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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.

Do you wish to partner in this unique program? Let us know.

# Research – Geometric Group Theory

#### Research Track leader

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.

## 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 ....

## Arithmetical Dynamics: Part 4

We are here with the Part 4 of the Arithmetical Dynamics Series. Let's get started.... Arithmetical dynamics is the combination of dynamical systems and number theory in mathematics. $P^m(z) = z \ and \ P^N(z)=z \ where \ m|N \Rightarrow (P^m(z) - z) | (P^N(z)-z)$...

## Arithmetical Dynamics: Part 3

We are here with the Part 3 of the Arithmetical Dynamics Series. Let's get started.... Arithmetical dynamics is the combination of dynamical systems and number theory in mathematics. Theory: Let $\{ \zeta_1 , ......., \zeta_m \}$ be a ratinally indifferent cycle...

## Research for School

Research projects for school students, in mathematics and data science. For advanced learners who are in love with mathematical science.

## Arithmetical Dynamics: Two possible problems

Today, we are going to discuss two possible problems for Arithmetical Dynamics in this post. 1.1. Existence of (pre)Periodic Points. These are the topics expanding on I.N. Baker’s theorem. Related reading: (1) Silverman Arithmetic of Dynamical Systems: p 165....

## Arithmetical Dynamics: An intro:

Here I gave some introduction of Arithmetical Dynamics. What is it and why do we study it. Also there is one motivational question upraised.

# How it works

• Training bursts (3 to 4 weekly training sessions once every two months)
• Weekly presentation/problem solving (moderated)
• Bi-weekly advisor meeting
• 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