This Teachers’ Enrichment Workshop is especially meant for mathematics teachers of arts and science colleges in and around Chennai. Some foundational concepts of algebra, analysis, topology will be covered in a non-standard way by exhibiting their manifestations in the p-adic realms. We shall try to cover roughly the contents of the book titled “p-adic analysis compared with real” by S. Katok. The workshop will be an intensive one and only those who are willing to work hard and actively participate are encouraged to apply.
Speakers, with affiliations, and topics
| Speaker | Affiliation | Syllabus Covered | Number of lecture hours |
Number of tutorial hours |
| S. Gun | IMSc | The p-adic expansion of rational numbers, numbers Qp , Metrics and norms of on the rational numbers: Ostrowski’s Theorem, Elementary analysis in Qp : Sequences and series, Properties of p-adic exponential and logarithm, continuous and uniformly continuous functions. Reference book: p-adic analysis compared with real by S. Katok. |
6 | 4 |
| A. Mukhopadhyay | IMSc | Construction of the completion of a normed field, Algebraic properties of p-adic integers, Euclidean models of Z p , Locally constant functions. Reference book: p-adic analysis compared with real by S. Katok. |
6 | 4 |
| D. S. Nagaraj | IMSc | Normed fields, Arithmetical operations in Qp , Hensel’s lemma and congruences, Cantor sets, Elementary analysis in Qp : p-adic power series. Reference book: p-adic analysis compared with real by S. Katok. |
7.5 | 2 |
| P. Sankaran | IMSc | Arithmetic of the p-adic numbers, The field of p-adic numbers Qp , Elementary topological properties, Elementary analysis in Qp : Sequences and series, Zeros of p-adic power series. Reference book: p-adic analysis compared with real by S. Katok. |
7.5 | 2 |
Timetable
| Time | 09:45–11:15 | 11:30 to 13:00 | 14:00 to 15:00 | 15:15 to 16:15 | |||
| Mon 21st | PS L1 | DSN L1 | L | AM L1 | PS/DSN T1 S | ||
| Tue 22nd | PS L2 | T | DSN L2 | U | SG L1 | T | PS/DSN T2 N |
| Wed 23rd | DSN L3 | E | AM L2 | N | SG L2 | E | SG/AM T3 A |
| Thu 24th | PS L3 | A | DSN L4 | C | AM L3 | A | SG/AM T4 C |
| Fri 25th | PS L4 | DSN L5 | H | SG L3 | SG/AM T5 K | ||
| Sat 26th | PS L5 | AM L4 | SG L4 | SG/AM T6 |