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 Notice that below you will find a lot of unpublished material for internal use only.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