**Gromov–Witten invariant Wikipedia**

tional structure allows us to do complex analysis on the surface, so that Riemann surfaces are central objects in geometry, analysis, and mathematical physics, for example string theory.... We use Quillen's theorem and algebraic geometry to investigate the modular transformation properties of some quantities of interest in string theory. In particular, we show that the spin structure dependence of the chiral Dirac determinant on a Riemann surface is given by Riemann's theta function

**Taming Superconductors With String Theory Quanta Magazine**

conjectured by Bouchard and Marino~ using topological string theory. Contents 1. Introduction 1 2. The Laplace transform of the ELSV formula 6 3. The cut-and-join equation and its Laplace transform 9 4. The Bouchard-Marino~ recursion formula for Hurwitz numbers 14 5. Residue calculation 19 6. Analysis of the Laplace transforms on the Lambert curve 22 7. Proof of the Bouchard-Marino... As a string travels through spacetime it traces out a surface, called the worldsheet of the string. Unfortunately, the moduli space of such parametrized surfaces, at least a priori , is infinite-dimensional; no appropriate measure on this space is known, and thus the path integrals of the theory …

**M-theory the theory formerly known as Strings**

One, two, three.... particles (quarks, gluons, gravitons....) Can have strong interactions during scattering events Comfort zone of string theory... Even though though string theory is normally used as a theory of quantum gravity, it is not how string theory was originally discovered. Namely, loops of (p, q) strings in the z-plane will be closed in general only on the covering surface ~N-l' so that such strings effectively wrap the Riemann surfaces.

**Generalized string equations for Hurwitz numbers**

surface observables for any even k. This relation between correlators of large observables and This relation between correlators of large observables and geodesics in the bulk theory oﬀers a probe of the bulk spacetime [2].... Algebraic geometry and string theory Tom Bridgeland. Back to school: curves in the plane Algebraic geometry is the study of solutions sets to polynomial equations. These sets are called algebraic varieties. x2 + y2 = 1 xy = 1 y2 = x3 x + 1 Circle Hyperbola Elliptic curve. Fertile ground for interactions Algebraic geometry has interactions with many other areas of maths, for example number

## Pdf String Theory And Hurwitz Surface

### Leibniz and Monads University of Houston

- Cavalieri R. Miles E. Riemann Surfaces and Algebraic
- Theta functions modular invariance and strings
- THE LAPLACE TRANSFORM OF THE CUT-AND-JOIN EQUATION
- TOPOLOGICAL STRING THEORY AND ENUMERATIVE GEOMETRY

## Pdf String Theory And Hurwitz Surface

### a two-dimensional gauge theory on a Riemann surface and a string theory with the same manifold as its target space. Recall that in two dimensions pure Yang-Mills

- What can string theory teach us about condensed matter physics? HARVARD Department of Physics, UC Berkeley, October 3, 2011 sachdev.physics.harvard.edu Tuesday, October 4, 2011. Rob Myers Ajay Singh Liza Huijse Tuesday, October 4, 2011. 1. Quantum critical points and string theory Entanglement and emergent dimensions 2. Some difﬁcult condensed matter questions and answers from string theory
- Recursion structures in topological string theory and enumerative geometry organized by Vincent Bouchard, Motohico Mulase, and Brad Safnuk Workshop Summary Summary. The goal of this workshop is to solve the mystery that is exciting a number of researchers working on topological string theory, integrable systems, and enumerative geometry. The central theme is a newly discovered topological
- PDF Analogue of classical Hurwitz numbers is defined in the work for regular coverings of surfaces with marked points by seamed surfaces. Class of surfaces includes surfaces of any genus and
- String theory made understandable. Barton Zwiebach is once again faithful to his goal of making string theory accessible to undergraduates. He presents the main concepts of string theory in a concrete and physical way to develop intuition before formalism, often through simplified and illustrative examples.

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