Related papers: Quantum Singularity Theory for A_{r-1} and r-Spin …
The quantum modularity conjecture, first introduced by Don Zagier, is a general statement about a relation between $\mathfrak{sl}_2$ quantum invariants of links and 3-manifolds at roots of unity related by a modular transformation. In this…
In this paper we discuss singularity theorems in quantum gravity using effective field theory methods. To second order in curvature, this effective field theory contains two new degrees of freedom which have important implications for the…
We provide an explicit formula for all primary genus-zero $r$-spin invariants. Our formula is piecewise polynomial in the monodromies at each marked point and in $r$. To deduce the structure of these invariants, we use a tropical…
For a finite group G acting on a smooth projective variety X, we construct two new G-equivariant rings: first the stringy K-theory of X, and second the stringy cohomology of X. For a smooth Deligne-Mumford stack Y we also construct a new…
In this note, we study the $p$-complete topological cyclic homology of the affine line relative to a ring $A$ which is smooth over a perfectoid ring $R$. Denoting by $NTC(A; \mathbb{Z}_p)$ the spectrum which measures the failure of…
Quantum field theory is mostly known as the most advanced and well-developed theory in physics, which combines quantum mechanics and special relativity consistently. In this work, we study the spinless quantum field theory, namely the…
We discuss a remarkable formula discovered by Jerison and Lee to classify constant scalar curvature pseudohermitian structures on the sphere. We show that the formula is valid in the wider context of Einstein pseudohermitian manifolds. As…
We introduce a novel quantum spin-glass model, a Sherrington-Kirkpatrick model with a transverse mean-field type random magnet. We rigorously derive the exact expression of the free energy of this model at the entire parameter region. The…
In this paper, we prove the mirror symmetry conjecture between the Saito-Givental theory of exceptional unimodular singularities on Landau-Ginzburg B-side and the Fan-Jarvis-Ruan-Witten theory of their mirror partners on Landau-Ginzburg…
In a recent paper [3], Bakalov and Milanov proved that the total descendant potential of a simple singularity satisfies the W-constraints, which come from the W-algebra of the lattice vertex algebra associated to the root lattice of this…
Parity-conserving single-spin asymmetries provide a specific measure of coherent spin-orbit dynamics in quantum chromodynamics. The origin of these effects can be traced to the interplay of chiral dynamics and confinement in the theory. The…
We construct and study various properties of a negative spin version of the Witten $ r $-spin class. By taking the top Chern class of a certain vector bundle on the moduli space of twisted spin curves that parametrises $ r $-th roots of the…
By employing polynomial-reduced KP integrability, combined with the string equation, this work establishes explicit relationships between the generalized Kontsevich model, the topological recursion of the spectral curve, and the geometry of…
This undergraduate thesis is concerned with developing the tools of differential geometry and semiclassical analysis needed to understand the the quantum ergodicity theorem of Schnirelman (1974), Zelditch (1987), and Colin de Verdi\`ere…
We establish the spin-statistics theorem for topological quantum field theories (TQFTs) in the framework of Atiyah. We incorporate spin via spin structures on bordisms, and represent statistics using super vector spaces. Unitarity is…
We propose two conjectures on Huwritz numbers with completed $(r+1)$-cycles, or, equivalently, on certain relative Gromov-Witten invariants of the projective line. The conjectures are analogs of the ELSV formula and of the Bouchard-Mari\~no…
We define the symmetric (outer) automorphism group of a right-angled Artin group and construct for it a (spine of) Outer space. This `symmetric spine' is a contractible cube complex upon which the symmetric outer automorphism group acts…
A great effort has been devoted to formulate a classical relativistic theory of spin compatible with quantum relativistic wave equations. The main difficulty in order to connect classical and quantum theories rests in finding a parameter…
In this paper, A. Avila's theorem on convergence of the exact quantization scheme of A. Voros is related to the reality proofs of eigenvalues of certain PT-symmetric boundary value problems. As a result, a special case of a conjecture of C.…
We construct the $g=1$ sector of the open $r$-spin theory, that is, an open $r$-spin theory on the moduli space of cylinders. This is the second construction of a $g>0$ open intersection theory, which includes descendents (the first is the…