
Rossi, Hugo
by Hugo Rossi.

Bekerman, Florent
In this thesis, we investigate the local and global properties of the eigenvalues of [beta]ensembles. A lot of attention has been drawn recently on the universal properties of [beta]ensembles, and how their local statistics relate to those of Gaussian ensembles. We use transport methods to prove universality of the eigenvalue gaps in the bulk and at the edge, in the single cut and multicut regimes. In a different direction, we also prove Central Limit Theorems for the linear statistics of [beta]ensembles at the macroscopic and mesoscopic scales.

Grant, David R., MD, FRCSC
by David R. Grant.

Kleppe, Hans
by Hans Kleppe.

Baker, Mark David
by Mark David Baker.

Ritter, Niles David
by Niles David Ritter.

Kwiatkowski, David Joseph
Thesis. 1975. Ph.D.Massachusetts Institute of Technology. Dept. of Mathematics.

Poulsen, Niels Kristian Skovhus
Thesis (Ph. D.)Massachusetts Institute of Technology, Dept. of Mathematics, 1970.

Magnuson, Alan William
by Alan William Magnuson.

Smith, William Allan
Massachusetts Institute of Technology. Dept. of Mathematics. Thesis. 1966. Ph.D.

Bavarian, Mohammad
Parallel repetition is a fundamental operation for amplifying the hardness inherent in multiplayer games. Through the efforts of many researchers in the past two decades (e.g. Feige, Kilian, Raz, Holentstein, Rao, Braverman, etc.), parallel repetition of twoplayer classical games has become relatively wellunderstood. On the other hand, games with entangled players (quantum games), crucial to the study of quantum nonlocality and quantum cryptography, and multiplayer games were poorly understood until recently. In this thesis, we resolve some of the major problems regarding the parallel repetition of quantum and multiplayer games by establishing the first exponentialrate hardness amplification results for these...

Rush, David B., Ph. D. Massachusetts Institute of Technology
Let G be a connected complex reductive algebraic group with Lie algebra g. The LusztigVogan bijection relates two bases for the bounded derived category of Gequivariant coherent sheaves on the nilpotent cone 11 of g. One basis is indexed by ..., the set of dominant weights of G, and the other by [Omega], the set of pairs ... consisting of a nilpotent orbit ... and an irreducible Gequivariant vector bundle ... The existence of the LusztigVogan bijection ... was proven by Bezrukavnikov, and an algorithm computing [gamma] in type A was given by Achar. Herein we present a combinatorial description...

Harrington, Leo Anthony
by Leo A. Harrington.

Harrington, Leo Anthony
by Leo A. Harrington.

Giever, John Bertram, 1919
by John Bertram Giever.

Giever, John Bertram, 1919
by John Bertram Giever.

Vainsencher, Israel
Thesis. 1977. Ph.D.Massachusetts Institute of Technology. Dept. of Mathematics.

Vainsencher, Israel
Thesis. 1977. Ph.D.Massachusetts Institute of Technology. Dept. of Mathematics.

Carpentier, Sylvain, Ph. D. Massachusetts Institute of Technology
A key feature of integrability for systems of evolution PDEs ut = F(u), where F lies in a differential algebra of functionals V and u = (U1, ... , ul) depends on one space variable x and time t, is to be part of an infinite hierarchy of generalized symmetries. Recall that V carries a Lie algebra bracket {F, G} = XF(G)  XG(F), where XF denotes the evolutionnary vector field attached to F. In all known examples, these hierarchies are constructed by means of LenardMagri sequences: one can find a pair of matrix differential operators (A(a), B(a)) and a...

Carpentier, Sylvain, Ph. D. Massachusetts Institute of Technology
A key feature of integrability for systems of evolution PDEs ut = F(u), where F lies in a differential algebra of functionals V and u = (U1, ... , ul) depends on one space variable x and time t, is to be part of an infinite hierarchy of generalized symmetries. Recall that V carries a Lie algebra bracket {F, G} = XF(G)  XG(F), where XF denotes the evolutionnary vector field attached to F. In all known examples, these hierarchies are constructed by means of LenardMagri sequences: one can find a pair of matrix differential operators (A(a), B(a)) and a...