Mark A Adler

Professor of Mathematics

Departments/Programs

Mathematics

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. Webpage

Courses 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	141a	Real Analysis
MATH	141b	Complex Analysis
MATH	164a	Partial Differential Equations
MATH	212b	Functional Analysis

Awards and Honors

elected Fellow of the American Math Society (FAMS) (2019)

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, K. Johansson, P. van Moerbeke. "A Singular Toeplitz determinant and the discrete tacnode Aztec Diamond." arXiv arXix:1912.02511. (2020)

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.