AIS - Advanced Linear Algebra (2020)
Speakers and Syllabus
Name of the Speaker with affiliation | No. of Lect. | Detailed Syllabus |
R. B. Bapat ISI Delhi |
4 | Title: Topics in Nonnegative Matrices
Syllabus/Outline: |
Apoorva Khare IISc |
3 | Title: Totally nonnegative (TN) and totally positive (TP) matrices Syllabus/Outline: (a) Definitions, examples. (b) TP is dense in TN. (c) Eigenvalues of square TP/TN matrices are positive/nonnegative. Parts (b) and (c) should remind one of the exact same statements for positive (semi)definite matrices -- the analogue of (c) is Sylvester's criterion. The proofs for TN/TP matrices will including my covering Perron's theorem for matrices with positive entries, Kronecker's theorem for compound matrices, and a black-box result on the continuity of the roots of complex polynomials as functions of the coefficients. |
Jugal Verma IIT Bombay |
6 | Title: Solutions of real and complex polynomial equations via eigenvalues
Syllabus/Outline: Pre-requisites: |
Gautam Bharali IISc |
4 | Title: The role of linear algebra in complex analysis
Syllabus/Outline: |
Praneeth Netrapalli Microsoft Research, Bangalore |
4 | Title: Efficient computation of top singular vectors/principal components
Syllabus/Outline: |
Sreedhar Inamdar | 4 | Title: Advanced linear algebra Syllabus/Outline: Cholesky decomposition, Singular value decomposition, Spectral theorem, Jordan canonical form, positive matrices, Positive definite functions, geometry of positive matrices. |
Manish Kumar ISI Bangalore |
4 | Title: Representation theory
Syllabus/Outline: |
Rajesh Sharma Himachal Pradesh University |
2 | Title: Numerical Range:
Syllabus/Outline: |
Gadadhar Misra IISc |
3 | Title: Curvature inequalities
Syllabus/Outline: TBA |
Manjunath Krishnapur IISc |
3 | Title: Curvature inequalities Syllabus/Outline: Graph Laplacian and the relationships between spectral properties of the Laplacian and the properties of the graph. This will include counting spanning trees of a graph and Cayley's theorem. Cheeger's inequality on graphs. Nodal domain theorem. Resistance metric on a graph. |
Tutorial Assistants:
Sr.n | Name | Affiliation |
1 | TBA | TBA |
2 | TBA | TBA |
3 | TBA | TBA |
Time Table
Names of speakers and course associates/tutors
Day | Date | Lecture 1 (9.30–11.00) |
Tea (11.05 –11.25) |
Lecture 2 (11.30–1.00) |
Lunch (1.05–2.25) |
Tutorial (2.30–3.30) |
Tea (3.35-3.55) |
Tutorial (4.00-5.00) |
5.05-5.30 |
speaker | speaker | L U N C H |
speaker + tutors | speaker + tutors | S N A C K S |
||||
Mon | 11 May | SI | MK | SI + | MK + | ||||
Tues | 12 May | SI | MK | SI + | MK + | ||||
Wed | 13 May | SI | MK | SI + | MK + | ||||
Thu | 14 May | SI | MK | SI + | MK + | ||||
Fri | 15 May | RB | GB | RB+ | GB+ | ||||
Sat | 16 May | RB | GB | RB+ | GB+ | ||||
SUNDAY : OFF | |||||||||
Mon | 18 May | RB | GB | L U N C H |
RB+ | GB+ | S N A C K S |
||
Tues | 19 May | RB | GB | RB+ | GB+ | ||||
Wed | 20 May | KR | RS | KR+ | RS+ | ||||
Thu | 21 May | KR | AK | KR+ | AK+ | ||||
Fri | 22 May | KR | AK | KR+ | AK+ | ||||
Sat | 23 May | RS | AK | RS+ | AK+ | ||||
SUNDAY : OFF | |||||||||
Mon | 25 May | PN | JV | L U N C H |
PN+ | JV+ | S N A C K S |
||
Tues | 26 May | PN | JV | PN+ | JV+ | ||||
Wed | 27 May | PN | JV | PN+ | JV+ | ||||
Thu | 28 May | GM | JV | GM+ | JV+ | ||||
Fri | 29 May | GM | JV | GM+ | JV+ | ||||
Sat | 30 May | GM | JV | GM+ | JV+ |
- AK: Apoorva Khare
- MK: Manish Kumar
- GM: Gadadhar Misra
- RS: Rajesh Sharma
- PN: Praneeth Netrapalli
- GB: Goutam Bharali
- KR: Manjunath Krishnapur
- SI: Sreedhar Inamdar
- JV: Jugal Verma
- RB: R B Bapat