A ``general
audience'' seminar on asymptotics of zeroes of polynomials
(open with Acrobat Reader version 7 or later to see the
animations)
M. Bertola,
M. Gekhtman, J. Szmigielski, “Cubic String Boundary Value
Problems and Cauchy Biorthogonal Polynomials”, arXiv:0904.2188.
M. Bertola,
M. Gekhtman, J. Szmigielski, “Cauchy Biorthogonal Polynomials”,
arXiv:0904.2602.
M. Bertola,
S. Y. Lee, M. Y. Mo, “Mesoscopic colonization of a spectral
band”, arXiv:0904.1171.
M. Bertola,
A. PratsFerrer, “Topological Expansion for the Cauchy
MatrixModel”, arXiv:0903.2512.
M. Bertola,
“The dependence of the monodromy data of the isomonodromic tau
function”, arXiv:0902.4716.
M. Bertola,
“Moment determinants as
isomonodromic tau functions”, arXiv:0805.0446,
Nonlinearity, 22(2009),
no. 1, 2950.
M.
Bertola, O. Marchal, “The
partition function of the two—matrix model as an isomonodromic
tau—function”, Journal of Mathematical Physics, 50(2009),
no. 1, 013529, 17pp.
M. Bertola,
S. Y. Lee, “First
colonization of a hardedge in random matrix theory”,
Constructive Approximation, in press (2009).
M. Bertola,
M. Gekhtman, J. Szmigielski, “The
Cauchy two—matrix model”, Communications in Mathematical
Physics, 287 (2009), no. 3, 9831014.
F. Balogh,
M. Bertola, “Regularity
of a vector potential problem and its spectral curve”,
Journal of Approximation Theory, in press (2009).
M. Bertola,
A. PratsFerrer, “HarishChandra
integrals as nilpotent integrals”, Int. Math. Res. Not.
IMRN 2008, no.16, Art. ID rnn062, 15pp.
M. Bertola,
M. Gekhtman, J. Szmigielski, “Peakons
and Cauchy Biorthogonal Polynomials”, arXiv:0711.4082,
submitted.
M. Bertola,
S. Y. Lee, “First
Colonization of a Spectral Outpost in Random Matrix Theory”,
Constructive Approximation DOI:10.1007/s003650089026y, in
press.
M. Bertola,
“Boutroux
curves with external field: equilibrium measures without a
variational problem”, arXiv:0705.3062, submitted (open with
Acrobat Reader 7 or later to see the animations.)
M. Bertola,
M. Gekhtman, “Effective
inverse spectral problem for rational Lax matrices and
applications”, International Mathematical Research Notices
(IMRN), 2007 Volume 2007: article ID rnm103, 39 pages
DOI:10.1093/imrn/rnm103
M. Bertola,
M. Y. Mo, “Commuting
difference operators, spinor bundles and the asymptotics of
orthogonal polynomials with respect to varying complex weights”,
Advances in Mathematics 220 (2009), pp. 154218
DOI:10.1016/j.aim.2008.09.001
M. Bertola,
M. Gekhtman, "Biorthogonal
Laurent polynomials, Toeplitz determinants, minimal Toda orbits
and isomonodromic tau functions", Constructive
Approximation (2007) OF1OF48, DOI:10.1007/s0036500606561
M. Bertola,
“Biorthogonal polynomials for
twomatrix models with semiclassical potentials.” J.
Approx. Theory 144 (2007), no. 2, 162—212.
M. Bertola,
“Twomatrix model with
semiclassical potentials and extended Whitham hierarchy”,
J. Phys. A 39 (2006), no. 28, 8823—8855.
M. Bertola,
B. Eynard, J. Harnad, "Semiclassical
orthogonal polynomials, matrix models and isomonodromic tau
functions", Communications in Mathematical Physics
(2006), Vol. 263, Issue 2, pp. 401437,
DOI:10.1007/s0022000515054
M. Bertola,
M. Y. Mo, "Isomonodromic
deformation of resonant rational connections",
International Mathematical Research Papers (IMRP) Volume 2005
(2005) Issue 11, pag. 565635, DOI:10.1155/IMRP.2005.565
M. Bertola,
``Bilinear
semiclassical moment functionals and their integral
representation'' J. Approx. Theory 121
(2003), no. 1, 7199, DOI:10.1016/S00219045(02)000448
M. Bertola,
“Second and
third order observables of the two—matrix model.”, J.
High Energy Phys. 2003, no. 11, 062, 30 pp. (electronic).
M. Bertola,
B. Eynard, J. Harnad, “Differential
systems for biorthogonal polynomials appearing in 2—matrix
models and the associated Riemann—Hilbert problem”, Comm.
Math. Phys. 243 (2003), no. 2, 193—240.
M. Bertola,
B. Eynard, J. Harnad, “Duality,
biorthogonal polynomials and multi—matrix models”, Comm.
Math. Phys. 229 (2002), no. 1, 73—120.
M. Bertola,
``Free Energy of the twomatrix
model/dToda taufunction'', Nucl. Phys B 669,
no. 3 435461 (2003).
M. Bertola,
B. Eynard, J. Harnad, ``The duality
of spectral curves that arises in twomatrix models'', Theor.
Math. Phys. 134 (2003), no. 1, 2738
M. Bertola,
J. Bros, V. Gorini, U. Moschella, R. Schaeffer, ``Decomposing
Quantum Fields on Branes'', Nuclear Phys. B 581
(2000), 575603
