# Mark A Adler

Degrees

New York University, Ph.D.Cooper Union, B.S.

Expertise

Analysis and Probability Theory, Differential equations,Completely integrable systems,Random matrix theory.Profile

Although I was trained in the general area of differential equations and analysis, I have mostly worked as a mathematical physicist, involved in mathematical problems related to physics. This has lead me to study integrable systems, matrix models and finally random matrices, the latter which is part of statistical mechanics. In order to do research in these topics, I needed to learn to some extent, differential geometry, Lie algebra, algebraic geometry,combinatorics and finally probability theory, so i am a jack of all trades, mathematically speaking. WebpageCourses Taught

MATH | 20a | Multi-variable Calculus |

MATH | 35a | Advanced Calculus and Fourier Analysis |

MATH | 36a | Probability |

MATH | 36b | Mathematical Statistics |

MATH | 37a | Differential Equations |

MATH | 102a | Introduction to Differential Geometry |

MATH | 126a | Introduction to Stochastic Processes and Models |

MATH | 141a | Real Analysis |

MATH | 141b | Complex Analysis |

MATH | 212b | Functional Analysis |

Awards and Honors

Appointed Research Professor at Mathematical Sciences Research Institute in Random Matrix program (2011)

National Science Foundation research grant (2001)

Sloan Fellowship (1981 - 1983)

Two math awards at Cooper Union (1969)

Scholarship

Adler, Mark A, Johansson,K.,van Moerbeke,P.. "Tilings of non-convex Polygons, skew-Young Tableaux and determinantal processes." __Comm. in Math. Physics__ Vol. 364. No. 1 (2019): 288-342.

Adler, Mark A, van Moerbeke,P.. "Probability Distributions for Random Tilings of Non-convex Polygons." __Journal of Math. Physics__ 59. (2019).

Adler, Mark A, van Moerbeke,P.. "The AKS theorem, A.C.I. syatems and random matrix theory." __J. Phys. A: Math. Theor.__ 51. (2019): 2-47.

P. Ferrari,.., Mathematical Physics,Analysis and Geometry, ed. __A New Universality Class arising from random Lozenge Tilings of Non-convex Polygons__. Springer, 21 2018.

Adler, Mark A, S. Chhita,K. Johansson,P. van Moerbeke, ed. __Tacnode GUE-minor Processes and Double Aztec Diamonds__. p.275-375: Prob. Theory,Related Fields, 162 2015.

Adler, Mark A, ed. __Double Aztec Diamonds__. Advances of Math: Vol. 252, p. 518-571 2014.

Adler,M, ed. __Consecutive Minors for Dyson's Brownian Motion__. Stochastic Processes and Their Applications: Vol. 124, Issues6, p. 2023-2051 2014.

Adler, Mark A, ed. __Non-Intersecting random walks in the neighborhood of a symmetric tacnode__. Ann. Prob.: Vol.41,No. 4, p. 2599-2647 2013.

Adler, Mark A, ed. __Random matrix minor processes related to percolation theory__. Random Matrices, Theory and Application: Vol.2 ,Issue 4, p. 1-72 2013.

Adler, Mark A. "From the Pearcey to the Airy process." __Electronic Journal of Probabilty__ 16. (2012): 1048-106

Adler, Mark A. "Non-intersecting Brownian Motions Leaving from and going to Several Points." __Physica D: Nonlinear Phenomena__ Issue 5. (2012): p. 443-460.

Adler, Mark A. "Nonlinear PDEs for gap probabilities in random matrices and KP theory." __Physica D: Nonlinear Phenomeana__ 241. 23-24 (2012): 2265-2284.

Adler, Mark A. "Spectral statistics of orthogonal and symplectic ensembles." __The Oxford Handbook of Random Matrix Theory__. vol. 1 Ed. G. Akemann, J. Baik and P. Di Franco. Oxford: Oxford University Press, 2011. 86-102.

Adler, Mark A. __Integrable Systems,Random matrices and Random processes__. Proc. of Random matrices,Random processes and Integrable Systems. Montreal: Springer, 2011.

Adler, Mark A, ed. __Airy Processes with Wanderers and New Universality Classes__. 38,no.2 2010.

Adler, Mark A, ed. __Dyson's non-intersection Brownian motions with a few outliers__. New York: Wiley Periodicals, 62 2010.

Adler, Mark A. "Universality of the Pearcey Process." __arXiv:Math-pr 10901.4520__ Math-pr 10901. 4520 (2010)

Adler, Mark A, van Moerbeke,P., ed. __PDE's for the Gaussian Ensemble with external source and the Pearcey distribution__. Comm. Pure and Applied Math., 60,no.9 2009.

Adler, Mark A, Borodin,A.,Van Moerbeke, P., ed. __Expectations of hook products on large partitions__. Forum Math., 19,no.1 2007.