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Two-dimensional Yang-Mills theory via integrable probability
Thibaut Lemoine (IRMA)
https://arxiv.org/abs/2508.16162 https://arxiv.org/pdf/2508.16162

Two-dimensional Yang-Mills theory via integrable probability
In this paper, we review the construction and large $N$ study of the continuous two-dimensional Yang-Mills theory with gauge group $\mathrm{U}(N)$ through probability, combinatorics and representation theory. In a first part, we define the continuous Yang-Mills measure using Markovian holonomy fields, following a construction by L{é}vy, then we show in a second part how to derive Migdal's character expansion of the partition function for any compact structure group from this setting. We contin…

Remark on twists of Frobenius algebra and link homology
Noboru Ito, Keita Nakagane, Jun Yoshida
https://arxiv.org/abs/2508.13731 https://arxiv.org/pdf/2508…

Remark on twists of Frobenius algebra and link homology
We discuss twists on Frobenius algebras in the context of link homology. In his paper in 2006, Khovanov asserted that a twist of a Frobenius algebra yields an isomorphic chain complex on each link diagram. Although the result has been widely accepted for nearly two decades, a subtle gap in the original proof was found in the induction step of the construction of the isomorphism. Following discussion with Khovanov, we decided to provide a new proof. Our proof is based on a detailed analysis of c…

Legendre-Gauss-Lobatto Collocation Method for Optimal Control via Polynomial Approximations of Differential Equation Vector Fields
Gabriela Abadia-Doyle, William W. Hager, Anil V. Rao
https://arxiv.org/abs/2506.13938

Legendre-Gauss-Lobatto Collocation Method for Optimal Control via Polynomial Approximations of Differential Equation Vector Fields
A new method is described for solving optimal control problems using direct collocation at Legendre-Gauss-Lobatto points. The approach of this paper employs a polynomial approximation of the right-hand side vector field of the differential equations and leads to the following important outcomes. First, the first-order optimality conditions of the LGL integral form are derived, which lead to a full-rank transformed adjoint system and novel costate estimate. Next, a derivative-like form of the LG…

This https://arxiv.org/abs/2401.04391 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Kawamata-Miyaoka type inequality for canonical $\mathbb Q$-Fano varieties II: Terminal $\mathbb Q$-Fano threefolds
We prove an optimal Kawamata-Miyaoka type inequality for terminal $\mathbb Q$-Fano threefolds with Fano index at least $3$. As an application, we obtain that any terminal $\mathbb Q$-Fano threefold $X$ satisfies the following Kawamata-Miyaoka type inequality \[ c_1(X)^3 < 3c_2(X)c_1(X). \]

Spanning path-cycle systems with given end-vertices in regular graphs (full version)
Yoshimi Egawa, Mikio Kano, Kenta Ozeki
https://arxiv.org/abs/2508.11302 https://

Spanning path-cycle systems with given end-vertices in regular graphs (full version)
We prove the following theorem. Let $r\ge 4$ be an integer, and $G$ be a $K_{1,r}$-free $r$-edge-connected $r$-regular graph. Then, for every set $W$ of even number of vertices of $G$ such that the distance between any two vertices of $W$ in $G$ is at least 3, $G$ has vertex-disjoint paths and cycles $P_1, \ldots, P_m, C_1, \ldots, C_n$ such that (i) $V(G)=V(P_1) \cup \cdots \cup V(P_m) \cup V(C_1) \cup \cdots \cup V(C_n)$, (ii) each path $P_i$ connects two vertices of $W$, and (iii) the set of…

This https://arxiv.org/abs/2408.11643 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

K3 surfaces with maximal complex multiplication
Following Valloni, we study complex projective K3 surfaces having complex multiplication by rings of integers.

This https://arxiv.org/abs/2308.01456 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Decomposing a signed graph into rooted circuits
We prove a precise min-max theorem for the following problem. Let $G$ be an Eulerian graph with a specified set of edges $S \subseteq E(G)$, and let $b$ be a vertex of $G$. Then what is the maximum integer $k$ so that the edge-set of $G$ can be partitioned into $k$ non-zero $b$-trails? That is, each trail must begin and end at $b$ and contain an odd number of edges from~$S$. This theorem is motivated by a connection to vertex-minors and yields two conjectures of Máčajová and Škoviera as cor…

Judicious Partitions in Edge-Weighted Graphs with Bounded Maximum Weighted Degree
G. Gutin, M. A. Nielsen, A. Yeo, Y. Zhou
https://arxiv.org/abs/2507.05827

Judicious Partitions in Edge-Weighted Graphs with Bounded Maximum Weighted Degree
In this paper, we investigate bounds for the following judicious $k$-partitioning problem: Given an edge-weighted graph $G$, find a $k$-partition $(V_1,V_2,\dots ,V_k)$ of $V(G)$ such that the total weight of edges in the heaviest induced subgraph, $\max_{i=1}^k w(G[V_i])$, is minimized. In our bounds, we also take into account the weight $w(V_1,V_2,\dots,V_k)$ of the cut induced by the partition (i.e., the total weight of edges with endpoints in different parts) and show the existence of a par…

This https://arxiv.org/abs/2401.04391 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Kawamata-Miyaoka type inequality for canonical $\mathbb Q$-Fano varieties II: Terminal $\mathbb Q$-Fano threefolds
We prove an optimal Kawamata-Miyaoka type inequality for terminal $\mathbb Q$-Fano threefolds with Fano index at least $3$. As an application, we obtain that any terminal $\mathbb Q$-Fano threefold $X$ satisfies the following Kawamata-Miyaoka type inequality \[ c_1(X)^3 < 3c_2(X)c_1(X). \]

A non-face characterization of spheres on few vertices
Shuai Huang, Jasper Miller, Daniel Rose-Levine, Steven Simon
https://arxiv.org/abs/2507.06120 https:…

A non-face characterization of spheres on few vertices
We give a relatively simple characterization of simplicial $d$-spheres on $d+4$ vertices; our criteria are in terms of the intersection patterns of a simplicial complex's minimal non-faces. Namely, let $Σ$ be a simplicial complex with vertex set $[d+4]$ and let $\mathcal{F}=\{A_0,\ldots, A_{n-1}\}$ be its family of minimal non-faces, indices taken in $\mathbb{Z}_n$. Then $Σ$ is a $d$-sphere if and only if the following hold: $n\geq 3$ is odd, successive $A_i$ are disjoint, and the alternating…