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Algorithmic and Hardness Results for Fundamental Fair-Division Problems
The theory of fair division addresses the fundamental problem of dividing a set of resources among the participating agents in a satisfactory or meaningfully fair manner. This thesis examines the key computational challenges ...
A computational systems biology approach for elucidating molecular features of primary and metastatic melanoma
Malignant melanoma, a cancer arising from melanocytes, is reported to have one of
the fastest growing incidence rates worldwide, and is considered to be one of the most
aggressive human malignancies. According to the ...
On the Kobayashi geometry of domains
In this thesis we study questions broadly related to the Kobayashi (pseudo)distance and (pseudo)metric on domains in ℂn. Specifically, we study the following subjects:
Estimates for holomorphic images of subsets in convex ...
Sparse bounds for various spherical maximal functions
Harmonic analysis mainly deals with the qualitative and quantitative properties of functions
and transforms of those functions. It has applications in various areas of Mathematics like PDE,
Differential geometry, Ergodic ...
Homogenization of PDEs on oscillating boundary domains with L1 data and optimal control problems
This thesis comprehensively studies the homogenization of partial differential equations (PDEs) and optimal control problems with oscillating coefficients in oscillating domains. After the introduction, the thesis is divided ...