NCMW - Groups and Computation (2023)
Speakers and Syllabus
Syllabus:
| Name of speaker with affiliation | Number of lectures | Topics |
| 1. Dr. Rishi Vyas (Krea University, Sri City) |
3 | Decision problems in groups: Turing machines; recursive functions; halting problem; recursive sets; overview of the unsolvability of the word problem; Markov properties; undecidable and decidable problems in group theory; overview of the Higman embedding theorem; open questions. |
| 2.Dr. T.V.H. Prathamesh (Krea University, Sri City) |
3 | Automata and term rewriting in groups: introduction to finite state automata (deterministic/non-deterministic/generalized ); regular languages and regular expressions; pumping lemma and equivalences; Myhill-Nerode lemma; term rewriting; applications to group theory. |
| 3.Dr. Soumya Dey (Krea University, Sri City) |
3 | Introduction to automatic groups: basic constructions in combinatorial and geometric group theory (Cayley graphs, word metrics, Dehn functions, free products (with amalgamation), HNN extensions, normal forms, van Kampen diagrams; introduction to automatic groups (definitions, examples, basic properties, fundamental theorems). |
| 4.Dr. Arpan Kabiraj (Indian Institute of Technology, Palakkad) |
3 | Automaticity in geometric group theory: brief account of automatic and bi-automatic groups; overview of automaticity or bi-automaticity of the following classes of groups: word hyperbolic groups, braid groups, Artin groups and mapping class groups. |
| 5.Prof. V. Arvind (The Institute of Mathematical Sciences, Chennai) |
3 | Algorithms for groups and graphs: Lecture 1: algorithms for permutation groups presented by generating set as input: membership testing; checking if a given group is nilpotent, is solvable; efficiently computing the lower central series and commutator series of a group. Lecture 2: the graph isomorphism problem and related questions. Connection to the permutation group problems discussed in the first lecture. An efficient algorithm for the special case of graphs of degree bounded by 3. The problem reduces to computing the intersection of a nilpotent permutation group with another group which can be solved efficiently using technique discussed in the first lecture. Lecture 3: Extending the algorithm described for trivalent graph isomorphism in lecture 2 to graphs of bounded degree. |
| 6.Prof. Siddhartha Gadgil (Indian Institute of Science, Bengaluru) | 3 | Computer proofs in group theory: in this mini-course we will introduce using Lean 4, which is a programming language seamlessly integrated with an interactive theorem prover, for: 1) formalization (computer verification) of results in group theory; 2) writing programs implementing algorithms in group theory; 3) proving that our programs are correct, and hence results of their computation are formally proved. |
| Name of tutors with affiliation | Number of tutorials | |
| 1. | Dr. Oorna Mitra (Indian Statistical Institute, Bengaluru) | 6 |
| 2. | Dr. Pratik Ghosal (Chennai Mathematical Institute, Chennai) | 6 |
Time Table
| 9:30 - 11:00 | 11:00 - 11:30 | 11:30 - 1:00 | 1:00 - 2:00 | 2:00 - 3:30 | 3:30 - 4:00 | 4:00 - 5:00 | 5:00 - 5:30 | |
| July 03 | RV 1 |
Tea |
TP 1 | SD 1 |
Tea |
Tutorial (RV + OM + PG) |
Snacks |
|
| July 04 | RV 2 | TP 2 | SD 2 | Tutorial (TP + OM + PG) | ||||
| July 05 | RV 3 | TP 3 | Lunch | SD 3 | Tutorial (SD + OM + PG) | |||
| July 06 | VA 1 | SG 1 | AK 1 | Tutorial (VA + OM + PG) | ||||
| July07 | VA2 | SG2 | AK2 | Tutorial (SG + OM + PG) | ||||
| July08 | VA3 | SG3 | AK3 | Tutorial (AK + OM + PG) |