In this thesis, we focus on two well-connected topics: quantum measurement and quan- tum uncertainty relation. The first topic is the well-known “pre- and postselected mea- surements”. Aharonov, Bergmann, and Lebowitz ...

In this thesis, we investigate holomorphy and special values of Artin L-functions. Let K/F be a Galois extension of number fields with Galois group G. Artin conjectured that Artin L-functions associated to non-trivial ...

A Dold manifold is defined as the quotient space Sm × CP n /∼, where (s, L) ∼ (−s, L̄). These manifolds were first introduced by Albrecht Dold in 1956 to construct generators in odd dimensions for Thom’s unoriented cobordism ...

This thesis is divided into two parts. The first part includes the Demazure crystal structure for flagged reverse plane partitions and flagged skew semi-standard tableaux. The second part addresses the saturation property ...

Cells make decisions based on underlying gene regulatory networks (GRNs). GRNs may be modeled as a Boolean network (BN) in which nodes and directed edges represent genes or proteins and their interactions respectively. In ...

A central goal of computer science is to understand the capabilities and limitations of various computational devices. To understand various computational devices we formalize them using mathematical models called "models ...

This thesis explores the derivation of chiral current algebras from different gravita- tional theories, including R1,3 gravity, AdS4 gravity, and 3d conformal gravity. We propose chiral boundary conditions consistent ...

The central theme of this thesis is to study some analytic and arithmetic properties of values of L-functions at “special points”. The values of L-functions encode a lot of arithmetic data and are at the heart of several ...