Program

Monday, May 11

09:00 - 10:30:  Mini-Course 1 Day 1 (Li)

10:30 - 11:00:  Coffee

11:00 - 12:00:  Problems (Li)

12:00 - 13:30:  Lunch

13:30 - 15:00:  Mini-Course 2 Day 1 (Gillespie, Levinson) 

15:00 - 15:30:  Coffee

15:30 - 16:30:  Problems (Gillespie, Levinson)

Tuesday, May 12

09:00 - 10:00: Mini-Course 1 Day 2 (Li)

10:00 - 10:30: Coffee

10:30 - 11:30: Problems (Li)

11:30 - 13:00: Lunch

13:00 - 14:00: Mini-Course 2 Day 2 (Gillespie, Levinson) 

14:00 - 14:30: Coffee

14:30 - 15:30: Problems (Gillespie, Levinson)

16:00 - 17:00: Research talk - Rob Silversmith - Counting configurations of points in projective space

Wednesday, May 13

09:00 - 10:00: Mini-Course 1 Day 3 (Li)

10:00 - 10:30: Coffee

10:30 - 11:30: Problems (Li)

11:30 - 13:00: Lunch

13:00 - 14:00: Mini-Course 2 Day 3 (Gillespie, Levinson) 

14:00 - 14:30: Coffee 

14:30 - 15:30: Problems (Gillespie, Levinson)

15:30 - 17:00: Free afternoon

Thursday, May 14

09:00 - 10:00: Mini-Course 1 Day 4 (Li)

10:00 - 10:30: Coffee 

10:30 - 11:30: Problems (Li)

11:30 - 13:00: Lunch

13:00 - 14:00: Mini-Course 2 Day 4 (Gillespie, Levinson) 

14:00 - 14:30: Coffee 

14:00 - 15:30: Problems (Gillespie, Levinson)

15:30 - 16:30: Research talk - Siddarth Kannan - The Chow groups of the braid matroid as representations of the symmetric group

Friday, May 15

8:30 - 9:00: Coffee 

9:00 - 10:00: Research Talk - Nate Bottman - The associahedra and 2-associahedra in symplectic geometry

10:00 - 11:00: Research Talk - Daria Poliakova - Higher categorical associahedra 

11:00 - 12:30: Posters, PIzza and Pop (poster session with pizza, refreshments and coffee)

12:30 - 13:30:  Research talk - José González - Polymatroids and moduli of points in flags

Satellite events that might interest participants:

14:00 - 15:00: LACIM Seminar (PK-4323) Sheila Sundaram (Minnesota) - Some conjectures around on a curious variant of Lie(n)

15:30 - 16:30: CRM Colloquium (CRM, Salle / Room 1140, Pavillon André Aisenstadt Université de Montréal) - Melanie Matchett Wood (Harvard)

Titles and Abstracts talks

• Nate Bottman (Vermont) - The associahedra and 2-associahedra in symplectic geometry

Categorical symplectic geometry probes symplectic manifolds M by studying maps from Riemann surfaces into M. In the early 1990s, Fukaya discovered that the associahedra play a central role in assembling these maps into coherent algebraic structures. I will explain why studying the functoriality properties of these structures gives rise to the so-called {\em 2-associahedra}, and explain how the latter's combinatorial structure has lately been coming into better view. I will state a result, joint with Backman and Poliakova, in which we produce fan realizations of 2-associahedra. If there is time, I will make a connection with wonderful compactifications.

• José González (UC Riverside) - Polymatroids and moduli of points in flags

We will discuss two compactifications associated with configurations of labeled points in a flag of affine spaces. The first, constructed using the weighted Fulton-MacPherson compactifications of Routis, gives a moduli space of n distinct weighted labeled points in the flag up to translation and scaling. The second, constructed using the generalized Fulton-MacPherson compactifications of Kim-Sato, gives a compactification of the configuration space of n not necessarily distinct points in the flag. For suitable choices of weights, the first space is toric and identifies with the polypermutohedral variety of Crowley-Huh-Larson-Simpson-Wang, while the second is toric and identifies with the polystellahedral variety of Eur-Larson. We will also describe a fibration on the polypermutohedral compactification whose fibers are Losev-Manin spaces, as well as a geometric quotient relating the polystellahedral and polypermutohedral compactifications. This is joint work with Patricio Gallardo and Javier Gonzalez-Anaya.

• Siddarth  Kannan (MIT) - The Chow groups of the braid matroid as representations of the symmetric group

The rational Chow ring of the braid matroid Bn, with respect to the maximal building set, is a finite-dimensional graded representation of the symmetric group $S_n$. I will discuss joint work with Lukas Kühne where we determine the characters of these graded $S_n$-representations for all n. A key geometric input into our calculation is the identification of the corresponding wonderful variety with a moduli space of multiscale differentials, established by Devkota, Robotis, and Zaharuic. We determine the classes of these moduli spaces in the Grothendieck ring of varieties and prove our formula by specializing these classes to $S_n$-equivariant Poincare polynomials. Our calculation of these polynomials relies crucially on symmetric function theory. I will aim to make this talk accessible to first-year graduate students.

• Daria Polyakova (University of Hamburg) - Higher categorical associahedra 

Associahedra are compactifications of moduli spaces of n points on a line. What if one considers $k$ vertical lines in $\mathbb{R}^2$, with $n_i$ points on each? This gives rise to 2-associahedra of Bottman. What if one iterates this, replacing $\mathbb{R}^2$ with $\mathbb{R}^n$, and lines with hyperplanes, each carrying some arrangement as before? This gives rise to higher categorical associahedra, introduced by Backman, Bottman and myself. I will report on our work about those, where we realise them geometrically as complete fans, generalising Loday's construction for the classic associahedron. Time permitting,  I will mention some newer results on these objects.

• Rob Silversmith (Emory University) - Counting configurations of points in projective space

The cross-ratio degree problem is a combinatorial problem in involving $M_{0,n}$: it counts configurations of points in $\mathbb{P}^1$ such that specified subsets have fixed cross-ratio. No combinatorial answer is known, though we do know various constraints involving the theory of matchings of bipartite graphs. I’ll discuss what is known about this problem, some interesting special cases and equivalent characterizations, and the natural generalization to higher dimensions.