Related papers: Seiberg-Witten geometry, modular rational elliptic…

By the quantization condition compact quantizable Kaehler manifolds can be embedded into projective space. In this way they become projective varieties. The quantum Hilbert space of the Berezin-Toeplitz quantization (and of the geometric…

We consider a class of super-conformal beta-deformed N=1 gauge theories dual to string theory on $AdS_5 \times X$ with fluxes, where $X$ is a deformed Sasaki-Einstein manifold. The supergravity backgrounds are explicit examples of…

We study the quantum moduli space of N=2 Chern-Simons quivers with generic ranks and CS levels, proving along the way exact formulas for the charges of bare monopole operators. We then derive N=2 Chern-Simons quiver theories dual to AdS_4 x…

Motivated by Miranda and Ascher--Bejleri's works on compactifications of the moduli space of rational elliptic surfaces with a section, we study constructions and boundaries of compact moduli spaces of elliptic surfaces with a multiple…

It is known that characters of BPS representations of extended superconformal algebras do not have good modular properties due to extra singular vectors coming from the BPS condition. In order to improve their modular properties we apply…

We describe a block-spin-like transformation on a simplified subset of the space of supersymmetric quiver gauge theories that arise on the worldvolumes of D-brane probes of orbifold geometries, by sequentially Higgsing the gauge symmetry in…

We study four-dimensional N=1 gauge theories arising on D3-branes probing toric singularities. Toric dualities and flows between theories corresponding to different singularities are analyzed by encoding the geometric information into (p,q)…

We study generalisations to totally real fields of methods originating with Wiles and Taylor-Wiles. In view of the results of Skinner-Wiles on elliptic curves with ordinary reduction, we focus here on the case of supersingular reduction.…

We study the twisted elliptic genera of 2d $(0,4)$ SCFTs associated with the BPS strings in the twisted circle compactification of 6d rank-one $(1,0)$ SCFTs. Such objects can arise when the 6d gauge algebra allows outer automorphism, thus…

We introduce a new fundamental domain for the cusp stabilizer of a Hilbert modular group over a real quadratic field K=Q(sqrt n). This is constructed as the union of Dirichlet domains for the maximal unipotent group, over the leaves in a…

I review some recent results on four-manifold invariants which have been obtained in the context of topological quantum field theory. I focus on three different aspects: (a) the computation of correlation functions, which give explicit…

The moduli space of cubic surfaces in complex projective space is known to be isomorphic to the quotient of the complex 4-ball by a certain arithmetic group. We apply Borcherds' techniques to construct automorphic forms for this group and…

We associate to a bound quiver (Q,I) a CW-complex which we denote by B(Q,I), and call the classifying space of (Q,I). We show that the fundamental group of B(Q,I) is isomorphic to the fundamental group of (Q,I). Moreover, we show that this…

The aim of this paper is to give an explicit extension of the classical elliptic integrals to the Hilbert modular case for $\mathbb{Q}(\sqrt{5})$. We study a family of Kummer surfaces corresponding to the Humbert surface of invariant $5$…

The Seiberg-Witten family of elliptic curves defines a Jacobian rational elliptic surface $\Z$ over $\mathbb{C}\mathrm{P}^1$. We show that for the $\bar{\partial}$-operator along the fiber the logarithm of the regularized determinant $-1/2…

We develop a method to build new 5D $\mathcal{N}=1$ gauge models based on Sasaki-Einstein manifolds $Y^{p,q}.$ These models extend the standard 5D ones having a unitary SU$\left( p\right) _{q}$ gauge symmetry based on $% Y^{p,q}$.…

We develop the diagrammatic technique of quiver subtraction to facilitate the identification and evaluation of the $\mathrm{SU}(n)$ hyper-K\"ahler quotient (HKQ) of the Coulomb branch of a $3d$ $\mathcal{N}=4$ unitary quiver theory. The…

We study surfaces constructed from groups of units in quaternion orders $\Lambda$ over the integers in real quadratic fields k. A short presentation of some general theory of such surfaces is given, in particular, we construct certain…

We generalize the mathematical definition of Coulomb branches of $3$-dimensional $\mathcal N=4$ SUSY quiver gauge theories in arXiv:1503.03676, arXiv:1601.03686, arXiv:1604.03625 to the cases with symmetrizers. We obtain generalized affine…

Quiver quantum mechanics describes the low energy dynamics of a system of wrapped D-branes. It captures several aspects of single and multicentered BPS black hole geometries in four-dimensional $\mathcal{N} = 2$ supergravity such as the…