AIM Problem Lists

For any random walk on the free group or free semigroup, the Gromov boundary with the hitting measure is a topological model for the Poisson boundary.

Let $P_n(z) = \sum_{0\le k\le n} \frac1{\sqrt{k}} \xi_k z^k$ with $\xi_k$ iid centered random variables of variance one, and consider the random measures $\mu_n$ on $S^1$ with dens…

Are there examples in higher dimension given as surface bundles over a surface? Can these be compact examples? In particular, for $g,h \ge 2$ does there exist an $\Sigma_g$-bundle…

Understand the higher Du Bois singularities in the case of cubics and see what are some examples of Hodge structures in the case of cubics.

Is it true that the lazy non-backtracking random walk (NBRW) mixes faster than the lazy simple random walk (SRW)?

Can we find a set of conditions such that the homogeneous equation is globally well-posed, but the inhomogeneous equation blows up? Can this be down for the isotropic Landau equati…

This group should aim to understand to what extent LaTeX does and does not meet the needs of current mathematicians. After such an understanding is had, it should aim to create a l…

The goal of this group should be to investigate what tools exist for knowledge tracing and should outline what tools could be developed to continue this pursuit, now that interest…

The goal of this group is to create a survey of what work has been done on educational proof software and to describe the goals which spurred its creation. The group should aim to…

The sole object of this group is to decide whether or not to finish the software SpaceMath.

The group has the express goal of finding ways in which current computer algebra systems can interact with formal theorem provers, such as Lean, and vice versa. The guiding motivat…

The goals of this group are to reevaluate the aims of math communication, using specific examples, and introduce new concepts that they believe will impact the future of how mathem…

The goal of this group is to discuss ways to create an online database of mathematical visualizations. While creating such a database in a week is not feasible, the group aims to f…

The goal of this group is to produce an example of an "on-ramp" which could be given to someone with little to no experience in software, from which they could learn to do some pro…

This group aims to find examples of open-source project groups that did and did not succeed at long-term sustainability. The concrete goal is to discover principles that underlie t…

This problem asks generally how to build a database of databases to help users navigate to the resource where the information they wish to obtain is. The concrete goal of this obje…

begin{enumerate}[label=alph)] item Relate $tr(T(m,n))$ to rings of quasi-invariants and to A. Wilson's conjecture on $\nabla_{p_1}^n$. item Describe $H^*(\text{Hilb}(x^{nd}=y^n))$…

Find functors from derived horizontal trace computing $\mathcal{gl}(m|n)$-homology.

What is the action of the full twist on the trace of the Hecke category? Does it relate to $\nabla$? How does it act on Schur objects?

Relate categorification of Elliptic Hall algebra to the trace of the affine Hecke category and to End$\bigg(\displaystyle \bigoplus_n S$Bim$_n\bigg)$.

Can we categorify "simplier" Hall algebras such as the Hall algebra on the affine line?

Can we categorify the Elliptic Hall algebra?

Understand Maulik's proof of the Oblomkov-Shende conjecture, then categorify it!

Relate 3-row and more general Springer fibers to bow varieties and link homology.

Is there an affine Springer fiber model for colored link homology?