Related papers: Row-Column duality and combinatorial topological s…
A remarkable result at the intersection of number theory and group theory states that the order of a finite group $G$ (denoted $|G|$) is divisible by the dimension $d_R$ of any irreducible complex representation of $G$. We show that the…
Character tables of finite groups and closely related commutative algebras have been investigated recently using new perspectives arising from the AdS/CFT correspondence and low-dimensional topological quantum field theories. Two important…
A number of finite algorithms for constructing representation theoretic data from group multiplications in a finite group G have recently been shown to be related to amplitudes for combinatoric topological strings (G-CTST) based on…
We study the cohomology of $G$-representation varieties and $G$-character stacks by means of a topological quantum field theory (TQFT). This TQFT is constructed as the composite of a so-called field theory and the 6-functor formalism of…
This thesis contains various results on unitary 2-representations of finite groups and their 2-characters, as well as on pivotal structures for fusion categories. The motivation is extended topological quantum field theory (TQFT), where the…
We outline a general derivation of holographic duality between "TQFT gravity" - the path integral of a 3d TQFT summed over different topologies - and an ensemble of boundary 2d CFTs. The key idea is to place the boundary ensemble on a…
We introduce a class of generalized tube algebras which describe how finite, non-invertible global symmetries of bosonic 1+1d QFTs act on operators which sit at the intersection point of a collection of boundaries and interfaces. We develop…
Interchanging character and co-character groups of a torus $T$ over a field $k$ introduces a contravariant functor $T \rightarrow \widehat{T}$. Interpreting $\rho:T\rightarrow {\mathbb C}^\times$, half the sum of positive roots for $T$ a…
In this paper, we introduce Topological Quantum Field Theories (TQFTs) generalizing the arithmetic computations done by Hausel and Rodr\'iguez-Villegas and the geometric construction done by Logares, Mu\~noz, and Newstead to study…
The character table of the symmetric group $S_n$, of permutations of $n$ objects, is of fundamental interest in theoretical physics, combinatorics as well as computational complexity theory. We investigate the implications of an identity,…
We study the recent proposal of arXiv:2405.20366 which poses a precise holographic duality between a 3d TQFT summed over all topologies and a unitary ensemble of boundary 2d CFTs. In that proposal, the sum over topologies is obtained via…
This PhD Thesis is devoted to the study of Hodge structures on a special type of complex algebraic varieties, the so-called character varieties. For this purpose, we propose to use a powerful algebro-geometric tool coming from theoretical…
T-duality is one of the essential elements of string theory. Recently, Hull has developed a formalism where the dimension of the target space is doubled so as to make T-duality manifest. This is then supplemented with a constraint equation…
In his PhD thesis, Goosen combined the string-net and the generators-and-relations formalisms for arbitrary once-extended 3-dimensional TQFTs. In this paper we work this out in detail for the simplest non-trivial example, where the…
The two dimensional state sum models of Barrett and Tavares are extended to unoriented spacetimes. The input to the construction is an algebraic structure dubbed half twist algebras, a class of examples of which is real separable…
For simple and simply-connected complex algebraic group G, we conjecture the existence of a functor eta_G from the category of 2-bordisms to the category of holomorphic symplectic varieties with Hamiltonian action, such that gluing of…
The doubled formulation of string theory, which is T-duality covariant and enlarges spacetime with extra coordinates conjugate to winding number, is reformulated and its geometric and topological features examined. It is used to formulate…
$T\bar{T}$ deformed conformal field theories can be reformulated as worldsheet theories of non-critical strings. We use this correspondence to compute and study the $T\bar{T}$ deformed partition sum of a symmetric product CFT. We find that…
The combination of the group ring setting with the methods of character theory allows an elegant and powerful analysis of various combinatorial structures, via their character sums. These combinatorial structures include difference sets,…
We formulate a family of spin Topological Quantum Filed Theories (spin-TQFTs) as fermionic generalization of bosonic Dijkgraaf-Witten TQFTs. They are obtained by gauging $G$-equivariant invertible spin-TQFTs, or, in physics language,…