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We give a universal construction of a derived affine group scheme and its representation category from a symmetric monoidal infinity-category, which we shall call the tannnakization of a symmetric monoidal infinity-category. This can be…
By a generalized Tannaka-Krein reconstruction we associate to the admissible representations of the category O of a Kac-Moody algebra, and its category of admissible duals a monoid with a coordinate ring. The Kac-Moody group is the Zariski…
We propose a conceptually economical and computationally tractable completion of the foundations of gauge theory on quantum principal bundles \`{a} la Brzezi\'{n}ski--Majid to the case of general differential calculi and strong bimodule…
We introduce the notion of an arithmetic matroid, whose main example is given by a list of elements of a finitely generated abelian group. In particular we study the representability of its dual, providing an extension of the Gale duality…
Let {a,b} and {c,d} be two pairs of bounding simple closed curves on an oriented surface which intersect nontrivialy. We prove that if these pairs are invariant under the action of an orientation reversing involution, then the corresponding…
Determining the existence of compact invariant manifolds is a central quest in the qualitative theory of differential equations. Singularities, periodic solutions, and invariant tori are examples of such invariant manifolds. A classical and…
In this article, we study the Zariski closure of modular points in the two-dimensional universal deformation space when the residual Galois representation is reducible. Unlike the previous approaches in the residually irreducible case from…
Current theories of massless free particle assume {\sl unitary} space inversion and {\sl anti-unitary} time reversal operators. In so doing robust classes of possible theories are discarded. In the present work theories of massless systems…
We develop topological dynamics for the group of automorphisms of a monster model of any given theory. In particular, we find strong relationships between objects from topological dynamics (such as the generalized Bohr compactification…
Let X be a smooth projective curve of genus at least two over the complex numbers. A pair (E,\phi) over X consists of an algebraic vector bundle E over X and a holomorphic section \phi of E. There is a concept of stability for pairs which…
Motivated by the moduli theory of taut contact circles on spherical 3-manifolds, we relate taut contact circles to transversely holomorphic flows. We give an elementary survey of such 1-dimensional foliations from a topological viewpoint.…
We provide a mathematical proposal for the anomaly indicators of symmetries of (2+1)-d fermionic topological orders, and work out the consequences of our proposal in several nontrivial examples. Our proposal is an invariant of a super…
This paper is a sequel to [He7]. There a notion of marking of isolated hypersurface singularities was defined, and a moduli space $M_\mu^{mar}$ for marked singularities in one $\mu$-homotopy class of isolated hypersurface singularities was…
The Tutte polynomial for matroids is not directly applicable to polymatroids. For instance, deletion-contraction properties do not hold. We construct a polynomial for polymatroids which behaves similarly to the Tutte polynomial of a…
The first part of the paper is a brief overview of Hindman's finite sums theorem, its prehistory and a few of its further generalizations, and a modern technique used in proving these and similar results, which is based on idempotent…
We prove that Donaldson-Thomas type invariants are equal to weighted Euler characteristics of their moduli spaces. In particular, such invariants depend only on the scheme structure of the moduli space, not the symmetric obstruction theory…
Motivated by the $Z$-polynomials of matroids, Ferroni, Matherne, Stevens, and Vecchi introduced the inverse $Z$-polynomial of a matroid. In this paper, we prove several fundamental properties of the inverse $Z$-polynomial, including…
We classify conjugacy classes of involutions in the isometry groups of nondegenerate, symmetric bilinear forms over the field of two elements. The new component of this work focuses on the case of an orthogonal form on an even dimensional…
We revisit certain natural algebraic transformations on the space of 3D topological quantum field theories (TQFTs) called "Galois conjugations." Using a notion of multiboundary entanglement entropy (MEE) defined for TQFTs on compact…
Consider a finite-dimensional algebra $A$ and any of its moduli spaces $\mathcal{M}(A,\mathbf{d})^{ss}_{\theta}$ of representations. We prove a decomposition theorem which relates any irreducible component of…