The CACAAG seminar at IIT Bombay is now taking a new avatar as** Facets of CACAAG. **

Facets of CACAAG will highlight various aspects of combinatorial commutative algebra-algebraic geometry, broadly interpreted. This includes closely related topics such as algebraic combinatorics and combinatorial representation theory. The talks will start at a level accessible to graduate students and will eventually touch upon some of the modern developments and future directions.

Update on 26 November, 2020.

Upcoming talks:

December 03, Ezra Miller, Duke University.

December 10, Raman Sanyal, Goethe-Universität Frankfurt.

December 15, Satoshi Murai, Waseda University.

Update on 18 July, 2020.

The schedule:

July 9, Nathan Ilten, Simon Fraser University. Here is the recording of Nathan’s talk.

Upcoming:

July 23, Mateusz Michalek, Max Planck Institute for Mathematics in the Sciences. Here is the recording of Mateusz’s talk.

July 30, R Venkatesh, Indian Institute of Science, Bangalore.

August 7, Gunnar Fløystad, University of Bergen.

August 13, Arvind Ayyer, Indian Institute of Science, Bangalore.

September 3, Amritansu Prasad, Institute of Mathematical Sciences, Chennai.

October 8, Alex Fink, Queen Mary University of London.

November 26: Alexey Garber, The University of Texas Rio Grande Valley.

We plan to start with a talk by Nathan Ilten (https://www.sfu.ca/~nilten/) next week, July 9 and R Venkatesh (http://math.iisc.ac.in/~rvenkat/) will speak on July 30. More updates will follow soon.

We will create a repository of the recordings of the talks and upload the lecture material (with the permission of the speaker).

The following is a record of the CACAAG seminar.

- Update from 5 June, 2020.

Greg Blekherman spoke yesterday “Do Sums of Squares Dream of Free Resolutions”. The next CACAAG seminar in on June 11 and the speaker is Timo de Wolff, Technische Universität Braunschweig (had to be postponed from May 28). He will speak on Nonnegativity, Discriminants and Tropical Geometry.

- Update from 22 May, 2020

The next CACAAG seminar in on May 28 and the speaker is Timo de Wolff, Technische Universität Braunschweig. He will speak on Nonnegativity, Discriminants and Tropical Geometry.

After that we have Greg Blekherman, Georgia Institute of Technology speaking on June 4.

- Update from 30 April, 2020:

The next CACAAG seminar is on May 7 and the speaker is Justin Chen, Georgia Institute of Technology on Free resolutions of function classes via order complexes.

- Update from 18 April, 2020:

We are currently hosting the CACAAG seminar via video conferencing (so far via Zoom). We had a series of three Lectures by Jugal Verma on toric ideals and integer programming. Our next seminar is by Ayush Kumar Tewari, TU Berlin and is scheduled for Thursday 23 April 2020 (6pm IST=2:30 PM CET=1:30 PM GMT).

- Update from 2 March, 2020:

This semester we have had introductory lectures on tropical algebraic geometry. In the next few weeks, we will have lectures on uniformization of elliptic curves (complex and at some point non-archimedean) (Speaker: Poornima) and Bruhat-Tits trees (Speaker: Dipendra Prasad).

- Update from 7 August 2019:

This semester we plan to have following list of topics:

- An Introduction to the Geometry of Numbers: Madhusudan Manjunath.
- Gubeladze’s proof of Anderson’s Conjecture (on projective modules over monoid rings), Manoj Keshari and Maria Matthew.
- The Polynomial Method in Discrete geometry, Mrinal Kumar.
- Aspects of Toric Ideals: Integer Programming and Invariant Theory: Jugal Verma.
- Tightness of Surfaces and Betti numbers of Ideals (as in the work of Murai): Sameer Shukla and Madhusudan Manjunath.
- Brill-Noether theory (and/ or Toric Local Cohomology): Madhusudan Manjunath.

Update from January 2019:

This semester we plan to have talks on three themes:

i. Zeta Functions Associated to Graphs: We will study the Ihara Zeta Function, the two variable Zeta Function due to Lorenzini.

ii. Combinatorial Brill-Noether Theory: I will talk about some ongoing work on this topic.

iii. Hilbert Series and Free Resolutions in Complexity Theory.

- Update from 7 July, 2018:

Last semester, we explored various aspects of Green’s conjecture. This semester we plan to continue some parts of it that were not covered last time. We plan to have a mix of topics around combinatorial algebraic geometry such as graph complexes, Tutte polynomial and so on…

- Update from the 17 January, 2018 meeting:

This semester we’ll have talks on two themes i. Tropical curves and their divisor theory, ii. Green’s conjecture on syzygies of canonical curves. We’ll start with the basics of tropical part (about 2-3 weeks) and then move to basics of Green’s conjecture part (2-3 weeks). We’ll then move on to more advanced aspects of both these topics.

- Update from 8-th September meeting:

This semester (probably the next) we plan to focus on aspects of syzygies: combinatorial, algebraic, geometric. We’ll devote the first few lectures to the basics of syzygies.

In the future, we plan to cover various aspects of the interplay between Combinatorics and Commutative Algebra-Algebraic Geometry. Some possible topics are

i. Syzygies: connections to Combinatorics, Syzygies of curves particularly Green’s conjecture and the related conjecture for Graph Curves, Boij-Soederberg theory, Syzygies in Tropical geometry.

ii. Vector Bundles with potential connections to Tropical Geometry.

iii. Dessins D’enfants:

iv. Brill-Noether theory on Algebraic curves and Tropical curves, Combinatorial Aspects of Moduli Spaces.

v. Non-archimedean Geometry in connection with Tropical Geometry, particular Berkovich Spaces,

vi. Combinatorics and Hodge theory, Vector Partition Functions.

vii. Ideals of Powers of Linear Forms.

viii. Tutte Polynomials of Graphs, Zeta Functions associated to Graphs.

ix. Syzygies in Real Algebraic Geometry.

x. Tropical Geometry in Dimensions Two and Higher.

We plan to pick a theme every semester followed by talks by local faculty and students. These talks will be introductory and will assume very little background. We will then invite speakers from outside for more specialized talks on this theme.