There are many similarities to be seen when comparing Mesoamerican civilizations to the southwest and southeast societies in North America. It is evidenced that these similarities arose from trade routes between the civilizations, allowing things such as art, religion, and architecture to be transferred. The largest similarities are those in technology and science.
North America is scattered with mounds that were built by early Indians (Week 7, Lecture 3). These mounds came in a few different shapes including simple geometric and platform. The platform mounds were basically hills that had the top flattened. This is very referential to the temples built by the Olmec civilization at the site of La Venta (Week 6, Lecture 1). It is believed that in both regions priests would live on top of these mounds due to their social position of being closer to the gods. Further evidence for this similarity is that obsidian has been found at the sites of platform mounds in Mississippi, indicating trade (http://www.public.asu.edu/~mesmith9/1-CompleteSet/MES-10-TradeEncyc.pdf). The Mayans held a large portion of the obsidian trade, and it would not be out of the question for the Mayans to have traded with Indians in modern-day Mississippi.
The act of ritual sacrifice was not uncommon in Mesoamerican societies. There is evidence that the Cahokia people took part in similar sacrifices and ritual burials (Cahokia: America’s Lost City). These rituals are believed to be connected to a form a religion. Sacrifice was most likely done to appease the gods, while complex burials were to provide the deceased individual with materials for their afterlife. These religious ideas and ceremonies could have been passed through trade.
Corn farming was a large aspect of Pueblo culture. The Pueblo people developed agricultural techniques to grow corn into their main food source (http://www.nps.gov/band/historyculture/ancestral-pueblo-farming.htm). The Pueblo people used a resevoir-canal irrigation system to provide water for growing their corn (http://www.american-indians.net/empires.htm). The majority of Mesoamerican societies, most notably the Aztec, formed a canal-based irrigation system to promote farming in their dry and arid land (Week 6, Lecture 2). The techniques used by these two civilizations are very similar, suggesting that there may have been communication between these people.
Overall, there are a lot of connections through science and technology that support the idea of there being trade and communication between Mesoamerican civilizations and southwest and southeast societies of North America.