Describe the process of neurogenesis in the adult brain

Describe the process of neurogenesis in the adult brain and its significance in cognitive function, mood regulation, and neuroplasticity. How do neural stem cells in specialized regions of the brain, such as the hippocampus and subventricular zone, give rise to new neurons throughout life? Furthermore, how do environmental factors, physical activity, and neurotrophic factors like brain-derived neurotrophic factor (BDNF) influence neurogenesis and synaptic connectivity, contributing to learning, memory formation, and emotional well-being?