Related papers: The Freund-Rubin Coset, Textures and Group Theory

We present a method to find the number of real and imaginary observable parameters coming from the Yukawa sector in an arbitrary gauge theory. The method leads naturally to a classification of Yukawa couplings according to their symmetries…

I present an algorithm in the search for symmetric textures in the quark Yukawa matrices. This is based on a talk at the Coral Gables conference in January 1993. I include the macro tables2.tex for making tables, and use the Santa Barbara…

In a series of papers, we have shown that from the \repn theory of a compact groupoid one can reconstruct the groupoid using the procedure similar to the Tannaka-Krein duality for compact groups. In this part we introduce the Tannaka…

This paper is a collection of thoughts and observations, being partly a review and partly a report of current research, on recent work in various aspects of Gr\"unbaum colorings, their existence and usage. In particular, one of the most…

These lecture notes are devoted to formal and phenomenological aspects of F-theory. We begin with a pedagogical introduction to the general concepts of F-theory, covering classic topics such as the connection to Type IIB orientifolds, the…

The existence of a "Plastikstufe" for a contact structure implies the Weinstein conjecture for all supporting contact forms.

We combine the Duke-Imamoglu-Ikeda lifting with the theta lifting to produce new CAP representations of metaplectic, symplectic and orthogonal groups. These constructions partially generalize the theories of Waldspurger on the Shimura…

In earlier papers we introduced a representation of isotopy classes of compact surfaces embedded in the three-sphere by so called rectangular diagrams. The formalism proved useful for comparing Legendrian knots. The aim of this paper is to…

The correspondence between definable connected groupoids in a theory $T$ and internal generalised imaginary sorts of $T$, established by Hrushovski in ["Groupoids, imaginaries and internal covers," Turkish Journal of Mathematics, 2012], is…

We give a complete description of partially wrapped Fukaya categories of graded orbifold surfaces with stops. We show that a construction via global sections of a natural cosheaf of A$_\infty$ categories on a Lagrangian core of the surface…

We present a new group field theory describing 3d Riemannian quantum gravity coupled to matter fields for any choice of spin and mass. The perturbative expansion of the partition function produces fat graphs colored with SU(2) algebraic…

This is an informal (and mostly conjectural) discussion of some aspects of Fukaya categories. We start by looking at exact symplectic manifolds which are obtained from a closed Calabi-Yau by removing a hyperplane section. We look at the…

A Comment on the Letter by Atsushi Ikeda and Kunimasa Miyazaki, [arXiv:1003.5472v2, Phys. Rev. Lett. 104, 255704 (2010)].

We describe the (bigraded) Hochschild cohomology of graded gentle algebras along with the Gerstenhaber bracket and cup product. In particular, this yields a description of the Hochschild cohomology of partially wrapped Fukaya categories of…

Heterotic compactifications on Calabi-Yau threefolds frequently exhibit textures of vanishing Yukawa couplings in their low energy description. The vanishing of these couplings is often not enforced by any obvious symmetry and appears to be…

We relate the Morrison-Kawamata cone conjecture for Calabi-Yau fiber spaces to the existence of Shokurov polytopes. For K3 fibrations, the existence of (weak) fundamental domains for movable cones is established. The relationship between…

We formulate an analogue of the Ichino-Ikeda conjectures for the Whittaker-Fourier coefficients of automorphic forms on quasi-split reductive groups. This sharpens the conjectures of Sakellaridis-Venkatesh in the case at hand.

We describe various approaches to understanding Fukaya categories of cotangent bundles. All of the approaches rely on introducing a suitable class of noncompact Lagrangian submanifolds. We review the work of Nadler-Zaslow (math/0604379,…

F-theory is one of the frameworks where all the Yukawa couplings of grand unified theories are generated and their computation is possible. The Yukawa couplings of charged matter multiplets are supposed to be generated around codimension-3…

We consider a version of the relative Fukaya category for anticanonical Lefschetz pencils. There are direct connections between the behaviour of this category and enumerative geometry: some of these are results announced here, others remain…