## Test your intuition 47: AGC-GTC-TGC-GTC-TGC-GAC-GATC-? what comes next in the sequence?

Before getting to the main topic of this post, first, Happy New Year 2022 and Merry Christmas to all readers, and second, a quick update: A community blog to discuss open problems in algebraic combinatorics was created. Everybody is invited to check out the problems posted there, to subscribe, and to contribute their own problems.

### Virtual Poll:

What will be the next term in the sequence AGC-GTC-TGC-GTC-TGC-GAC-GATC- ???

1. GTC
2. GATC
3. TAGC
4. GCTC
5. C:GAT
6. Another answer

Oberwolfach, Geometric, algebraic and topological combinatorics, 2019. Giulia Codenotti, Aldo Conca, Sandra Di Rocco, Bruno Benedetti, and Lorenzo Venturello

### Our August 2019 Oberwolfach meeting.

At the end of August 2019 we had in Oberwolfach a very fruitful meeting on Geometric, algebraic, and topological combinatorics. (In this post, I mentioned an open problem from the problem session.) I came to Oberwolfach just after a visit, with my son-in-law, Eran, to CERN near Genève. (See this post for pictures from ATLAS, CERN, and this post regarding my CERN colloquium.)

The August 2019 Oberwolfach meeting was the seventh meeting in a series of meetings that started in 1995.  Here is, by the way, is  very nice article in Quanta Magazine about an Oberwolfach Meeting. (And feel free to share Oberwolfach memories in the comment section.)

The sequence in the title of the post is not a DNA sequence or something similar but rather it refers to these meetings in Oberwolfach and this post is devoted to these series of meetings and other meetings in Oberwolfach.

## Oberwolfach: AGC, 1995; GTC, 1999; TGC, 2003; GTC, 2007; TGC, 2011; GAC, 2015; GATC, 2019.

Here A stands for ‘Algebraic’, G stands for ‘Geometric’, T stands for ‘Topological’ and C stands for ‘Combinatorics’.

These series of conferences are devoted to algebraic, geometric, and topological combinatorics. Both algebraic and geometric combinatorics are very large areas (and topological combinatorics is pretty large) and usually participants of the conference are divided into several overlapping, much appreciated minorities. Actually, living in a country where every citizen is a member of a much appreciated minority seems like a nice political setting to me.

Here is the review of the first conference in the series AGC95.

### AGC 1995

I was slightly younger than 40 years old. The meeting, organized by Anders Björner, Günter Ziegler and me, took place before a sabbatical semester at IAS, Princeton in the fall 1995. Here are a few topics that were discussed:

Cluster algebras to be. Sergey Fomin’s lecture was on Piecewise-linear maps, total positivity, and pseudoline arrangements, it represented a joint work with Arkady Bernstein and Andrei Zelevinsky. This paper was the starting point of vastly influential cluster algebras that Sergey, Arkady, and Andrei started developing around that time.

Polytopes spheres and face numbers. Tom Braden talked about Intersection homology and polytopes – recent progress, this was about his paper with Bob MacPherson where (among other things) a conjecture that I made some years earlier was settled.

Convexity in the Grassmannian. Eli Goodman talked about a joint work with Ricky Pollack on  some combinatorial questions for convex sets on affine Grassmanian. Finding the right notion of convexity for a subset of the Grassmannian is a fascinating and unexplored question.

Optimization. Monique Laurent talked about  the geometry of the set of positive semidefinite matrices with diagonal entries. Rekha Thomas talked about using Gröbner bases to solve integer programs (and a comparison between linear and integer programming).

The two 2-lecture series.  Nati Linial gave a series of two lectures on the geometry of graphs. He talked about his program to think about graphs as metric objects and apply insights regarding metric spaces to theoretical computer science. This was shortly after the Linial-London Rabinovich paper that had large impact in theoretical computer science and combinatorics had appeared.  Rade Zivaleivich  gave two lectures on methods of obstruction theory, related to topological and colorful Tverberg theorems and measure partitions and other questions. We came back to this topic in subsequent  conferences in the series.

Real algebraic geometry. Ricky Pollack talked about Complexity and algorithms in real algebraic geometry.

Triangulations of cyclic polytopes and the generalized Baues Conjecture.
Jorg Rambau talked about a counterexample to the “Generalized Baues Conjecture” and Vic Reiner talked about Triangulations of cyclic polytopes: the higher Stasheff-Tamari posets.

Universality. Jürgen Richter Gebert explained why Realization spaces of 4-polytopes are universal!

See the review for some more talks on the topics listed above and on other topics such as Lattices of parabolic subgroups, Discrepancy theory, Combinatorics of knots and more.

Here are links to the workshop pages (WP) and full reviews (FR) of AGC, 1995 (WP, FR) ; GTC, 1999 (WP, FR); TGC, 2003  (WP, FR); GTC, 2007 (WP, FR); TGC, 2011 (WP, FR); GAC, 2015 (WP, FR); and GATC, 2019 (WP, FR).

Flashback: my first meeting at Oberwolfach

### Konvexe Körper 1982

I was a 27 year old graduate student. It was just after the 1982 Lebanon war. I had a one year old daughter and following the meeting my wife and I toured Italy for a week. It was great!  My thesis supervisor Micha A. Perles and my academic brother Michael Kallay also participated. At that conference I met for the first time many mathematicians and some of them have remained my good friends ever since. The meetings on Konvexe Körper took place every two years and I participated in several subsequent meetings.

### Oberwolfach’s Combinatorics meetings from January 2000 to January 2020

The other series of conferences in Oberwolfach that I attended regularly, is the combinatorics meeting that takes place in the first week of January every 2-3 years. The first one in the series was also the first Oberwolfach meeting after 2000.  The last meeting in this series was in January 2020 and just before the meeting my wife and I spent four great days in Rome. This was in fact our last trip outside Israel until September 2021 (not counting a 1-day visit to Petra).

## And the answer is: GATC (2023)

Half a year ago Isabella Novik, Paco Santos, Volkmar Welker and I submitted a proposal for a 2023 meeting which is going to be the 8th meeting in this series. Recently the meeting was approved! It will take place on December 10-16, 2023.

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### 1 Response to Test your intuition 47: AGC-GTC-TGC-GTC-TGC-GAC-GATC-? what comes next in the sequence?

1. - says:

Hah! Loved the idea of the puzzle!