Related papers: The Crepant Transformation Conjecture implies the …
We discuss some examples in which symplectic monodromy (provably or conjecturally) splits off the symplectic mapping class group, hoping to illustrate different techniques and inputs to the arguments. Along the way we formulate several open…
In 2007, Dmytrenko, Lazebnik and Williford posed two related conjectures about polynomials over finite fields. Conjecture~1 is a claim about the uniqueness of certain monomial graphs. Conjecture~2, which implies Conjecture~1, deals with…
We prove a conjecture of Sturmfels, Timme and Zwiernik on the ML-degrees of linear covariance models in algebraic statistics. As in our previous works on linear concentration models, the proof ultimately relies on the computation of certain…
We conjecture an upper bound on the growth of the Yokota invariant of polyhedral graphs, extending a previous result on the growth of the $6j$-symbol. Using Barrett's Fourier transform we are able to prove this conjecture in a large family…
The Nekrasov conjecture predicts a relation between the partition function for N=2 supersymmetric Yang-Mills theory and the Seiberg-Witten prepotential. For instantons on R^4, the conjecture was proved, independently and using different…
Given a complex structure, we investigate diverging sequences of projective structures on the fixed complex structure in terms of Thurston's parametrization. In particular, we will give a geometric proof to the theorem by Kapovich stating…
The goal of this article is to clarify the relationship between the topos of triads and the neo-Riemannian PLR-group. To do this, we first develop some theory of generalized interval systems: 1) we prove the well known fact that every pair…
Let E be an elliptic curved defined over $\Q$ and let $K/\Q$ be a finite Galois extension with Galois group G. The equivariant Birch-Swinnerton-Dyer conjecture for $h^1(E\times_{\Q} K)(1)$ viewed as a motive over $\Q$ with coefficients in…
The BKMP Remodeling Conjecture \cite{Ma,BKMP09,BKMP10} predicts all genus open-closed Gromov-Witten invariants for a toric Calabi-Yau $3$-orbifold by Eynard-Orantin's topological recursion \cite{EO07} on its mirror curve. The proof of the…
Let $G$ be a polyhedral group $G\subset SO(3)$ of types $\mathbb{Z}/n\mathbb{Z}$, $D_{2n}$ and $\mathbb{T}$. We prove that there exists a one-to-one correspondence between flops of $G$-Hilb$\mathbb{C}^3$ and mutations of the McKay quiver…
A composition of birational maps given by Laurent polynomials need not be given by Laurent polynomials; however, sometimes---quite unexpectedly---it does. We suggest a unified treatment of this phenomenon, which covers a large class of…
We prove the conjectural correspondence between logarithmic Gromov-Witten theory and logarithmic Donaldson/Pandharipande-Thomas theory for pairs $(Y|\partial Y)$ consisting of a toric threefold $Y$ and any torus invariant divisor $\partial…
In recent work, the authors derived a tropical interpretation of monotone and strictly monotone double Hurwitz numbers. In this paper, we apply the technique of tropical flows to this interpretation in order to provide a new proof of the…
We prove the Hilbert-Chow crepant resolution conjecture in the exceptional curve classes for all projective surfaces and all genera. In particular, this confirms Ruan's cohomological Hilbert-Chow crepant resolution conjecture. The proof…
We develop a probabilistic approach to the celebrated Jacobian conjecture, which states that any Keller map (i.e. any polynomial mapping $F\colon \mathbb{C}^n \to \mathbb{C}^n$ whose Jacobian determinant is a nonzero constant) has a…
We provide a general framework for wall-crossing of equivariant K-theoretic enumerative invariants of appropriate moduli stacks $\mathfrak{M}$, by lifting Joyce's homological universal wall-crossing arXiv:2111.04694 to K-theory and to…
We study the relationship between Gromov-Witten invariants of local $\mathbb{P}^4$ and Gromov-witten invariants of $[\mathbb{C}^5/\mathbb{Z}_5]$ for all genera. We state the crepant resolution conjecture in explicit form and prove this…
In the previous author's paper the Macdonald norm conjecture (including the famous constant term conjecture) was proved. This paper contains the proof of the remaining two (the duality and evaluation conjectures). The evaluation theorem is…
A new construction of BPS monodromies for 4d ${\mathcal N}=2$ theories of class S is introduced. A novel feature of this construction is its manifest invariance under Kontsevich-Soibelman wall crossing, in the sense that no information on…
We propose a conjectural determination of the Gromov-Witten theory of a root stack along a smooth divisor. We verify our conjecture under an additional assumption.