Group Meeting

The theory of Bridgeland stability conditions assigns a complex manifold to the derived category of coherent sheaves on a smooth projective variety. The structure of this complex manifold is central for applications to algebraic geometry, but describing even a connected component is often a difficult, open problem. In this talk, I will give a proposal for the stability manifold of any non-commutative abelian variety in terms of an auxiliary generalized complex torus, extending a conjecture of Kontsevich. As applications, I will describe the stability manifold for many abelian threefolds, and I will complete the description of mirror symmetry for abelian varieties, after Golyshev-Lunts-Orlov. This is based on work in progress, joint with Fabian Haiden.

Part of Heidelberg Algebraic Geometry Seminar series: https://sites.google.com/view/heidelbergag/algebraic-geometry-seminar?authuser=0

I’ll ask you to come join me on a short joyride on total cotangent (super)geometries. If we’re lucky, we will be able to spot the notoriously elusive Atiyah class disguised as an ext group, together with several other wild beasts living in the woods surrounding Heidelber(g)ezin.

Within the ever-shifting landscape of this post-modern playground, we uncover the hidden threads that tie Adinkras and Koszul duality in a tapestry of unimagined elegance. The boundaries between theoretical physics and abstract mathematics blur, and the very notion of 'discipline' metamorphoses into an ever-fluid idea.

In this kaleidoscopic endeavor, we offer a prism through which Adinkras and Koszul duality emerge as kindred spirits, inviting us to revel in their harmonious chaos. As we surf the waves of post-modern inquiry, we unearth the potential for a renewed perspective on these enigmatic realms. This is more than an academic exercise; it's a testament to the enduring allure of eclecticism and the never-ending quest to expand the boundaries of knowledge.

As we conclude this abstract, we celebrate the post-modern spirit that keeps us guessing, challenging, and reshaping our understanding of the universe. In the epoch of eclectic inquiry, the boundaries are permeable, and knowledge is a kaleidoscope of endless possibilities.

Kinetic mixing between gauge fields of different $U(1)$ factors is a well-studied phenomenon in 4d EFT. In string compactifications with $U(1)$s from sequestered D-brane sectors, kinetic mixing becomes a key target for the UV prediction of a phenomenologically important EFT operator. Surprisingly, in many cases kinetic mixing is absent due to a non-trivial cancellation. In particular, D3-D3 kinetic mixing in type-IIB vanishes while D3-anti-D3 mixing does not. This follows both from exact CFT calculations on tori as well as from a leading-order 10d supergravity analysis, where the key cancellation is between the $C_2$ and $B_2$ contribution. We take the latter approach, which is the only one available in realistic Calabi-Yau settings, to a higher level of precision by including sub-leading terms of the brane action and allowing for non-vanishing $C_0$. The exact cancellation persists, which we argue to be the result of $SL(2,\mathbb{R})$ self-duality. We note that a $B_2C_2$ term on the D3-brane, which is often missing in the recent literature, is essential to obtain the correct zero result. Finally, allowing for $SL(2,\mathbb{R})$-breaking fluxes, kinetic mixing between D3-branes arises at a volume-suppressed level. We provide basic explicit formulae, both for kinetic as well as magnetic mixing, leaving the study of phenomenologically relevant, more complex situations for the future.

In general, a Lagrangian does not fully characterise a 4d gauge theory; for instance, in Yang-Mills theories with adjoint matter, the Lagrangian does not determine whether the gauge group is SU(N), PSU(N) or any intermediate SU(N)/G where G is a subgroup of the center. In order to define a 4d gauge theory, one needs to choose a maximal collection of Wilson-'t Hooft line operators, local with respect to dynamical particles and mutually local; this choice in turn determines the global form of the gauge group. All of this can be reformulated in terms of one-form global symmetries. Choices of global structures are encoded in a topological field theory in 5d dubbed SymTFT, which allows to compute the one-form symmetry even in non-Lagrangian gauge theories, provided they have a well-behaved Coulomb phase in the IR. This is the case for N=3 S-folds, an interesting class of 4d QFTs with N=3 supersymmetries constructed in type IIB string theory through a procedure generalizing orientifolds. The one-form symmetries and dualities of such theories hints for the existence of non-invertible symmetry defects. My goal is to motivate and explain the method and results of 2303.07299 [hep-th].

tba

Dubrovin Frobenius manifold is a geometric interpretation of a remarkable system of differential equations, called WDVV equations. Since the beginning of the nineties, there has been a continuous exchange of ideas from fields that are not trivially related to each other, such as: Topological quantum field theory, non-linear waves, singularity theory, random matrices theory, integrable hier- archies of KdV type, and Painleve equations. Dubrovin Frobenius manifolds theory is the bridge between them. In this talk, I will review the notion of Dubrovin-Frobenius manifolds and its relationship with finite reflection groups and its extensions, isomonodromic deformation equations and Integrable hier- archy of KdV type.

We construct a generalization of Poisson--Chern--Simons theory, defined on any supermanifold equipped with an appropriate filtration of the tangent bundle. Our construction recovers interacting eleven-dimensional supergravity in Cederwall's formulation, as well as all possible twists of the theory, and does so in a uniform and geometric fashion. Among other things, this proves that Costello's description of the maximal twist is the twist of eleven-dimensional supergravity in its pure spinor description. It also provides a pure spinor lift of the interactions in the minimally twisted theory. Our techniques enhance the BV formulation of the interactions of each theory to a homotopy Poisson structure by defining a compatible graded-commutative product; this suggests interpretations in terms of deformations of geometric structures on superspace, and provides concrete evidence for a first-quantized origin of the theories.

tba