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# Dream

1000 research tracks. 300 mathematics cafes. 5000 researchers and students.

We dream of rejuvenating the research atmosphere in India. Cheenta Research Track specifically caters to that dream.

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# Research – Geometric Group Theory

Ashani Dasgupta

Pursuing Ph.D. at University of Wisconsin Milwaukee on Geometric Group Theory

# Understand the problem

Suppose a relatively finitely presented group G is acting stably and minimally on a real tree T. Create a graph of groups decomposition of G using this group action.

Rips theory is used to analyze the action of finitely presented groups on real trees. We propose to extend the theory to relatively finitely presented case.

## Bayes’ in-sanity || Cheenta Probability Series

Listen to a frequentist’s carping over Bayesian school of thinking!

## Laplace in the World of Chances| Cheenta Probability Series

In this post we will be discussing mainly about, naive Bayes Theorem, and how Laplace, developed the same idea as Bayes, independently and his law of succession goes.

## Bayes and The Billiard Table | Cheenta Probability Series

This post discusses how judgements can be quantified to probabilities, and how the degree of beliefs can be structured with respect to the available evidences in decoding uncertainty leading towards Bayesian Thinking.

## Nonconglomerability and the Law of Total Probability || Cheenta Probability Series

This explores the unsung sector of probability : “Nonconglomerability” and its effects on conditional probability. This also emphasizes the idea of how important is the idea countable additivity or extending finite addivity to infinite sets.

## Judgements in a Fitful Realm | Cheenta Probability Series

This post discusses how judgements can be quantified to probabilities, and how the degree of beliefs can be structured with respect to the available evidences in decoding uncertainty leading towards Bayesian Thinking.

## Probability From A Frequentist’s Perspective || Cheenta Probability Series

This post discusses about the history of frequentism and how it was an unperturbed concept till the advent of Bayes. It sheds some light on the trending debate of frequentism vs bayesian thinking.

## Some Classical Problems And Paradoxes In Geometric Probability||Cheenta Probability Series

This is our 6th post in our ongoing probability series. In this post, we deliberate about the famous Bertrand’s Paradox, Buffon’s Needle Problem and Geometric Probability through barycentres.

## Arithmetical Dynamics: Part 6

Arithmetical dynamics is the combination of dynamical systems and number theory in mathematics. Again, we are here with the Part 6 of the Arithmetical Dynamics Series. Let's get started.... Consider fix point of $R(z) = z^2 - z$ . Which is the solution of  R(z)...

## Arithmetical Dynamics: Part 5

Arithmetical dynamics is the combination of dynamical systems and number theory in mathematics. The basic objective of Arithmetical dynamics is to explain the arithmetic properties with regard to underlying geometry structures. Again, we are here with the Part 5 of...

## Arithmetical Dynamics: Part 0

Arithmetical dynamics is the combination of dynamical systems and number theory in mathematics. We are here with the Part 0 of the Arithmetical Dynamics Series. Let's get started.... Rational function $R(z)= \frac {P(z)}{Q(z)}$ ; where P and Q are polynimials ....

# How it works

• Training bursts (3 to 4 weekly training sessions once every two months)
• Weekly presentation/problem solving (moderated)
• Students are required to present at least once per month
• Students are required to submit an expository article once every 6 months

# Papers

Henry Wilton – Rips Machine

Topological Methods in Group Theory by Scott and Wall

# Books

• Contemporary Abstract Algebra (Gallian)
• Bridson Haeflager
• Scott and Wall
• Hatcher