multivariable basic hypergeometric series
[Vadim
Kuznetsov Memorial Issue on Integrable Systems and Related
Topics,
SIGMA
3 (2007), 056, 30 pp.]

Elliptic enumeration of nonintersecting lattice paths
[J. Combin. Theory Ser. A 114 (3) (2007),
505521]

Some curious $q$series expansions and beta integral
evaluations
(jointly with
George Gasper)
[Ramanujan
J. 13 (13) (2007), 229242]

Elliptic determinant evaluations and the Macdonald identities for affine
root systems
(jointly with
Hjalmar Rosengren)
[Compos. Math.
142 (4) (2006), 937961]

Noncommutative extensions of Ramanujan's $_1\psi_1$ summation
[Electron. Trans.
Numer. Anal. 24 (2006), 94102]

Explicit computation of the $q,t$LittlewoodRichardson
coefficients
[Proceedings
of the Workshop on Jack,
HallLittlewood and Macdonald polynomials (V. Kuznetsov
and S. Sahi, eds.) Edinburgh, ICMS, Sept. 2326, 2003;
Contemp.
Math. 417 (2006), 335343]

Inversion of the Pieri formula for Macdonald polynomials
(jointly with
Michel Lassalle)
[Adv.
Math. 202 (2) (2006), 289325]

Summation, transformation, and expansion formulas for
multibasic theta hypergeometric series
(jointly with
George Gasper)
[Adv. Stud. Contemp. Math. (Kyungshang) 11 (2005), no. 1, 6784;
also in
Proceedings
of the Workshop Elliptic
Integrable Systems (M. Noumi
and K. Takasaki,
eds.) Kyoto,
RIMS, 2004;
Rokko Lectures
in Mathematics 18 (2005), 117]

Another proof of Bailey's $_6\psi_6$ summation
(jointly with
Frédéric
Jouhet)
[Aequationes
Math. 70 (12) (2005), 4350]

On Warnaar's elliptic matrix inversion and KarlssonMintontype elliptic
hypergeometric series
(jointly with
Hjalmar Rosengren)
[J.
Comput. Appl. Math. 178 (2005), 377391]

AbelRothe type generalizations of Jacobi's triple product identity
[in Theory
and Applications of Special Functions. A Volume Dedicated to Mizan Rahman
(M. E. H. Ismail and
E. Koelink, eds.),
Dev.
Math. 13 (2005), 383400]

$q$Analogues of the sums of consecutive integers, squares, cubes,
quarts and quints
[Electron. J. Combin.
11 (1) (2004), #R71, 12 pp.]

Some curious extensions of the classical beta integral evaluation
[in Mathematics
and Computer Science, III (M. Drmota,
P. Flajolet,
D. Gardy,
B. Gittenberger, eds.)
Vienna, 2004; Trends
Math., Birkhäuser, Basel, 2004, pp. 5968]

An analytic formula for Macdonald polynomials
(jointly with
Michel Lassalle)
[C.
R. Math. Acad. Sci. Paris 337 (9) (2003), 569574]

Summations and transformations for multiple basic and
elliptic hypergeometric series by determinant evaluations
(jointly with
Hjalmar Rosengren)
[Indag.
Math. (N.S.) 14 (2003), 483514]

A nonterminating $_8\phi_7$ summation for the root system $C_r$
[J.
Comput. Appl. Math. 160 (2003), 283296]

Inversion of bilateral basic hypergeometric series
[Electron. J. Combin.
10 (2003), #R10, 27 pp.]

