相关论文: The strong Kervaire invariant problem in dimension…

We consider the singular $SU(3)$ Toda system with multiple singular sources \begin{align*} \left\{\begin{array}{ll}-\Delta w_1=2e^{2w_1}-e^{w_2}+2\pi\sum_{\ell=1}^m\beta_{1,\ell}\delta_{P_{\ell}}\quad\text{in }\mathbb{R}^2\\…

In this paper, we consider the following elliptic Toda system associated to a general simple Lie algebra with multiple singular sources \begin{equation*} \begin{cases} -\Delta…

We derive the continuous nilpotent symmetries of the four (3 + 1)-dimensional (4D) model of the Hodge theory (i.e. 4D Abelian 2-form gauge theory) by exploiting the beauty and strength of the symmetry invariant restrictions on the…

The vector space $\V$ generated by the conjugacy classes in the fundamental group of an orientable surface has a natural Lie cobracket $\map{\delta}{\V}{\V\times \V}$. For negatively curved surfaces, $\delta$ can be computed from a geodesic…

About six years ago, semitoric systems on 4-dimensional manifolds were classified by Pelayo & Vu Ngoc by means of five invariants. A standard example of such a system is the coupled spin-oscillator on $\mathbb{S}^2 \times \mathbb{R}^2$.…

We derive the off-shell nilpotent (anti-)BRST symmetry transformations by exploiting the (anti-)chiral superfield approach (ACSA) to Becchi-Rouet-Stora-Tyutin (BRST) formalism for the four (3+1)-dimensional (4D)…

We construct automorphic forms on the 5-dimensional complex ball which give the inverse of the period map for cyclic 4-ple coverings of the complex projective line branching at eight points with branching index (1/4,...,1/4).

We show how to construct semi-invariants and integrals of the full symmetric sl(n) Toda lattice for all n. Using the Toda equations for the Lax eigenvector matrix we prove the existence of semi-invariants which are homogeneous coordinates…

We show that Kervaire invariant one elements in the homotopy groups of spheres exist only in dimensions at most 126. By Browder's Theorem, this means that smooth framed manifolds of Kervaire invariant one exist only in dimensions 2, 6, 14,…

Over the past two decades, there has been much progress on the classification of symplectic linear quotient singularities V/G admitting a symplectic (equivalently, crepant) resolution of singularities. The classification is almost complete…

We prove the vanishing of many Welschinger invariants of real symplectic $4$-manifolds. In some particular instances, we also determine their sign and show that they are divisible by a large power of 2. Those results are a consequence of…

In analogy with the Liouville case we study the $sl_3$ Toda theory on the lattice and define the relevant quadratic algebra and out of it we recover the discrete $W_3$ algebra. We define an integrable system with respect to the latter and…

We give an explicit regular model for the quadric fibration studied in Pirutka (2011). As an application we show that this construction furnishes a counterexample for the integral Tate conjecture in any odd characteristic for some…

We describe a computational proof that the fifth secant variety of the Segre product of five copies of the projective line is a codimension 2 complete intersection of equations of degree 6 and 16. Our computations rely on pseudo-randomness,…

We study 2-term tilting complexes of Brauer tree algebras in terms of simplicial complexes. We show the symmetry and convexity of the simplicial complexes as lattice polytopes. Via a geometric interpretation of derived equivalences, we show…

By analyzing the connection between complex Hadamard matrices and spectral sets we prove the direction ``spectral -> tile'' of the Sectral Set Conjecture for all sets A of size at most 5 in any finite Abelian group. This result is then…

It was proved in [8,9] that every Lagrangian submanifold $M$ of a complex space form $\tilde M^{5}(4c)$ of constant holomorphic sectional curvature $4c$ satisfies the following optimal inequality: {align}\tag{A}\delta(2,2)\leq…

A category of Brauer diagrams, analogous to Turaev's tangle category, is introduced, and a presentation of the category is given; specifically, we prove that seven relations among its four generating homomorphisms suffice to deduce all…

We show that on conformal manifolds of even dimension $n\geq 4$ there is no conformally invariant natural differential operator between density bundles with leading part a power of the Laplacian $\Delta^{k}$ for $k>n/2$. This shows that a…

The Theta invariant is the simplest 3-manifold invariant defined with configuration space integrals. It is actually an invariant of rational homology spheres equipped with a combing over the complement of a point. It can be computed as the…