Mihai Stoiciu

Stoiciu

  • B.S. Mathematics, University of Bucharest.
  • Ph.D. Mathematics, California Institute of Technology.

 

Publications

  • An estimate for the number of bound states of the Schrödinger operator in two dimensions, Proc. Amer. Math. Soc. 132 (2004), 1143-1151.  The pdf, dvi and ps files are posted here.
  • Zeros of Random Orthogonal Polynomials on the Unit Circle, Ph.D. Thesis at Caltech, June 2005. The pdf file is posted here.
  • The statistical distribution of the zeros of random paraorthogonal polynomials on the unit circle, J. Approx. Theory  39 (2006), 29-64. [pdf]
  • The Eigenvalue Distribution of Random Schrödinger Operators and CMV Matrices, Mathematisches Forschunginstitut Oberwolfach Report, 9/2006, 20-22. The pdf file is posted here.
  • Poisson Statistics for Eigenvalues: From Random Schrödinger Operators to Random CMV Matrices, CRM Proceedings and Lecture Notes, volume 42, 2007, 465-475. The pdf file is posted here.
  • (with J.B. Friedlander and F. Luca) On the Irrationality of a Divisor Function Series, Integers 7 (2007), A31, 9 pp. (electronic). The pdf file is posted here.
  • (with R. Killip) Eigenvalue Statistics for CMV Matrices: From Poisson to Clock via Random Matrix Ensembles, Duke Mathematical Journal 146 (2009), no.3, 361-399. The pdf file is posted here.
  • (with K. Gittins, N. Peyerimhof, and D. Wirosoetisno) Some Spectral Applications of McMullen’s Hausdorff Dimension Algorithm, Conform. Geom. Dyn. 16 (2012), 184-203. The pdf file is posted here.
  • Spectral properties of Random and Deterministic Matrices, Math. Model. Nat. Phenom., Vol.  9, No. 5 (2014), 270-281. The pdf file is posted here: MMNP_Paper.
  • (with F. Gong, O. Meyerson, J. Meza, and A. Ward) Explicit Bounds for the Pseudospectra of Various Classes of Matrices and Operators,  Involve, Vol.  9, No. 3 (2016), 517-540.  The pdf file is posted here: PseudospectraGMMSW.

 

Current Teaching

 

Recent Teaching

  • Spring 2020: Math 341 – Probability
  • Fall 2019: Math 102T – Foundations in Quantitative Skills, Math 404 – Random Matrix Theory
  • Spring 2017: Math 402 – Measure Theory and Probability
  • Fall 2016: Math 102T – Foundations in Quantitative Skills, Math 318T – Numerical Problem Solving
  • Spring 2016: Math 150 – Multivariable Calculus
  • Winter Study 2016: Math 100 – Mathematics Immersion
  • Fall 2015: Math 102T – Foundations in Quantitative Skills, Math 401 – Functional Analysis

 

Undergraduate Research Supervised

Williams College “SMALL” REU, June-August 2007, Mathematical Physics Group: James Arnemann, Scott Smedinghoff, Miles Wheeler, Sunmi Yang. Project: “Clock Theorems for Eigenvalues of Finite CMV Matrices”. The pdf file is posted here.

Williams College “SMALL” REU, June-August 2010, Mathematical Physics Group: Matthew Coudron, Amalia Culiuc, Philip Vu, Stephen Webster. Project: “Spectral Analysis of Non-Hermitian Matrices”. The pdf file is posted here.

Williams College “SMALL” REU, June-August 2014, Mathematical Physics Group: Feixue Gong, Olivia Meyerson, Jeremy Meza, Abigail Ward. Project: “Explicit Bounds for the Pseudospectra of Various Classes of Matrices and Operators”. The pdf file is posted here: SMALL_2014_Paper

Williams College “SMALL” REU, June-August 2018, Mathematical Physics Group: Michael Curran, Eli Cytrynbaum, Benjamin Foster, Miriam Gordin. Project: “Questions in Random Matrix Theory”. The pdf file is posted here: Random_Matrix_Theory

Honors (thesis) students:

  • Brian Simanek ’07 – “Spectral Properties of Random Unitary Band Matrices”. pdf file
  • Sunmi Yang ’08 – “A Numerical Analysis of the Spectrum of the Almost Mathieu Operator”. pdf file
  • Irina Zhecheva ’08 – “Ergodic Properties of Random Schrödinger Operators”. pdf file
  • Zhaoning Nancy Wang ’11 – “Sturm-Liouville Oscillation Theory for Differential Equations and Applications to Functional Analysis”. pdf file
  • Gregory White ’12 – “Stochastic Calculus and Applications to Mathematical Finance”. pdf file
  • Liyang Zhang ’12 – “Spectral Theory for Matrix Orthogonal Polynomials on the Unit Circle”. pdf file
  • Nicholas Gardner ’15 – “History Dependent Stochastic Processes and Applications to Finance”. Neeko_Gardner_Thesis
  • Andy Yao ’17 – “Spectral Analysis of New Classes of Deterministic and Random Orthogonal Polynomials on the Unit Circle”. Andy_Yao_Thesis
  • Alexander Bank ’20 – “Asymptotic Expansions for Bounds of Epsilon-Pseudospectra of Nonnormal Matrices”. Alex_Bank_Thesis
  • Eli Cytrynbaum ’20 – “Point Process Convergence and the Circular Beta Ensemble”. Eli_Cytrynbaum_Thesis

Contact Information
E-mail: [email protected]
Office: 206 Bascom House
Phone: (413) 597-2428
Fax: (413) 597-4061
Mailing address: Williams College, Department of Mathematics and Statistics, Williamstown, MA 01267, USA

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