Department of Mathematics
http://hdl.handle.net/1721.1/7841
2015-01-23T09:30:53ZOn moduli stacks of finite group schemes
http://hdl.handle.net/1721.1/93003
On moduli stacks of finite group schemes
Zhang, Zhaohui, 1972-
Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2000.; Includes bibliographical references (p. 41-42).
2000-01-01T00:00:00ZWitt spaces : a geometric cycle theory for KO-homology at odd primes.
http://hdl.handle.net/1721.1/91309
Witt spaces : a geometric cycle theory for KO-homology at odd primes.
Siegel, Paul Howard
Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1979.; MICROFICHE COPY AVAILABLE IN ARCHIVES AND SCIENCE.; Vita.; Bibliography: leaves 131-133.
1979-01-01T00:00:00ZTesting models of ultra-fast India-Asia convergence : new paleomagnetic results from Ladakh, Western Himalaya
http://hdl.handle.net/1721.1/90648
Testing models of ultra-fast India-Asia convergence : new paleomagnetic results from Ladakh, Western Himalaya
Bailey, Elizabeth A
Rapid India-Asia convergence has led to a major continental collision and formation of the Himalayas, the highest mountain range on Earth. Knowledge of the paleolatitude of the Kohistan-Ladakh Arc (KLA), an intermediate tectonic unit currently situated between the converging Indian and Eurasian continents in Western Himalaya, would constrain the tectonic history and dynamics of Himalayan orogenesis. We present new paleomagnetic data from the Khardung volcanic rocks of the Shyok-Nubra valley region of Ladakh, western Himalaya. Samples from all four sites (KP1-KP4) display high-temperature components indicating a roughly equatorial paleolatitude, with the average of site mean directions implying a paleolatitude of 5'N. We interpret results of a positive baked contact test at one site (KP3) to imply that the high-temperature components in the distal volcanic bedrock predate bedding tilt and dike formation. Previous studies of the Khardung unit (Bhutani 2009, Dunlap 2002) have measured 40Ar-39Ar and U-Pb dates of -52-67 Ma. Assuming these ages apply to our samples, our results support the two-stage collision model of Jagoutz and Royden (in prep), which indicates an approximately equatorial India-KLA collision at 50 Ma.
Thesis: S.B., Massachusetts Institute of Technology, Department of Mathematics, 2014.; Author received an S.B. from the Department of Mathematics, but her thesis was submitted to the Department of Earth, Atmospheric and Planetary Sciences for the degree of S.B. Cataloged from PDF version of thesis.; Includes bibliographical references (pages 29-32).
2014-01-01T00:00:00ZThe affine Yangian of gl₁, and the infinitesimal Cherednik algebras
http://hdl.handle.net/1721.1/90192
The affine Yangian of gl₁, and the infinitesimal Cherednik algebras
Tsymbaliuk, Oleksandr
In the first part of this thesis, we obtain some new results about infinitesimal Cherednik algebras. They have been introduced by Etingof-Gan-Ginzburg in [EGG] as appropriate analogues of the classical Cherednik algebras, corresponding to the reductive groups, rather than the finite ones. Our main result is the realization of those algebras as particular finite W-algebras of associated semisimple Lie algebras with nilpotent 1-block elements. To achieve this, we prove its Poisson counterpart first, which identifies the Poisson infinitesimal Cherednik algebras introduced in [DT] with the Poisson algebras of regular functions on the corresponding Slodowy slices. As a consequence, we obtain some new results about those algebras. We also generalize the classification results of [EGG] from the cases GL, and SP2n to SOl. In the second part of the thesis, we discuss the loop realization of the affine Yangian of gl₁. Similar objects were recently considered in the work of Maulik-Okounkov on the quantum cohomology theory, see [MO]. We present a purely algebraic realization of these algebras by generators and relations. We discuss some families of their representations. A similarity with the representation theory of the quantum toroidal algebra of gl₁ is explained by adapting a recent result of Gautam-Toledano Laredo, see [GTL], to the local setting. We also discuss some aspects of those two algebras such as the degeneration isomorphism, a shuffle presentation, and a geometric construction of the Whittaker vectors.
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2014.; Cataloged from PDF version of thesis.; Includes bibliographical references (pages 183-186).
2014-01-01T00:00:00Z