Open problems/Research Suggestions

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In summary, the conversation involves a second year student seeking suggestions for a research project in geometric group theory, infinite group theory, and growth functions. They have a 6-7 week break to do some reading and come up with ideas, and are advised to check out past REUs and contact well-known experts in the field. A list of geometric group theorists around the world is also provided.
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I'm going to be doing research next semester on a topic of almost entirely my choice. I'd like to research anything related to geometric group theory, infinite group theory (specifically infinite geometric group theory), growth functions, etc. To give a bit of background; I'm a second year student currently enrolled in a first semester linear algebra course, and abstract algebra course. I will be in the second semester of abstract algebra next semester. I have a 6-7 week winter break during which time I will be doing a good deal of reading and probably come up with some inquiries/ideas but I wanted to see what you all thought...so...suggestions?
 
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Why not check out past REUs and see what they've done? I know there's been an REU at Cornell that has done stuff along the lines of what you want to do. Why not email someone well-known in the field and ask them what's of interest right now in those fields? There's a geometric group theorist at my university, you can check out his home page here http://www.math.msu.edu/~robertbe/" . He's a really nice guy and has done a lot with undergraduates, so I'm sure he'd definitely be willing to suggest some kind of research project on those topics if you give him your background and interests.

Best of luck with research!
 
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  • #3
Also, here's a list of geometric group theorists around the world:

http://www.math.ucsb.edu/~jon.mccammond/geogrouptheory/people.html"
 
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Yet again, Physics Forums delivers. Thanks for the replies.
 

Related to Open problems/Research Suggestions

1. What are open problems in the field of research?

Open problems in research refer to areas or questions that have not yet been fully explored or answered by scientists. These problems often require further investigation and experimentation in order to reach a conclusive answer. They can also serve as potential research suggestions for scientists to pursue.

2. How are open problems identified in research?

Open problems in research can be identified through various methods, such as literature reviews, conferences, and discussions with other scientists in the field. These problems are often identified based on gaps in current knowledge or areas that require further development.

3. Why is it important to address open problems in research?

Addressing open problems in research is crucial for the advancement of scientific knowledge. By exploring and finding solutions to these problems, scientists can contribute to the development of new theories, technologies, and applications that can benefit society as a whole.

4. How can researchers approach open problems?

Researchers can approach open problems through various methods, such as conducting experiments, analyzing data, and collaborating with other scientists. It is also important for researchers to have a clear understanding of the problem and to constantly review and update their methods in order to find the most effective approach.

5. Can anyone suggest a research problem?

Yes, anyone can suggest a research problem. In fact, many scientific breakthroughs have come from suggestions made by individuals outside of the scientific community. However, it is important for the suggested problem to be well-defined, relevant to the field of research, and based on existing knowledge and evidence.

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