A multidimensional generalization of Shukla's $_8\psi_8$ summation
[Constr.
Approx. 19 (2003), 163178]

Elementary derivations of identities for bilateral basic hypergeometric
series
[Selecta
Math. (N.S.) 9 (2003) 1, 119159]

A new $A_n$ extension of Ramanujan's $_1\psi_1$
summation with applications to multilateral basic hypergeometric
series (jointly with
Stephen C. Milne)
[in Special Functions 2000
(J. Bustoz and
S. K. Suslov, eds.),
Rocky Mount. J. Math. 32 (2) (2002), 759792]

A simple proof of Bailey's verywellpoised $_6\psi_6$ summation
[Proc.
Amer. Math. Soc. 130 (2002), 11131123]

Multilateral transformations of $q$series with quotients of parameters
that are nonnegative integral powers of $q$
[in $q$Series
with Applications to Combinatorics, Number Theory, and Physics
(B. C. Berndt and
K. Ono, eds.),
Amer. Math. Soc.,
Providence, R. I., Contemp.
Math. 291 (2001), 203227]

A new multidimensional matrix inversion in $A_r$
[in $q$Series from a Contemporary Perspective
(M. E. H. Ismail and
D. Stanton, eds.),
Amer. Math. Soc.,
Providence, R. I., Contemp.
Math. 254 (2000), 413432]

Summation theorems for multidimensional basic
hypergeometric series by determinant evaluations
[Discrete
Math. 210 (2000), 151169]

Some new applications of matrix inversions in $A_r$
[Ramanujan
J. 3 (1999), 405461]

A new multidimensional matrix inverse with applications to multiple
$q$series (jointly with
Christian
Krattenthaler)
[(H. W. Gould Anniversary Volume)
Discrete
Math. 204 (1999), 249279; selected to be included in
Discrete
Math., spec. vol. ``Editors' Choice, Edition 1999'']

Multidimensional matrix inversions and multiple basic hypergeometric
series associated to root systems
[in Special
functions and differential equations
(K. Srinivasa Rao,
R. Jagannathan,
G. Vanden Berghe, and
J. Van der Jeugt, eds.),
Proceedings of a workshop, WSSF '97, Madras, India, January 1324, 1997;
Allied Publ., New Delhi (1998), 2530]

$C_n$ and $D_n$ verywellpoised $_{10}\phi_9$ transformations
(jointly with Gaurav Bhatnagar)
[Constr.
Approx. 14 (1998), 531567]

Multidimensional matrix inversions and $A_r$ and $D_r$
basic hypergeometric series
[Ramanujan
J. 1 (1997), 243274]

Multidimensional matrix inversions
[Sém. Lothar. Combin.
35 (1995), B35g, 24 pp.]
 Books and special issues edited:
 Topics in QSeries
(jointly with M. E. H. Ismail
and D. Stanton),
Special Issue of
Integral Transforms and
Special Functions,
in process (submission deadline: December 31, 2018).
 Elliptic
Hypergeometric Functions and Their Applications
(jointly with S. V. Spiridonov and
S. Ole Warnaar),
Special Issue of
SIGMA,
in process (submission deadline: January 31, 2018).

Ramanujan
Rediscovered (jointly with
N. D. Baruah,
B. C. Berndt,
S. Cooper and
T. Huber),
Proceedings of a Conference on Elliptic Functions, Partitions, and
$q$Series in Memory of K. Venkatachaliengar, Bangalore (15 June, 2009);
Ramanujan Mathematical Society
Lecture Notes Series, Vol. 14, 2010
(also published by International Press, Somerville, MA, USA, 2012)
Editorial boards:
Postdocs:
 Current:
 Past:
 Meesue Yoo
 Alessandro Conflitti
Ph.D. students:
 Current:
 Josef Küstner
 Gülşen Serin
 Zsófia Kereskényiné Balogh
 Past:
Selected events:

15th
International Symposium on Orthogonal Polynomials, Special Functions
and Applications (RISC, Hagenberg, July 2226, 2019)

Topics on Orthogonal
Matters Fest, An informal gathering to celebrate Tom Koornwinder's
75th birthday (Radboud University, Nijmegen, December 1011, 2018)

81st Séminaire
Lotharingien de Combinatoire (KrattenthalerFest) 2018
(Strobl, September 912, 2018)

ESI Workshop
Elliptic Hypergeometric Functions in Combinatorics,
Integrable Systems and Physics (Vienna, March 2024, 2017)
Curiosities:

Would you like to see me
play
(and lose) against one of today's best players of the world?
However, I am (or was) also able to win games
here and
there.