Related papers: Superpotential algebras and manifolds
We classify the simple modules of the exceptional algebraic supergroups over an algebraically closed field of prime characteristic.
We study orientability issues of moduli spaces from gauge theories on Calabi-Yau manifolds. Our results generalize and strengthen those for Donaldson-Thomas theory on Calabi-Yau manifolds of dimensions 3 and 4. We also prove a corresponding…
Superpotentials in ${\cal N}=2$ supersymmetric classical mechanics are no more than the Hamilton characteristic function of the Hamilton-Jacobi theory for the associated purely bosonic dynamical system. Modulo a global sign, there are…
This review gives an introduction to cohomological Donaldson-Thomas theory: the study of a cohomology theory on moduli spaces of sheaves on Calabi-Yau threefolds, and of complexes in 3-Calabi-Yau categories, categorifying their numerical DT…
We study aspects of Calabi-Yau four-folds as compactification manifolds of F-theory, using mirror symmetry of toric hypersurfaces. Correlation functions of the topological field theory are determined directly in terms of a natural ring…
We consider the bulk algebra and topological D-brane category arising from the differential model of the open-closed B-type topological Landau-Ginzburg theory defined by a pair $(X,W)$, where $X$ is a non-compact Calabi-Yau manifold and $W$…
For each prime number $s$ we introduce examples of $(s-1)$- and $s$-representation infinite algebras in the sense of Herschend, Iyama and Oppermann, which arise from skew group algebras of some metacyclic groups embedded in…
In this talk I describe some applications of random matrix models to the study of N=1 supersymmetric Yang-Mills theories with matter fields in the fundamental representation. I review the derivation of the…
We review the geometrical framework required for understanding the moduli space of $(2,2)$ superconformal-field theories, highlighting various aspects of its phase structure. In particular, we indicate the types of phase diagrams that…
We address the macroscopic theory of superconductivity - the Ginzburg-Landau theory. This theory %Macroscopic theory of superconductivity is based on the celebrated Ginzburg - Landau equations. First developed to explain and predict…
This is a survey article on Hall algebras and their applications to the study of motivic invariants of moduli spaces of coherent sheaves on Calabi-Yau threefolds. It is a write-up of my talks at the 2015 Salt Lake City AMS Summer Research…
We extend the construction of Calabi-Yau manifolds to hypersurfaces in non-Fano toric varieties, requiring the use of certain Laurent defining polynomials, and explore the phases of the corresponding gauged linear sigma models. The…
We study superstring propagations on the Calabi-Yau manifold which develops an isolated ADE singularity. This theory has been conjectured to have a holographic dual description in terms of N=2 Landau-Ginzburg theory and Liouville theory. If…
Let $A$ be a finite dimensional $Q-$algebra and $\Gamma subset A$ a $Z-$order. We classify those $A$ with the property that $Z^2$ does not embed in $\mathcal{U}(\Gamma)$. We call this last property the hyperbolic property. We apply this in…
In these lecture notes, we survey the landscape of Calabi-Yau threefolds, and the use of machine learning to explore it. We begin with the compact portion of the landscape, focusing in particular on complete intersection Calabi-Yau…
We show that there are infinitely many commensurability classes of pseudomodular groups, thus answering a question raised by Long and Reid. These are Fuchsian groups whose cusp set is all of the rationals but which are not commensurable to…
We describe the representation theory of finitely generated indecomposable modules over artin algebras which do not lie on cycles of indecomposable modules involving homomorphisms from the infinite Jacobson radical of the module category.
The thesis is devoted to abstract, geometric and symmetric aspects of modern elementary particle theories. A new direction in constructing supersymmetric and superstring models based on consequent and strong consideration and inclusion of…
Some basic facts about the prepotential in the SW/Whitham theory are presented. Consideration begins from the abstract theory of quasiclassical $\tau$-functions , which uses as input a family of complex spectral curves with a meromorphic…
Atiyah and Hirzebruch gave examples ofeven degree torsion classes in the singularcohomology of a smooth complex projective manifold, which arenot Poincar\'{e} dual to an algebraiccycle. We notice that the order ofthese classes are small…