When did the Mauryas rule?

When it comes to building a chronology of events in India’s history, a student is confused by the wide variation in dates of certain events. For example, when did Mahabharata war happen? Was it 1924 B.C or 3137 B.C? When did Adi Shankara live? Was it 8^th century CE or 5^th century B.C? Partly such confusion exists due to the existence of multiple methodologies that exist (Puranic genealogies, archaeological evidence etc), and they often contradict each other. Partly the confusion is due to the fact even now people don’t understand that when something is 3000 years old, it does not date to 3500 B.C.
While most of us learned that Chandragupta Maurya lived around the 3^rd century B.C, there is a set of people (via DesiPundit) who believe that he lived in 1534 B.C. This means that if we choose 1924 B.C as the date for Mahabharata war, then the Mauryan empire was established just 300 later. Then what happened to Buddha? Oh well he lived just 100 years after Mahabharata.
What can help in solving this mystery is some archaeology. Specifically if we can find out when humans settled in the areas where the Mauryan empire was located, then some of these dates can be ridiculed and there is some effort in this direction in West Bengal.

The state archaeology department recently found the site, on the banks of Piyali riyal in South 24 Parganas district. “We would begin excavation in winter at Tilpi near Joynagar in South 24 Parganas which could be an early historic site of pre-Mauryan period,” West Bengal Archaeology and Museums Department director Gautam Sengupta told IANS.
“This could prove that human habitation existed in the area between 3rd century BC and 3rd century AD,” Sengupta said. The Maurya dynasty ruled India between 321 and about 240 BC. “We discovered the site recently and came across some terracotta articles, copper coins, stone beads and other artefacts. Excavation is likely to reveal more artefacts and those can be compared with our previous findings to ascertain the occupational history of the area,” he added.
“This new site is on the banks of Piyali, which is again a part of the river system of Vidyadhari, on the banks of which Chandraketugarh was discovered in the early years of last century,” he said. Chandraketugarh is located in North 24 Parganas district and its history dates back to almost 3rd century BC, even before the Maurya dynasty came up.
The archaeological significance of the Chandraketugarh area came to light in the early years of the last century when road-building activities exposed a brick structure and artefacts.From all indications Chandraketugarh was an important urban centre, most probably a port city. The new site at Tilpi could be linked to Chandraketugarh, Sengupta said.[Excavation near Kolkata to unearth pre-Mauryan history via IndiaArchaeology]