Dept. of Mathematics

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• (2017-12-03)
Given $\alpha>0$, the $\alpha$-Grushin plane is $\mathbb{R}^2$ equipped with the sub-Riemannian metric generated by the vector fields $X = \partial_1$ and $Y = |x_1|^{\alpha} \partial_2$. It is a standard example in ...

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• (2017-10-30)
In this thesis we prove the existence of Jordan Decomposition in $D_{G/k}$, the ring of invariant differential operators on a semisimple algebraic group over a field of positive characteristic, and its corollaries. In ...

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• (2017-12-08)
We study two different problems: generic behavior of a measure preserving transformation and extending partial isometries of a compact metric space. In Chapter $1$, we consider a result of Del Junco--Lema\'nczyk [\ref{DL_B}] ...

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• (2017-11-28)
The equivariant 𝔼∞G operad has the property that 𝔼∞G(n) is the total space for the G-equivariant universal principal Σn bundle. There is a forgetful functor from 𝔼∞G-algebras to 𝔼∞-algebras, where 𝔼∞ is the classic ...

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• (2017-10-23)
In this thesis, we study certain aspects of Levy processes and their applications. In the first part of this thesis, we study the applications of Levy processes in actuarial mathematics. Our topics are closely related to ...

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