# The schedule and extra material of the Research experience program

# "On level crossing in (random) matrix pencils", June-July 2015

This program will concentrate on (random) plane curves obtained from pencils of (random) matrices, their branching points and monodromy.
Notice that below you will find a lot of unpublished material for internal use only. If you want to spread this, please,
send a message to shapiro@math.su.se. This site will be regularly updated.
Lecture notes by B.Shapiro,
# Schedule of meetings, June-July 2015

June 15, 10.00. rm. 345 AH, Introductory lecture 1
June 16, 10.00. rm. 345 AH, Introductory lecture 2
June 17, 10.00. rm. 345 AH, Introductory lecture 3
June 18, 10.00. rm. 345 AH, Introductory lecture 4
June 19, 10.00. rm.345 AH, Problem formulation and division into groups
Starting from Monday, June 22 and through Friday, July 24, we meet three times a week in rm 159:
Monday. Group 1: 9.00 -- 10.30; Group 2: 10.30 --12.00; Group 3: 13.00 -- 14.30
Thursday. Group 1: 9.00 -- 10.30; Group 2: 10.30 --12.00; Group 3: 13.00 -- 14.30
Friday. All groups 10.00 - 12.00
Group 1 (Complex Gaussian ensembles) : Hadrian Quan, Ruquan Chen, Raemeon Cowan, Elliot Kaplan
Group 2 (Gaussian Unitary and Gaussian orthogonal ensembles) : Emily Heath, Dara Zirlin, Matthew Ellis, Chris Lindon, Ian Ford, Sebastian Sanchez
Group 3 (monodromy of random bivariate polynomials): Julian Caballero, Joseph Rennie, Mary Angelica Tursi, Lan Wang
# Some publications related to the project,

# "On level crossing in (random) matrix pencils",

A.Galligo, A.Poteaux
"COMPUTING MONODROMY VIA CONTINUATION METHODS ON RANDOM RIEMANN SURFACES",
B.Valko
"Random matrices", lectures 2-5
B.Valko
"Random matrices", lectures 8-9
M.Mehta
"Random matrices", Ch.3
M.Mehta
"Random matrices", Ch.4
M.Mehta
"Random matrices", Ch.5
O.Foster
"Lectures on Riemann surfaces",
C.Teleman
"Riemann surfaces", Lecture notes, 2003.
P.Bleher, A.Its, eds,
"Random matrix models and their applications ", selected papers, 2011.
J.Harris,
"Geometry of algebraic curves", course lectures, 2001.
A.Ding,
"Plane algebraic curves", course lectures, 2012.
R.Miranda,
"Algebraic Curves and Riemann Surfaces", Graduate Studies in Math. vol. 5, 1995
F.Beukers,
"Notes on algebraic curves", course lectures, 2011.
C.Fischer,
"Plane Algebraic Curves", book, 2011.
S.Kargin, E.Yudovina,
"Random matrix theory", lecture course, 2011.
P.Diaconis, M.Shahshahani,
"On the Eigenvalues of Random matrices", J. Appl. Prob., Studies in Appl. Prob. v. 31, (1994), 49--62.
G.Anderson, A.Guionnet, O.Zeitouni,
"An Introduction to Random matrices", Cambridge Univ. Press, 2009
O.Angel, A.Holroyd, D.Romik, B. Virag,
"Random sorting networks", article sept. 2009
T.Tao,
"The asymptotic distribution of a single eigenvalue gap of a Wigner matrix", preprint, august 2012
J.Ongaro, B.Shapiro
"A note on planarity stratification of Hurwitz spaces", article, 2015
J.Ongaro,
"Plane Hurwitz numbers", November, 2014
C.Tracy, H.Widom
"Introduction to Random Matrices", article, Oct. 1992
M. Zirnbauer, J. Verbaarschot, and H. Weidenmueller,
"Destruction of order in nuclear spectra by a residual GOE interaction", article, July 1983
R. Quarez,
"Symmetric determinant representation of polynomials", article, 2012