NCMW - Topics in geometric combinatorics (2025)
Speakers and Syllabus
| Speaker and affiliation | Number of Lectures | Detailed Syllabus |
| Arvind Ayyer IISc | 5 | Polytopes, polyhedra, cones, face lattice, simple and simplicial polytopes, Pick’s theorem, Cones over polytopces, integer point transforms for cones, Ehrhart polynomials, h-star polynomials, Ehrhart– Macdonald reciprocity, Hibi’s palindromic theorem, Dehn–Sommerville relations. Reference: Computing the continuous discretely by Matthias Beck and Sinai Robins |
| PriyavratCMI Deshpande | 5 | Background and basic definitions of hyperplane ar- rangements, intersection poset, Möbius function, regions, faces, examples. Zaslavsky’s theorem for region counting, The finite field method. Combinatorics of reflection arrangements. Bijective techniques to compute the region numbers. Supersolvable arrangements and matriods. Reference: Hyperplane arrangements by Richard Stanley. |
| Anurag Singh IIT Bhilai | 2 | Advanced topics in combinatorics: posets and lattices, Möbius inversion, generating functions, quasi-polynomials, theory of valuations. Introduction to implementing combinatorics in SAGE Math. |
Time Table
| Day | Date | Lecture 1 9.30–11.00 |
Tea | Lecture 2 11.30–1.00 |
Lunch | Tutorial 2.30–3.30 |
Tea | Tutorial 4.00-5.00 |
Snacks |
| Mon | 30/6/2025 | AS | AA | AS+1 | AA+1 | ||||
| Tue | 1/7/2025 | AS | PD | AS+1 | PD+1 | ||||
| Wed | 2/7/2025 | AA | PD | AA+1 | PD+1 | ||||
| Thu | 3/7/2025 | AA | PD | AA+1 | PD+1 | ||||
| Fri | 4/7/2025 | PD | AA | PD+1 | AS+1 | ||||
| Sat | 5/7/2025 | PD | AA | AS+1 | AA+1 |
AS: Anurag Singh
AA: Arvind Ayyer
PD: Priyavrat Deshpande
| Tutorial Assistants: | ||
| S. No. | Name | Affiliation |
| 1 | Dr. Hiranya Kishore Dey | IISc |
| 2 | Dr. Shuchita Goyal | BITS, Pilani |
Tutorial Assistants:
S. No. Name Affiliation
1 Dr. Hiranya Kishore Dey IISc
2 Dr. Shuchita Goyal BITS, Pilani