Related papers: Strictly Commutative Complex Orientations of $Tmf_…
A conformal change of $TM\oplus T^*M$ is a morphism of the form $(X,\alpha)\mapsto(X,e^\tau\alpha)$ $(X\in TM,\alpha\in T^*M,\tau\in C^\infty(M))$. We characterize the generalized almost complex and almost Hermitian structures that are…
We uncover a topological classification applicable to open fermionic systems governed by a general class of Lindblad master equations. These `quadratic Lindbladians' can be captured by a non-Hermitian single-particle matrix which describes…
We study the implication of refined topological string amplitudes in the supersymmetric N=1 flux compactification. They generate higher derivative couplings among the vector multiplets and graviphoton with generically non-holomorphic moduli…
The paper is devoted to real Hamiltonian forms of 2-dimensional Toda field theories related to exceptional simple Lie algebras, and to the spectral theory of the associated Lax operators. Real Hamiltonian forms are a special type of…
We construct the twisted Fock module of quantum toroidal $\mathfrak{gl}_1$ algebra with a slope $n'/n$ using vertex operators of quantum affine $\mathfrak{gl}_n$. The proof is based on the $q$-wedge construction of an integrable level-one…
We give general expressions for singular vectors of the N=2 superconformal algebra in the form of {\it monomials} in the continued operators by which the universal enveloping algebra of N=2 is extended. We then show how the algebraic…
In this paper, we study the elliptic spectral sequence computing $tmf_*(\mathbb{R} P^2)$ and $tmf_* (\mathbb{R} P^2 \wedge \mathbb{C} P^2)$. Specifically, we compute all differentials and resolve exotic extensions by 2, $\eta$, and $\nu$.…
Let R be a commutative ring with unity and M be an R-module. In this study, we construct the \tilde{Spec}(M) topology using the prime spectrum of module M and multiplicatively closed subsets of R with the closed sets \tilde{V}(S)={P \in…
Let k be an algebraically closed field and A be a finitely generated, centrally finite, non- negatively graded (not necessarily commutative) k-algebra. In this note we construct a representation scheme for graded maximal Cohen-Macaulay A…
The construction of a family of real Hamiltonian forms (RHF) for the special class of affine 1+1-dimensional Toda field theories (ATFT) is reported. Thus the method, proposed in [1] for systems with finite number of degrees of freedom is…
We construct a triangulated category of cyclotomic complexes, a homological counterpart of cyclotomic spectra of Bokstedt and Madsen. We also construct a version of the Topological Cyclic Homology functor TC for cyclotomic complexes, and an…
We propose a topological plasmonic crystal structure composed of an array of parallel nanowires with unequal spacing. In the paraxial approximation, the Helmholtz equation that describes the propagation of light along the nanowires maps…
We discuss the connections between the complex SYK model at the conformal limit and warped conformal field theories. Both theories have an $SL(2,R) \times U(1)$ global symmetry. We present comparisons on symmetries, correlation functions,…
We generalize a recently proposed approach for the construction of pseudo-Hermitian Hamiltonians with real spectra. Present technique is based on a simple and straightforward similarity transformation of the coordinate and momentum.
We introduce a systematic mathematical language for describing fixed point models and apply it to the study to topological phases of matter. The framework is reminiscent of state-sum models and lattice topological quantum field theories,…
We provide a classification of generalized tilting modules and full exceptional sequences for the dual extension algebra of the path algebra of a uniformly oriented linear quiver modulo the ideal generated by paths of length two with its…
We present a unified framework to systematically embed complex knotted and linked structures, beyond the torus family, into diverse topological phases, including Hopf insulators, classical spin liquids, topological semimetals, and…
Modular functors, i.e. consistent systems of projective representations of mapping class groups of surfaces, have been constructed for non-semisimple modular categories already decades ago. Concepts from homological algebra have not been…
New exact modular branching rules are obtained for modules over the symmetric groups that are close to completely splittable modules. These results are based on some upper bounds for the Ext^1-spaces between simple modules.
Let $\Gamma = \Lambda[M]$ be the one-point extension of an algebra $\Lambda$ by a $\Lambda$-module $M$. We establish a method to lift projectively Wakamatsu tilting (PWT) modules from $\mathrm{mod}\,\Lambda$ to $\mathrm{mod}\,\Gamma$ by…