Related papers: Ramanujan and Quantum Black Holes
Ramanujan influenced many areas of mathematics, but his work on q-series, on the growth of coefficients of modular forms, and on mock modular forms stands out for its depth and breadth of applications. I will give a brief overview of how…
The study of black holes in string theory has led to the discovery of deep and surprising connections between black holes and modular forms -- which are two classical, a priori unrelated, subjects. This article explains the main physical…
Quantum aspects of black holes represent an important testing ground for a theory of quantum gravity. The recent success of string theory in reproducing the Bekenstein-Hawking black hole entropy formula provides a link between general…
Supersymmetric black holes provide an excellent theoretical laboratory to test ideas about quantum gravity in general and black hole entropy in particular. When four-dimensional supergravity is interpreted as the low-energy approximation of…
Partitions associated with mock theta functions have received a great deal of attention in the literature. Recently, Choi and Kim derived several partition identities from the third and sixth order mock theta functions. In addition, three…
We develop the theory of copartitions, which are a generalization of partitions with connections to many classical topics in partition theory, including Rogers-Ramanujan partitions, theta functions, mock theta functions, partitions with…
We review recent progress in our understanding of the physics of black holes. In particular, we discuss the ideas from string theory that explain the entropy of black holes from a counting of microstates of the hole, and the related…
Ramanujan studied the analytic properties of many $q$-hypergeometric series. Of those, mock theta functions have been particularly intriguing, and by work of Zwegers, we now know how these curious $q$-series fit into the theory of…
The theory of quadratic forms and class numbers has connections to many classical problems in number theory. Recently, class numbers have appeared in the study of black holes in string theory. We describe this connection and raise questions…
Black holes are the hydrogen atoms of quantum gravity. For instance solving the information loss paradox will likely require a deep understanding of how the long-sought quantum gravity theory works. In this thesis we explore how black holes…
Recently, Andrews, Dixit and Yee introduced partition functions associated with Ramanujan/Watson third order mock theta functions $\omega(q)$ and $\nu(q)$. In this paper, we find several new exact generating functions for those partition…
Quantum theory on manifolds with boundaries have been studied extensively through von Neumann analysis of self adjoint operators. We approach the issues through introduction of singular $\delta$ and $\delta'$ potentials. The advantages of…
This is the first in a sequence of papers to develop the theory of levels in quantum K-theory and study its applications. Our main results in this paper are toric mirror theorems for permutation-equivariant quantum K-theory with level…
We give an elementary review of black holes in string theory. We discuss black hole entropy from string microstates and Hawking radiation from these states. We then review the structure of 2-charge microstates, and explore how…
Recently, Andrews, Dixit and Yee defined two partition functions $p_{\omega}(n)$ and $p_{\nu}(n)$ that are related with Ramanujan's mock theta functions $\omega(q)$ and $\nu(q)$, respectively. In this paper, we present two variable…
We review recent developments concerning supersymmetric black holes in string theory. After a general introduction to the laws of black hole mechanics and to black hole entropy in string theory, we discuss black hole solutions in N=2…
Black holes are a continuing source of mystery. Although their classical properties have been understood since the 1970's, their quantum properties raise some of the deepest questions in theoretical physics. Some of these questions have…
The recent model of Quantum Mechanical Black Holes is discussed and its implications for cosmology, particle structure, low dimensionality and other issues are examined.
Andrews and the third author recently studied congruences for certain restricted two-color partitions. They made two conjectures for Ramanujan-type congruences and a vanishing identity for the limiting sequence. In this paper, we settle…
In this paper we present experimental ways of evaluating Ramanujan`s quantities which as someone can see are related with algebraic numbers. The good thing with algebraic numbers is that can be found in a closed form, from there…