Department of Mathematics
http://hdl.handle.net/1721.1/7841
2016-06-29T18:21:36ZSuperfluidity and random media
http://hdl.handle.net/1721.1/103194
Superfluidity and random media
Meng, Hsin-fei
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1993.; Includes bibliographical references (leaf 92).
1993-01-01T00:00:00ZUnimodal, log-concave and Pólya frequency sequences in combinatorics
http://hdl.handle.net/1721.1/103188
Unimodal, log-concave and Pólya frequency sequences in combinatorics
Brenti, Francesco, 1960-
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1988.; Includes bibliographical references.
1988-01-01T00:00:00ZAspects of biological sequence comparison
http://hdl.handle.net/1721.1/102708
Aspects of biological sequence comparison
Altschul, Stephen Frank
Thesis (Ph. D)--Massachusetts Institute of Technology, Dept. of Mathematics, 1987.; This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.; Bibliography: leaves 165-168.
1987-01-01T00:00:00ZPseudoholomorphic quilts with figure eight singularity
http://hdl.handle.net/1721.1/101823
Pseudoholomorphic quilts with figure eight singularity
Bottman, Nathaniel Sandsmark
In this thesis, I prove several results toward constructing a machine that turns Lagrangian correspondences into A[infinity],-functors between Fukaya categories. The core of this construction is pseudoholomorphic quilts with figure eight singularity. In the first part, I propose a blueprint for constructing an algebraic object that binds together the Fukaya categories of many different symplectic manifolds. I call this object the "symplectic A[infinity]-2-category Symp". The key to defining the structure maps of Symp is the figure eight bubble. In the second part, I establish a collection of strip-width-independent elliptic estimates. The key is function spaces which augment the Sobolev norm with another term, so that the norm of a product can be bounded by the product of the norms in a manner which is independent of the strip-width. Next, I prove a removable singularity theorem for the figure eight singularity. Using the Gromov compactness theorem mentioned in the following paragraph, I adapt an argument of Abbas-Hofer to uniformly bound the norm of the gradient of the maps in cylindrical coordinates centered at the singularity. I conclude by proving a "quilted" isoperimetric inequality. In the third part, which is joint with Katrin Wehrheim, I use my collection of estimates to prove a Gromov compactness theorem for quilts with a strip of (possibly non-constant) width shrinking to zero. This features local C[infinity]-convergence away from the points where energy concentrates. At such points, we produce a nonconstant quilted sphere.
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2015.; Cataloged from PDF version of thesis.; Includes bibliographical references (pages 107-109).
2015-01-01T00:00:00Z