Motivic analogues of MO and MSO

Abstract

This thesis makes progress in computing the coefficients of Algebraic Hermitian Cobordism (MGLR), a motivic C 2-equivariant spectrum constructed by P. Hu, I. Kriz, and K. Ormsby. In the process of my research, I realized it would be possible to construct motivic analogues of unoriented and oriented cobordism, which I refer to as MGLO and MSLO respectively. In chapters 2-3 of my thesis, I construct MGLO and MLSO and give a concrete description of the homotopy groups of each of them. In particular, my work on MGLO gives an answer to a question of Jack Morava. Using the tools of Tate cohomology and my computation of the coefficients of MGLO, the thesis ends with a computation of a localization of the homotopy groups of MGLR.

Inflation and leptogenesis in high-scale supersymmetry

“…In a particular basis, one of the fields may be associated with the volume modulus while the second appears as a matter-like field. Due to the underlying symmetry of the theory, either of the fields can play the role of the inflaton [14,15,18] whose potential can take the form of the Starobinsky potential [11]. However once supersymmetry is broken, and couplings to the Standard Model are introduced, these two classes of inflationary models appear quite different.…”

“…In fact, the two models listed above are simply two examples of a wide class of superpotential models which all generate the same scalar potential [15,18]. In the absence of supersymmetry breaking, one can show that these classes can be related by the underlying non-compact SU (2,1) SU (2)×U (1) no-scale symmetry [18]. Once the theory is coupled to matter and supersymmetry is broken, this symmetry is broken and different models will have different phenomenologies [26].…”

“…(17), and i = 1, 2 for the inverse hierarchy given by Eq. (18). Therefore, if we use the observationally determined value for the baryon asymmetry Y B 8.7 × 10 −11 , we obtain the following constraint: (69) This constraint is used in Fig.…”

“…and can be easily realized in no-scale supergravity [14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30]. These models must contain at least two chiral fields, which we will denote as T , a volume modulus, and φ, a matter-like field [15].…”

“…parametrizing a non-compact SU (2,1) SU (2)×U (1) coset manifold [14]. The inflationary models can be divided into two classes, in which either the volume modulus T or the matter-like field φ is identified as the inflaton [15,18]. Depending on the specific model, an additional chiral multiplet may be necessary to break supersymmetry [26,27].…”